Msc.nastran 2002 Thermal Analysis User's Guide

MSC.Nastran 2002 Thermal Analysis User’s Guide

Main Index

Corporate MSC.Software Corporation 2 MacArthur Place Santa Ana, CA 92707 USA Telephone: (800) 345-2078 Fax: (714) 784-4056 Europe MSC.Software GmbH Am Moosfeld 13 81829 Munich, Germany Telephone: (49) (89) 43 19 87 0 Fax: (49) (89) 43 61 71 6 Asia Pacific MSC.Software Japan Ltd. Shinjuku First West 8F 23-7 Nishi Shinjuku 1-Chome, Shinjyku-Ku, Tokyo 160-0023, Japan Telephone: (81) (03) 6911 1200 Fax: (81) (03) 6911 1201 Worldwide Web www.mscsoftware.com Disclaimer This documentation, as well as the software described in it, is furnished under license and may be used only in accordance with the terms of such license. MSC.Software Corporation reserves the right to make changes in specifications and other information contained in this document without prior notice. The concepts, methods, and examples presented in this text are for illustrative and educational purposes only, and are not intended to be exhaustive or to apply to any particular engineering problem or design. MSC.Software Corporation assumes no liability or responsibility to any person or company for direct or indirect damages resulting from the use of any information contained herein. User Documentation: Copyright  2004 MSC.Software Corporation. Printed in U.S.A. All Rights Reserved.

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Main Index

C O N T E N T S MSC.Nastran Thermal Analysis User’s Guide MSC.Nastran Thermal Analysis User’s Guide

Preface

■

List of MSC.Nastran Books, vi

■

Technical Support, vii

■

, ix

■

Internet Resources, x

■

, xi

■

Permission to Copy and Distribute MSC Documentation, xii

■

Introduction to the MSC.Nastran Thermal Analysis User’s Guide, 2

■

Introduction to Thermal Capabilities, 6

■

Elements, 7

■

Material Properties, 10

■

Thermal Loads, 12

■

Convection and Radiation Boundary Conditions, 16

■

Temperature Boundary Conditions and Constraints, 28

■

Initial Conditions, 30

■

Introduction to Interface and File Communication, 32

■

Execution of MSC.Nastran, 33

■

Input Data, 34

■

Files Generated by MSC.Nastran, 39

■

Plotting, 41

■

Introduction to Solution Methods, 58

■

Nonlinear Iteration Scheme, 59

■

Steady State Analysis, 61

1 Introduction

2 Thermal Capabilities

3 Interface and File Communication

4 Method of Solution

Main Index

■

Transient Analysis, 69

■

Steady State and Transient Analysis Examples, 83

■

Example 1a - Linear Conduction, 84

■

Example 1b - Nonlinear Free Convection Relationships, 88

■

Example 1c - Temperature Dependent Heat Transfer Coefficient, 95

■

Example 1d - Film Nodes for Free Convection, 100

■

Example 1e - Radiation Boundary Condition, 105

■

Example 2a - Nonlinear Internal Heating and Free Convection, 111

■

Example 2b - Nonlinear Internal Heating and Control Nodes, 116

■

Example 2c - Nonlinear Internal Heating and Film Nodes, 122

■

Example 3 - Axisymmetric Elements and Boundary Conditions, 127

■

Example 4a - Plate in Radiative Equilibrium, Nondirectional Solar Load with Radiation Boundary Condition, 130

■

Example 4b - Plate in Radiative Equilibrium, Directional Solar Load with Radiation Boundary Condition, 133

■

Example 4c - Plate in Radiative Equilibrium, Directional Solar Load, Spectral Surface Behavior, 138

■

Example 5a - Single Cavity Enclosure Radiation with Shadowing, 142

■

Example 5b - Single Cavity Enclosure Radiation with an Ambient Element Specification, 148

■

Example 5c - Multiple Cavity Enclosure Radiation, 153

■

Example 6 - Forced Convection Tube Flow - Constant Property Flow, 158

■

Example 7a - Transient Cool Down, Convection Boundary, 163

■

Example 7b - Convection, Time Varying Ambient Temperature, 166

■

Example 7c - Time Varying Loads, 172

■

Example 7d - Time Varying Heat Transfer Coefficient, 176

■

Example 7e - Temperature Dependent Free Convection Heat Transfer Coefficient, 181

■

Example 7f - Phase Change, 185

■

Example 8 - Temperature Boundary Conditions in Transient Analyses, 193

■

Example 9a - Diurnal Thermal Cycles, 200

■

Example 9b - Diurnal Thermal Cycles, 204

■

Example 10 - Thermostat Control, 210

■

Example 11 - Transient Forced Convection, 214

■

Example 12 - Thermostat Control with Deadband Applied to a Heat Source, 221

■

Example 13 - Cryogenic Heat Shielding, 223

5 Examples

Main Index

A ■

Commonly Used Terms, 228

■

Frequently Used Executive Control Statements, 230

■

Thermal Analysis Case Control Commands, 244

■

Commonly Used Bulk Data Entries, 276

■

Calculation of View Factors, 410

■

Fundamentals of View Factor Calculation, 411

■

Method of Poljak, 420

■

Method of Poljak - Radiation Exchange in Matrix Format, 422

■

Transformation from Element Heat Flows to Grid Point Heat Flows, 423

■

Example of Element/Grid Transformation, 424

■

Two Element Example for Radiant Exchange, 426

■

Resistive Network Approach to the Two Surface Problem, 428

■

Radiation Enclosure Analysis, 429

Radiation Exchange – Real Surface Approximation

■

Real Surface Approximation and Radiation Exchange, 434

INDEX

■

MSC.Nastran Thermal Analysis User’s Guide

Nomenclature for Thermal Analysis

B Executive Control Section

C Case Control Commands

D Bulk Data Entries

E View Factor Calculation Methods

F Radiation Enclosures

G

Main Index

Main Index

Preface

■ List of MSC.Nastran Books ■ Technical Support ■ Internet Resources ■ Permission to Copy and Distribute MSC Documentation

Main Index

vi

List of MSC.Nastran Books Below is a list of some of the MSC.Nastran documents. You may order any of these documents from the MSC.Software BooksMart site at www.engineering-e.com.

Installation and Release Guides ❏ Installation and Operations Guide ❏ Release Guide

Reference Books ❏ Quick Reference Guide ❏ DMAP Programmer’s Guide ❏ Reference Manual

User’s Guides ❏ Getting Started ❏ Linear Static Analysis ❏ Basic Dynamic Analysis ❏ Advanced Dynamic Analysis ❏ Design Sensitivity and Optimization ❏ Thermal Analysis ❏ Numerical Methods ❏ Aeroelastic Analysis ❏ Superelement ❏ User Modifiable ❏ Toolkit

Main Index

Preface

Technical Support For help with installing or using an MSC.Software product, contact your local technical support services. Our technical support provides the following services:

• Resolution of installation problems • Advice on specific analysis capabilities • Advice on modeling techniques • Resolution of specific analysis problems (e.g., fatal messages) • Verification of code error. If you have concerns about an analysis, we suggest that you contact us at an early stage. You can reach technical support services on the web, by telephone, or e-mail: Web

Go to the MSC.Software website at www.mscsoftware.com, and click on Support. Here, you can find a wide variety of support resources including application examples, technical application notes, available training courses, and documentation updates at the MSC.Software Training, Technical Support, and Documentation web page.

Phone and Fax

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Paris, France Telephone: (33) (1) 69 36 69 36 Fax: (33) (1) 69 36 45 17

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Gouda, The Netherlands Telephone: (31) (18) 2543700 Fax: (31) (18) 2543707 Madrid, Spain Telephone: (34) (91) 5560919 Fax: (34) (91) 5567280

Main Index

vii

viii

Email

Send a detailed description of the problem to the email address below that corresponds to the product you are using. You should receive an acknowledgement that your message was received, followed by an email from one of our Technical Support Engineers. MSC.Patran Support MSC.Nastran Support MSC.Nastran for Windows Support MSC.visualNastran Desktop 2D Support MSC.visualNastran Desktop 4D Support MSC.Abaqus Support MSC.Dytran Support MSC.Fatigue Support MSC.Interactive Physics Support MSC.Marc Support MSC.Mvision Support MSC.SuperForge Support MSC Institute Course Information

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Training The MSC Institute of Technology is the world's largest global supplier of CAD/CAM/CAE/PDM training products and services for the product design, analysis and manufacturing market. We offer over 100 courses through a global network of education centers. The Institute is uniquely positioned to optimize your investment in design and simulation software tools. Our industry experienced expert staff is available to customize our course offerings to meet your unique training requirements. For the most effective training, The Institute also offers many of our courses at our customer's facilities. The MSC Institute of Technology is located at: 2 MacArthur Place Santa Ana, CA 92707 Phone: (800) 732-7211 Fax: (714) 784-4028 The Institute maintains state-of-the-art classroom facilities and individual computer graphics laboratories at training centers throughout the world. All of our courses emphasize hands-on computer laboratory work to facility skills development. We specialize in customized training based on our evaluation of your design and simulation processes, which yields courses that are geared to your business. In addition to traditional instructor-led classes, we also offer video and DVD courses, interactive multimedia training, web-based training, and a specialized instructor's program. Course Information and Registration. For detailed course descriptions, schedule information, and registration call the Training Specialist at (800) 732-7211 or visit www.mscsoftware.com. Main Index

Preface

Main Index

ix

x

Internet Resources MSC.Software (www.mscsoftware.com) MSC.Software corporate site with information on the latest events, products and services for the CAD/CAE/CAM marketplace. Simulation Center (simulate.engineering-e.com) Simulate Online. The Simulation Center provides all your simulation, FEA, and other engineering tools over the Internet. Engineering-e.com (www.engineering-e.com) Engineering-e.com is the first virtual marketplace where clients can find engineering expertise, and engineers can find the goods and services they need to do their job CATIASOURCE (plm.mscsoftware.com) Your SOURCE for Total Product Lifecycle Management Solutions.

Main Index

Preface

Main Index

xi

xii

Permission to Copy and Distribute MSC Documentation If you wish to make copies of this documentation for distribution to co-workers, complete this form and send it to MSC.Software. MSC will grant written permission if the following conditions are met:

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Main Index

xiii

xiv

Main Index

MSC.Nastran Thermal Analysis User’s Guide

CHAPTER

1

Introduction

■ Introduction to the MSC.Nastran Thermal Analysis User’s Guide

Main Index

2

1.1

Introduction to the MSC.Nastran Thermal Analysis User’s Guide The MSC.Nastran Thermal Analysis User’s Guide describes the heat transfer-specific material within MSC.Nastran required for performing thermal analyses. This book emphasizes fundamental capabilities, describing them in basic engineering format, and then detailing the interface to MSC.Nastran through the Bulk Data entry descriptions. A series of examples demonstrates a wide cross section of available features and their application with complete MSC.Nastran input listings. This user’s guide is not intended to provide an exhaustive treatment of heat transfer or finite element theory. Rather, it is designed to assist in building, analyzing, and designing basic thermal system models and to numerically study their thermal performance. Some advanced material is included in the appendices to direct the most efficient use of the more complicated features. The information contained here can be augmented with material available in the Getting Started with MSC.Nastran User’s Guide, MSC.Nastran Quick Reference Guide, and the MSC.Nastran Reference Manual as well as the MSC.Nastran Handbook for Nonlinear Analysis. These manuals can provide greater depth of coverage regarding finite element basics, modeling, input file structure, and nonlinear solution techniques. A complementary product, MSC.Patran, is available for performing pre- and post-processing functions for MSC.Nastran Heat Transfer. This engineering graphics package automates the reading of CAD geometry, automeshing of the finite element mesh, creation and application of the material properties, loads, boundary conditions, nonlinear solution control, analysis job submittal, results access, and results visualization. This product and its application are described in MSC.Nastran Preference Guide, Volume II - Thermal Analysis. Starting with Version 68 there have been substantial modifications made to the MSC.Nastran heat transfer capability. Along with many new and flexible features, a break with the past has occurred in terms of non-upward compatible Bulk Data entries. The primary areas where nonupward compatibilities arise include the specification of CHBDY surface elements, boundary and initial conditions, available solution sequences, and temperature boundary conditions.

General Capabilities • Solution methods: • Steady state, linear and/or nonlinear (SOL 153). • Transient, linear and/or nonlinear (SOL 159). • Heat conduction: • Temperature-dependent conductivity. • Temperature-dependent specific heat. • Anisotropic thermal conductivity. • Latent heat of phase change. Main Index

CHAPTER 1 Introduction

• Temperature-dependent internal heat generation. • Weighted temperature gradient dependent internal heat generation. • Time-dependent internal heat generation. • Free convection boundaries: • Temperature-dependent heat transfer coefficient. • Weighted temperature gradient dependent heat transfer coefficient. • Time-dependent heat transfer coefficient. • Nonlinear functional forms. • Weighted film temperatures. • Forced convection: • Tube fluid flow field relationships - H(Re,Pr). • Temperature dependent fluid viscosity, conductivity, and specific heat. • Time-dependent mass flow rate. • Temperature-dependent mass flow rate. • Weighted temperature gradient dependent mass flow rate. • Radiation to space: • Temperature-dependent emissivity and absorptivity. • Wavelength dependent emissivity and absorptivity. • Time-dependent exchange. • Radiation enclosures: • Temperature-dependent emissivity. • Wavelength-dependent emissivity. • Diffuse view factor calculations with self and third-body shadowing. • Adaptive view factor calculations. • Net view factors. • User-supplied exchange factors. • Radiation matrix control. • Radiation enclosure control. • Multiple radiation enclosures. • Applied heat loads: • Directional heat flux. • Surface normal heat flux. • Grid point nodal power. Main Index

• Temperature-dependent heat flux.

3

4

• Weighted temperature gradient dependent heat flux. • Time-dependent heat flux. • Temperature boundary conditions: • Specified constant temperatures for steady state and transient. • Specified time-varying temperatures for transient. • Initial conditions: • Starting temperatures for nonlinear steady state analysis. • Starting temperatures for all transient analyses. • Thermal control systems: • Local, remote, and time-varying control points for free convection heat transfer coefficients.

• Local, remote, and time-varying control points for forced convection mass flow rates.

• Local, remote, and time-varying control points for heat flux loads. • Local, remote, and time-varying control points for internal heat generation rates. • Transient nonlinear loading functions. • Perfect conductor algebraic constraint temperature relationships. • Output graphical display - basic: • Heat flows for conduction and boundary surface elements. • Temperature versus time for grid points. • Enthalpy versus time for grid points. • Isothermal contour plots. • Miscellaneous: • MSC.Nastran DMAP and DMAP Alter capability. • MSC.Nastran restart capability. • Direct matrix input to conduction and heat capacitance matrices. • Lumped mass and discrete conductor representations.

Example Problem Input Files Example problem input files are supplied with delivery. Refer to the MSC.Nastran 2005 Installation and Operations Guide for the location of these files.

Main Index

MSC.Nastran Thermal Analysis User’s Guide

CHAPTER

2

Thermal Capabilities

■ Introduction to Thermal Capabilities ■ Elements ■ Material Properties ■ Thermal Loads ■ Convection and Radiation Boundary Conditions ■ Temperature Boundary Conditions and Constraints ■ Initial Conditions

Main Index

6

2.1

Introduction to Thermal Capabilities This chapter covers the following topics:

• Element types and uses. • Material properties and consistent units. • Thermal loads and application. • Convection and radiation boundary conditions. • Enclosure radiation. • Temperature boundary conditions and constraints. • Initial conditions.

Main Index

CHAPTER 2 Thermal Capabilities

2.2

Elements MSC.Nastran is an analysis code based on the finite element method. Fundamental to the method is an element library, available for building discretized numerical models that approximate the structure or system of interest. Several categories of elements exist to facilitate model generation: conduction elements, surface elements, and specialty elements.

Conduction Elements Conduction elements are defined by the configuration generated when geometric grid points are connected in specific orientations and, for heat transfer, obey Fourier’s Law. These elements can be characterized geometrically as being either one, two, or three dimensional, or axisymmetric. Besides being associated with geometry, these elements have the material properties for thermal conductivity, density, and specific heat associated with them. A typical element definition Bulk Data entry is given below for a 2-D element: 1

2

3

4

5

6

7

8

9

CQUAD4

EID

PID

G1

G2

G3

G4

THETA or MCID

ZOFFS

T1

T2

T3

T4

10

Conduction Elements Available for Heat Transfer The following table presents the conduction elements available for heat transfer. These elements include one-dimensional elements, shell elements, axisymmetric elements, and solid elements. 1-D

2-D

AXIS CTRIAX6

3-D

CBAR

CQUAD4

CHEXA

CBEAM

CQUAD8

CPENTA

CBEND

CTRIA3

CTETRA

CONROD

CTRIA6

CROD CTUBE

Surface Elements Wherever a boundary condition is applied to the surface of a conduction element, it must be interfaced with a surface element. Surface elements provide the geometric connection between the structural conduction elements and the applied convection, radiation, or heat flux loads. In particular, surfaces that participate in radiation enclosures derive their cavity identity and their radiation material property pointers from the surface element Bulk Data description. Similarly, free- and forced-convection Bulk Data entries are identified through their mating surface element identification numbers.

Main Index

7

8

Surface Elements Available for Defining Heat Transfer Boundaries The following table presents the surface elements available for convection and radiation boundary conditions and certain applied heat flux loads. Element

CHBDYE

Surface Types

All

CHBDYG

CHBDYP

REV

POINT

AREA3

LINE

AREA4

ELCYL

AREA6

FTUBE

AREA8

TUBE

Surface element geometries are associated with surface types. Of the three forms of surface elements, the CHBDYG and the CHBDYP have their TYPE explicitly defined on their Bulk Data entries. The CHBDYE deals with the geometry type implicitly by reference to the underlying conduction element. The surface element Bulk Data entries are given below: 1

2

CHBDYG

EID

3

4

5

6

7

8

TYPE

IVIEWF

IVIEWB

RADMIDF

RADMIDB

G1

G2

G3

G4

G5

G6

G7

CHBDYE

EID

EID2

SIDE

IVIEWF

IVIEWB

RADMIDF

RADMIDB

CHBDYP

EID

PID

TYPE

IVIEWF

IVIEWB

G1

G2

RADMIDF

RADMIDB

GMID

CE

E1

E2

E3

9

10

G8

GO

Special Elements Several types of special elements are available for added modeling flexibility. Simple resistive components are represented by CELASi (i = 1, 2, 3, 4) elements. More complicated elements can be introduced into the system through generalized matrix input in the form of DMI, DMIG, and TF. Lumped thermal capacitance can be defined with the use of CDAMPi (i = 1, 2, 3, 4, 5) entries.

Key Points Regarding Elements • All element Bulk Data connection inputs signify that an element connection is performed among grid points.

• Every element must have a unique element identification number (EID) with respect to all other elements in the problem. This requirement applies to conduction elements, surface elements, and specialty elements. Main Index

CHAPTER 2 Thermal Capabilities

• Element definitions reference Bulk Data property entries that supply supplemental information about geometry and governing relationships, and subsequently refer to material property entries.

Main Index

9

10

2.3

Material Properties Material properties for heat transfer analysis are supplied on MAT4, MAT5, MATT4, MATT5, RADM, and RADMT entries. The MAT4, MAT5, and RADM entries provide constant valued material properties, while their companion entries MATT4, MATT5, and RADMT supply information about temperature-dependent properties through reference to material tables (TABLEMi (i = 1, 2, 3, 4)). The fields available on the material entries are described below.

Data Available on MAT4 Bulk Data Entry The format of the MAT4 Bulk Data entry is: 1 MAT4

2

3

4

5

6

7

8

9

MID

K

CP

r

H

m

HGEN

REFENTH

TCH

TDELTA

QLAT

10

MSC.Nastran Material Properties The following table describes the fields on the MAT4 Bulk Data entry. Symbol

Property

Consistent Units

K(T)

Thermal Conductivity*

W/m °C

CP(T)

Specific Heat*

J/kg °C

ρ

Density*

kg/m3

H(T)

Free Convection Heat Transfer Coefficient

W/m2 °C

µ (T)

Dynamic Viscosity*

N sec/m2

HGEN(T)

Volumetric Internal Heat Generation

W/m3

REFENTH

Reference Enthalpy

J/kg

TCH

Lower Temperature Limit for Phase Change

°C

TDELTA

Temperature Range for Phase Change

°C

QLAT

Latent Heat

J/kg

* Thermal conductivity, specific heat, density, and dynamic viscosity cannot currently be time dependent. Thermal heat flux loads can reference explicit functions of time. Thermal boundary conditions for convection and radiation utilize control node techniques for specifying time dependent behavior (see “Convection and Radiation Boundary Conditions” on page 16).

Data Available on RADM Bulk Data Entry The format of the RADM Bulk Data entry is as follows:

Main Index

CHAPTER 2 Thermal Capabilities

1 RADM

2

3

4

5

6

7

8

9

RADMID

ABSORP

EMIS1

EMIS2

EMIS3

EMIS4

EMIS5

EMIS6

EMIS7

-etc.-

10

The following table describes the fields for the RADM Bulk Data entry. Field

Description

Unit

ABSORP(T)

Absorptivity for Directional Heat Flux and Radiation Boundary Condition (QVECT and RADBC)

Nondimensional

EMIS(λ,T)

Emissivity for Radiation Boundary Condition Nondimensional and Enclosure Radiation (RADBC and RADSET)

Key Points Regarding Material Properties • It is the user’s responsibility to enforce consistent and rational units for material properties as well as for applied loads, boundary conditions, geometry, and various physical constants.

• Although the surface characteristics for free convection (heat transfer coefficient) and radiation (emissivity and absorptivity) are not normally considered to be material properties, they are included in the above entries.

• Temperature dependence of the quantity of interest is ultimately defined on a TABLEMi entry. The table is connected to the MAT4 through the MATT4 entry. Most material properties are directed toward a structural element and are referenced by the property entry for the element of interest.

Main Index

11

12

2.4

Thermal Loads MSC.Nastran makes a clear distinction between loads and boundary conditions. This distinction refers more to solution sequence methods than with the physical phenomena involved. In general, the specification of surface flux and internal heat generation are defined as loads. Loads are readily identified from their Bulk Data entries because they possess a load set identification (SID). This identifier has ramifications regarding the application of the load via Case Control. Case Control is discussed briefly in “Interface and File Communication” on page 31, but is introduced here for clarity. The Case Control Section:

• Selects loads and constraints (temperature boundary condition). • Requests printing, plotting, and/or punching of input and output data (plot commands are discussed in the MSC.Nastran Reference Manual and “Interface and File Communication” on page 31 of this guide). Punch files are generally intermediate files of data saved for use in a subsequent computation. Two common examples for heat transfer are the punch files of view factors that result from an execution of the VIEW MODULE, and a punch file of temperatures from a thermal solution to be used in a subsequent thermal-stress analysis.

• Defines the subcase structure for the analysis. For the current discussion, consider the selection of loads. In order to activate any of the loads stipulated in the Bulk Data Section, a load request must be made from the Case Control Section.

Key Points in Requesting Loads from Case Control • LOAD = SID; where SID is an integer used in steady state analysis (SOL 153) to request application of the load Bulk Data labeled with the given SID. Only one LOAD command per subcase may be specified in the Case Control Section.

• DLOAD = SID; used in transient analysis (SOL 159) to request the application of the dynamic load Bulk Data with the given SID. Only one DLOAD command per subcase may be specified in the Case Control Section.

• For steady state analysis, any number of loads defined in the Bulk Data may be referenced from a single Case Control request by specifying all loads of interest to have the same SID.

• For transient analysis, the static load entries are not selected by the Case Control SID; rather, they reference a TLOADi entry (DAREA field). The SID required for Case Control selection is given on the TLOADi entry (SID field). The schematic for this process is illustrated below.

Main Index

CHAPTER 2 Thermal Capabilities

Case Conrol DLOAD = SID

TLOAD1

SID

DAREA

DELAY

TYPE

TID

“LOAD”

SID

S

S1

L1

S2

L2

S3

L3

QVECT or other loading entries can be substituted for “LOAD” (see “” on page 13) DELAY

SID

TABLED1

TID x1

P1

C1

T1

P2

C2

T2

y1

x2

y2

x3

y3

x4

y4

• Unlike the steady state case where many loads may utilize the same SID, every TLOADi entry must have a unique SID. To apply multiple loads in a transient analysis, the multiple TLOADi first must be combined using a DLOAD Bulk Data entry. The SID on the DLOAD Bulk Data entry then becomes the reference SID on the DLOAD Case Control command.

• Nonlinear transient forcing functions (NOLINi) are requested in Case Control with the NONLINEAR = SID command. They are only available for transient analysis and cannot be referenced on the DLOAD Bulk Data entry.

Available Thermal Loads

Main Index

QVECT

Directional heat flux from a distant source.

QVOL

Volumetric internal heat generation.

QHBDY

Heat flux applied to an area defined by grid points.

QBDY1

Heat flux applied to surface elements.

QBDY2

Heat flux applied to grid points associated with a surface element.

QBDY3

Heat flux applied to surface elements with control node capability.

SLOAD

Power into a grid or scalar point.

NOLIN1

Nonlinear transient load as a tabular function.

NOLIN2

Nonlinear transient load as a product of two variables.

13

14

NOLIN3

Nonlinear transient load as a positive variable raised to a power.

NOLIN4

Nonlinear transient load as a negative variable raised to a power.

A complete description of the capability of each load type may be found in the appropriate Bulk Data entry description.

Thermal Load Flowchart The schematic below illustrates the Bulk Data relationship for a directional surface heat flux where temperature-dependent surface properties are important. Some typical surface loads are QVECT, QHBDY, QBDY1, QBDY2, and QBDY3. The CONTRLT entry can be used in transient analysis. For loads application, it is limited to QVOL, QVECT, and QBDY3.

Main Index

CHAPTER 2 Thermal Capabilities

Steady State

Transient

Case Control LOAD = SID

Case Control DLOAD = SID

QVECT

CHBDYG

Q0

TSOUR

+EID

+EID

-etc.-

EID

CE

E1

E2

E3

TYPE

IVIEWF

IVIEWB

RADMIDF

RADMIDB

CNTRLND

G1

G2

G3

G4

G5

G6

G7

G8

RADMID

ABSORP

EMIS1

EMIS2

EMIS3

EMIS4

EMIS5

EMIS6

EMIS7

-etc.-

RADMID

T(A)

T( ε 1)

T( ε 2)

T( ε 3)

T( ε 4)

T( ε 5)

T( ε 6)

T( ε 7)

-etc.-

TIDA

X1

x1

y1

x2

y2

x3

y3

-etc.-

TLOAD1

SID

EXCITEID

DELAY

TYPE

TID

CONTROL

ID

SENSOR

SFORM

CTYPE

PL

PH

PTYPE

DT

DELAY

TAUC

RADM

RADMT

TABLEM2

Main Index

SID

PZERO

15

16

2.5

Convection and Radiation Boundary Conditions The specification of boundary conditions was introduced in “Elements” on page 7. MSC.Nastran treats the application of radiation and convection as boundary conditions. Unlike flux loads, convection and radiation are therefore not Case Control selectable. The implications of this are twofold. In transient analysis, the transient load methodology (see “Thermal Loads” on page 12) is unavailable, and in steady state analysis, the solution sequence mechanism for load incrementing does not apply. To mitigate these shortcomings, transient control is introduced into the boundary conditions through the use of the control node. In addition, although the ability to do load incrementing is lost for these boundary conditions, their inclusion in a comprehensive tangent matrix significantly enhances both the overall stability and convergence rate.

Available Boundary Conditions • CONV

Free convection

• CONVM

Forced convection (fluid “element”)

• RADBC

Radiation exchange with space

• RADSET

Radiation exchange within an enclosure

Free Convection Application Free convection heat transfer is available through the CONV Bulk Data entry. In MSC.Nastran, free convection is governed by relationships of the following forms:

• q = H ⋅ ( T – TAMB ) expf ( T – TAMB ) • q = H ⋅ u CNTRLND ( T – TAMB ) expf ( T – TAMB ) • q = H ( T expf – TAMB expf ) • q = H ⋅ u CNTRLND ( T

exp f

– TAMB

exp f

)

where H = free convection heat transfer coefficient T = surface temperature TAMB = ambient temperature u CNTRLND = value of the control node (dimensionless)

Key Points - Free Convection Application • Free convection allows thermal communication between a surface and an ambient environment through a heat transfer coefficient (H) and a surface element (CHBDYi). Main Index

CHAPTER 2 Thermal Capabilities

• Free convection heat transfer coefficients are supplied on MAT4 Bulk Data entries. The coefficient can be made temperature dependent by using the MATT4 entry.

• The access temperature for the temperature-dependent coefficient can be varied by specifying the film node field (FLMND on CONV).

• Time dependence can be introduced into the heat transfer coefficient through the control node entry (CNTRLND on CONV). The following schematic illustrates the Bulk Data relationships for temperature- dependent-free convection and time-dependent-free convection.

Free Convection - Temperature-Dependent Heat Transfer Coefficient 1

2

3

4

5

6

7

8

9

CQUAD4

EID

PID

G1

G2

G3

G4

Q

ZOFFS

CHBDYE

EID

EID2

SIDE

IVIEWF

IVIEWB

RADMIDF

RADMIDB

CONV

EID

PCONID

FLMND

CNTRLND

TA1

TA2

TA3

10

TA4

The temperature of the FLMND is the temperature accessed in the TABLEMi entry PCONV

PCONID

MID

FORM

EXPF

MID

K

CP

r

TCH

TDELTA

QLAT

MATT4

MID

T(K)

T(CP)

TABLEM2

TID

X1

x1

y1

MAT4

x2

y2

H

m

HGEN

T(H)

T(µ)

T(HGEN)

x3

y3

-etc.-

REFENTH

.

Main Index

CHBDYE

Provides the surface element for convection application through reference to the underlying conduction element (CQUAD4).

CONV

Stipulates the application of free convection and identifies the film node, control node, and ambient node or nodes.

17

18

Main Index

PCONV

Provides supplemental information on the form of the convection relationship to be applied.

MAT4

Provides the free convection heat transfer coefficient.

MATT4

Provides for the free convection heat transfer coefficient temperature dependence.

TABLEM2

Specifies the actual table data for the heat transfer coefficient versus temperature.

CHAPTER 2 Thermal Capabilities

Free Convection - Time-Dependent Heat Transfer Coefficient

1

2

3

4

5

6

7

8

CHBDYE

EID

EID2

SIDE

IVIEWF

IVIEWB

RADMIDF

RADMIDB

CQUAD4

EID

PID

G1

G2

G3

G4

CONV

EID

PCONID

FLMND

CNTRLND

TA1

TA2

PCONID

MID

FORM

EXPF

MID

K

CP

TCH

TDELTA

QLAT

PCONV

MAT4

ρ

H

µ

Q

9

10

ZOFFS

TA3

TA4

HGEN

REFENTH

Case Control DLOAD = SID

TLOAD1

SID

EXCITEID

DELAY

TYPE

TID

DELAY

SID

P1

C1

T1

P2

C2

T2

TABLED2

TID

X1

x1

y1

x2

y2

x3

y3

-etc.-

SID

TYPE

TEMP1

GID1

TEMP2

GID2

TEMP3

TEMPBC

GID3

Forced Convection Application Streamwise-upwind Petrov-Galerkin Element (SUPG). Forced convection is available through the CONVM Bulk Data entry. Forced convection in MSC.Nastran is limited to onedimensional fluid flows. An SUPG element formulation allows for energy transport due to streamwise advection and diffusion and displays good spatial and temporal accuracy. Heat Main Index

19

20

transfer between the fluid stream and the surroundings is accounted for through a forced convection heat transfer coefficient based on locally computed Reynolds and Prandtl numbers. The pertinent heat transfer behavior is listed as follows: 1. Streamwise energy transport due to advection plus streamwise diffusion a. FLAG = 0 , no convective flow b. FLAG = 1 , diffusion and convection transport 2. Heat transfer coefficient to fluid tube wall a. If FORM = 0, then h = ( coef ⋅ Re EXPR ⋅ Pr EXPP ) hK b. If FORM = 1, then ------- ( = coef ⋅ Re EXPR ⋅ Pr EXPP ) d where DVρ Re = -----------µ Cp µ Pr = ---------k

Key Points - Forced Convection • Controlling Mass Flow Rate. The actual mass flow rate is specified by using a control node for mass flow, the CNTMDOT field on the CONVM Bulk Data entry. For forced convection, the control node can supply active or passive/local or remote system mass flow rate control. It is the user’s responsibility to ensure continuity of mass flow rate from element to element.

• The material properties of interest for determining energy transport and forced convection heat transfer coefficients are given on the MAT4 Bulk Data entries. Temperature-dependent material properties are given through the MATT4 statement, and a film node is available for the look-up temperature. The heat transfer coefficient (H) given on the MAT4 statement is for free convection ONLY.

• As with all boundary conditions, CONVM can only communicate to the structure through a surface element. The CHBDYP specification is identified on the CONVM entry as the EID field.

• Courant Number for Forced Convection. Time dependence can be introduced into the flow field mass flow rate through the control node (CNTMDOT on CONVM). Accurate resolution of the evolving flow field (transient analysis) requires some user control over the Courant number (CN). ∆t CN ≡ V ⋅ ----L where: Main Index

CHAPTER 2 Thermal Capabilities

V = Velocity of fluid ∆t = Time step size L = Element length For good resolution of transient flow fields, it is recommended that CN ≤ .10. Since the element length and mass flow rate are specified, this implies that the user must control the time step size. This may eliminate the use of the automatic time step selection scheme.

Radiation to Space A radiation boundary condition can be specified with a RADBC Bulk Data entry. This form of radiant exchange is solely between the surface element and a blackbody space node. The following relationships apply: 1. If CNTRLND = 0,

4 ) = ( σ ⋅ FAMB ) ⋅ ( ε e T e4 – α e T amb

2. If CNTRLND > 0,

4 )) = ( σ ⋅ FAMB ⋅ u CNTRLND ( ε e T e4 – α e T amb

Key Points - Radiation Boundary Conditions • Two PARAMETERS are required for any radiation calculation to be performed: TABS - Defines the absolute temperature scale. SIGMA - The Stefan-Boltzmann constant. PARAMETERS are discussed in “Parameters” on page 601 of the MSC.Nastran Quick Reference Guide. For these Bulk Data Section PARAMETERS, the statement would look like: PARAM,SIGMA,5.67E-08 PARAM,TABS,273.16

• The emissivity and absorptivity material surface properties are specified on the RADM Bulk Data entry. They may be constant, temperature-dependent (RADM/RADMT), and/or wavelength band-dependent (RADM/RADBND).

• Wavelength dependence is specified in a piecewise linear curve fashion with discrete break points defined on a RADBND Bulk Data entry. There can only be one set of break points in any given analysis, and any RADM definition must have break points that are coincident with those on the solitary RADBND. The theoretical treatment within MSC.Nastran of spectral radiation effects are discussed in some detail in “Radiation Exchange – Real Surface Approximation” on page 433.

• As with all boundary conditions, RADBC may only be used when it is applied to a surface element (CHBDYi).

Main Index

21

22

• Time dependence can be introduced into the RADBC in two ways. The Control Node Multiplier (CNTRLND) can be made to follow a specified time function, and the temperature of the ambient node (NODAMB) can be a function of time. Each has a unique effect on the overall heat transfer.

• RADBC is the only Bulk Data entry besides QVECT that uses the material’s absorptivity property in its calculations. For all enclosure radiation calculations, absorptivity is assumed to be equal to emissivity.

Enclosure Radiation Exchange Thermal radiation exchange among a group of surface elements is treated as a radiation enclosure. Defining radiation enclosures and accounting for the subsequent radiation heat transfer can be the most complicated and computationally expensive thermal calculation. As with the radiation boundary condition, the material surface properties can be constant, temperature dependent, and/or wavelength dependent. One of the more troublesome aspects of enclosure exchange is the geometric concept of view factors that relate the relative levels of radiant exchange between any and all individual surfaces in the enclosure set. A number of options are available for the calculation of view factors for black or gray diffuse surface character. “View Factor Calculation Methods” on page 409 describes the basis for enclosure exchange and the view factor calculation methods. 1. Enclosure options: MSC.Nastran is used to calculate the diffuse view factors using one of its two view factor modules. Once generated, the RADLST/RADMTX punch files can be retained for use in subsequent thermal runs that utilize the same geometry. Since view factor calculations tend to be lengthy, calculating them once and then reusing them is the preferable procedure. The INCLUDE Bulk Data entry is used to identify the view factor files to be used in the subsequent thermal analyses. View factors or exchange factors can be determined independently outside of MSC.Nastran and used in MSC.Nastran Thermal Analysis if the formats are consistent with the RADLST/RADMTX files that MSC.Nastran generates. The RADLST Bulk Data entry defines the type of matrix being used. 2. Calculation process - Radiant enclosure exchange where the view factors exist a. All conduction element surfaces involved in a radiation enclosure must be identified with surface elements (CHBDYi). The CHBDYi description of the surface element identifies the surface material entry (RADM). Multiple (and mutually exclusive) cavities may be defined within MSC.Nastran for modeling convenience, and to minimize the computation time. b. When the RADLST/RADMTX entries are available for the analysis, view factors need not be calculated. This is true as long as the existing RADLST/RADMTX entries are either already in the Bulk Data Section or are included in the input file through the Bulk Data INCLUDE entry. A punch file of view factors may have been generated in a prior run.

Main Index

CHAPTER 2 Thermal Capabilities

c. Including radiant enclosure exchange in an analysis is requested using the RADSET entry. RADSET identifies those cavities to be considered for enclosure radiation exchange. d. For an analysis where the view factors exist then, the following Bulk Data entries constitute the minimum required subset: CHBDYi RADLST RADMTX RADSET RADM / RADMT / RADBND In addition to these entries, include the parameters SIGMA and TABS. The above process is illustrated in the following schematic.

Main Index

23

24

Enclosure Radiation with Existing View Factors

CHBDYE

TYPE

IVIEWF

IVIEWB

RADMIDF

RADMIDB

G6

G7

y3

-etc.-

G1

G2

G3

G4

G5

RADSET

ICAVITY

ICAVITY

ICAVITY

ICAVITY

ICAVITY

RADLST

ICAVITY

MTXTYP

+EID

RADMTX

ICAVITY

INDEX

Fi,j

Fi+1,j

RADM

RADMID

ABSOR P

EMIS1

EMIS2

RADMT

RADMID

TIDA

TIDE1

TIDE2

TABLEM2

TID

X1

x1

y1

x2

y2

NUMBER

PLANCK2

LAMBD1

LAMBD2

RADBND

Main Index

EID

x3

G8

RADSET

Selects the radiation cavities to be included in the overall thermal analysis.

RADLST

Specifies which elements are to participate in a cavity experiencing radiation exchange.

RADMTX

Provides the F ij = A j f ji exchange factors for all the surface elements of a radiation enclosure specified in the corresponding RADLST.

CHBDYG

Identifies the radiation surface geometry and material.

RADM

Provides the surface properties for absorptivitiy and emissivity.

CHAPTER 2 Thermal Capabilities

RADMT

Provides the identification for any surface material properties that are temperature dependent.

TABLEMi

Defines a tabular function for use in generating temperature-dependent material properties.

RADBND

Provides Planck’s second constant and the wavelength break points used for spectral radiation exchange analysis. There can only be one RADBND statement in a given analysis, regardless of the number of cavitities. While this forces every exchange surface to have identical waveband break points, there may be different RADM/RADMT for potentially every surface.

3. Calculation process - Radiant enclosure exchange where the view factors must be calculated a. All conduction element surfaces involved in a radiation enclosure must be identified with surface elements (CHBDYi). The CHBDYi description of the surface element identifies the surface material entry (RADM) as well as the cavity identification (VIEW). Multiple cavities may be defined within MSC.Nastran for flexible modeling, user convenience, and eliminating shadowing calculations in determining view factors when groups of elements see only themselves to the exclusion of other groups of elements. b. Since no RADLST/RADMTX exists for this problem, they will be calculated. The calculation of view factors is instigated by including the VIEW Bulk Data entry which is referenced from the CHBDYi entries. VIEW lumps together those surface elements of a common cavity identification and provides some guidance regarding how the elements interact relative to any required shadowing calculations. c. Only one RADCAV Bulk Data entry exists for each cavity. This entry has an array of information available on it that is used to control the global aspects of the view factor calculation for the cavity in question. d. If the finite difference view factor module (default which may be described as an area subdivision method) is to be used for the view factor calculation, the entries discussed thus far are adequate for this part of the calculation. The minimum subset of Bulk Data entries for this method of view factor calculation is: For view factor calculation, use CHBDYi VIEW RADCAV To complete the thermal analysis, use RADSET RADM / RADMT / RADBND In addition, include the parameters TABS and SIGMA.

Main Index

25

26

e. If the Gaussian integration view factor calculation (the adaptive method) is desired, the VIEW3D Bulk Data entry must be included. It too is associated with a cavity ID, and includes fields which provide calculation control limits. The minimum subset of Bulk Data entries for this method of view factor calculation is: For view factor calculation, use CHBDYi VIEW VIEW3D RADCAV To complete the thermal analysis, use RADSET RADM / RADMT / RADBND In addition, include the parameters TABS and SIGMA. “View Factor Calculation Methods” on page 409 describes the calculation of view factors in added detail. The schematic below illustrates the Bulk Data interrelationship involved in the determination of view factors and depicts the additional entries required to complete the thermal analysis.

Enclosure Radiation - View Factor Calculation Required Input

CHBDYG

TYPE

IVIEWF

IVIEWB

RADMIDF

RADMIDB

G1

G2

G3

G4

G5

G6

G7

ICAVITY

ELEAMB

SHADOW

SCALE

PRTPCH

NFECI

RMAX

SET11

SET12

SET21

SET22

VIEW

IVIEW

ICAVIT Y

SHADE

NB

NG

DISLIN

VIEW3D

ICAVITY

GITB

BIPS

CIER

ETOL

ZTOL

RADCAV

Main Index

EID

WTOL

G8

RADCHK

CHBDYG

Identifies the radiation surface geometry and material.

VIEW

Groups the surface elements into their respective radiation cavities and provides control information for using the finite difference method when determining view factors (VIEW module). The VIEW Bulk Data entry also specifies that view factors be calculated.

CHAPTER 2 Thermal Capabilities

RADCAV

Identifies the characteristics of each radiation cavity and provides control information for using the finite difference method when determining view factors (VIEW module).

VIEW3D

Provides the control quantities involved in using the Gaussian integration adaptive view factor module (VIEW3D module).

Additional Enclosure Radiation Input Required to Determine the Radiation Exchange Thermal Response See CHBDYG

RADM

RADMID

ABSORP

EMIS1

EMIS2

EMIS3

EMIS4

EMIS5

EMIS6

ICAVITY

ICAVITY

ICAVITY

ICAVITY

ICAVITY

ICAVITY

ICAVITY

EMIS7

RADSET

ICAVITY ICAVITY

Main Index

RADM

Provides the surface properties for absorptivity and emissivity.

RADSET

Selects the radiation cavities to be included in the overall thermal analysis.

27

28

2.6

Temperature Boundary Conditions and Constraints A temperature boundary condition can be useful in defining independent GRID point or SPOINT temperature in an analysis. This applies to grid points associated with conduction elements, surface elements, ambient points, control nodes, or film nodes as well as to scalar points. The methods available for specifying these temperatures are discussed below. Temperature boundary conditions are treated like loads because they are selected from the Case Control Section.

Available Temperature Boundary Conditions and Constraints SPC

The single-point constraint is selected in the Case Control Section with SPC = SID. For heat transfer, an SPC may be used to define a temperature for steady state analysis or transient analysis if the boundary condition over all time is to remain at a constant value. This is the recommended approach to fixed temperature specification for both steady state and transient analysis. In the constant value case, these degrees of freedom are eliminated from the analysis set and therefore cannot influence the iterative convergence criteria. In steady state analysis, SPCs are subcase selectable. In transient analysis, SPCs must be selected above the subcase level. When used with SPCD, SPC1 can also be used to specify nonzero temperature boundary conditions.

TEMPBC

This form of boundary temperature specification is more flexible than the SPC definition since it can be used to define a temperature that varies with time throughout a transient analysis. The basic procedure for transient specification when the value varies with time is to use the dynamic load process as discussed in the load section (see “Thermal Loads” on page 12). The SID on the TEMPBC is referenced by a TLOADi Bulk Data entry (DAREA field). The TLOADi entry must be selected using the Case Control command (DLOAD = SID). Field 3 for TYPE is specified either as STAT or TRAN as desired. For steady state (STAT type) analysis, the Case Control command is SPC = SID where the SID is field 2 of the TEMPBC entry. For transient (type = TRAN) analysis, this boundary specification cannot eliminate the degrees of freedom from the analysis set. Rather, it internally implements a penalty method for maintaining the desired temperature value. The fixed matrix conductance term has a set value of 1.0E+10. In some instances, this magnitude may overwhelm the convergence criteria. In these cases, there is another approach to specified temperatures that can circumvent the problem (see the following discussion of CELASi).

Main Index

CHAPTER 2 Thermal Capabilities

CELASi

These 1-D elements provide a convenient resistive network element that can be used for thermal system modeling as well as for driving temperature boundary conditions. They may automatically have one end set to a zero or grounded value. A heat load (QHBDY) applied at the free end can be constant or time varying. The load and matrix conductance values can be adjusted to minimize the influence over the iterative convergence criteria.

MPC

Otherwise known as a multipoint constraint. This constraint can be used to specify a grid point temperature to be a weighted combination of any number of other grid point temperatures. An MPC is requested in the Case Control Section with the MPC = SID command. For transient analysis, an MPC must be requested above the subcase level.

Key Points - Temperature Boundary Conditions Key points for temperature boundary conditions are:

• No Bulk Data file may utilize more than one method for temperature specification. For example, an SPC entry and a TEMPBC entry of the type = STAT cannot exist in the same file.

• Whenever a TEMPBC entry of type = TRAN temperature boundary condition is specified in an analysis, the CONV field of the solution control entry (TSTEPNL) must be a U specification.

• Temperature initialization (see “Initial Conditions” on page 30) should always be set for all TEMPBC entries of type = TRAN temperature boundary conditions. Additionally, all temperature initial conditions must agree with the specified boundary conditions. For the MPC relationship then the initial temperature specifications must satisfy the given identity.

• In SOL 153, singularities in the stiffness matrix can be constrained automatically by Bulk Data entry PARAM,AUTOSPC,YES. However, AUTOSPC does not provide the correct action for the nonlinear stiffness matrix in SOL 159.

Main Index

29

30

2.7

Initial Conditions Setting initial temperatures is required in several situations. In steady state analysis, temperatures are usually required as a starting point for the nonlinear iteration process. In transient analysis, initial temperature specifications define the state from which the solution evolves.

Steady State Analysis Since most heat transfer problems are nonlinear due to material properties, variable boundary conditions, or radiation exchange, iteration is employed in the solution of the system equations. An initial temperature guess is required to initialize any temperature--dependent properties or boundary conditions. A good initial estimate can be helpful in achieving a converged solution. Case Control Required:

TEMP(INIT) = SID

Bulk Data Entries:

TEMP - Defines starting temperature on specific grid points. TEMPD - Automatically defines starting temperature on any remaining grid points not specified with a TEMP entry.

Transient Analysis Transient analysis, whether linear or nonlinear, employs a starting temperature as the initial condition from which the solution evolves. These starting temperatures are not, in general, arbitrary temperatures. Any noninitialized temperatures are presumed to have a value of zero. Case Control Required:

IC = SID.

Bulk Data Entries:

TEMP - Defines initial temperature on specific grid points. TEMPD - Automatically defines initial temperature on any grid points not set with a TEMP Bulk Data entry.

Main Index

MSC.Nastran Thermal Analysis User’s Guide

CHAPTER

3

Interface and File Communication

■ Introduction to Interface and File Communication ■ Execution of MSC.Nastran ■ Input Data ■ Files Generated by MSC.Nastran ■ Plotting

Main Index

32

3.1

Introduction to Interface and File Communication The formalities associated with MSC.Nastran inputs and outputs are developed in this chapter. The input is described in terms of an input data file that may be generated by hand or by a suitable preprocessor. Among the five separate sections involved in the general input is a complete description of the model, including:

• The type of analysis being performed. • The problem geometry as modeled. • The conduction elements that approximate the structure. • The surface elements that allow the structure to communicate with the boundary conditions.

• The boundary conditions associated with convection and radiation. • The loads associated with applied fluxes for all load conditions of interest. • The specification of the known temperatures in the analysis. • Requests for the desired output quantities along with their format and form.

Main Index

CHAPTER 3 Interface and File Communication

3.2

Execution of MSC.Nastran The MSC.Nastran input file is a text file that is given a filename and a .dat extension (e.g., EXAMPLE1.dat). To execute MSC.Nastran, the user types a system command followed by the name of the input file. The .dat extension is automatically assumed by MSC.Nastran if there is no file extension associated with the specified filename. A typical execution is NASTRAN EXAMPLE1

Main Index

33

34

3.3

Input Data MSC.Nastran input requires records that are 80 characters (or columns) in length. The input file is comprised of five sections that must be assembled in the following sequence: NASTRAN statement

File Management statements

Executive Control statements

Optional

Required Section

Required Delimiter

CEND

Case Control commands

Required Section

Required Delimiter

BEGIN BULK

Bulk Data entries

ENDDATA

Optional

Required Section

Required Delimiter Figure 3-1 Structure of the MSC.Nastran Input File

The records of the first four sections are input in free-field format, and only columns 1 through 72 are used for data. Any information in columns 73 through 80 may appear in the printed echo, but is not used by the program. If the last character in a record is a comma, then the record is continued to the next record. The Bulk Data entries have special free-field rules, but may be specified as fixed field. Both options are described in the MSC.Nastran Reference Manual. The Bulk Data entries may also make limited use of columns 73 through 80 for the purpose of continuation.

Main Index

CHAPTER 3 Interface and File Communication

NASTRAN Definition(s) (Optional Statement) The NASTRAN definition statement is optional and is used in special circumstances (see the “nastran Command and NASTRAN Statement” on page 1 of the MSC.Nastran Quick Reference Guide ).

File Management Statements (Optional Section) The File Management Section is optional and follows the NASTRAN definition(s). It ends with the specification of an Executive Control statement. This section provides for database initialization and management along with job identification and restart conditions. The File Management statements are described in the “File Management Statements” on page 31 of the MSC.Nastran Quick Reference Guide.

Executive Control Statements (Required) The Executive Control Section begins with the first Executive Control statement and ends with the CEND delimiter. It identifies the job and the type of solution to be performed. It also declares the general conditions under which the job is to be executed, such as maximum time allowed and the type of system diagnostics desired. If the job is to be executed with a solution sequence, the actual solution sequence is declared along with any alterations to the solution sequence that may be desired. If Direct Matrix Abstraction is used, the complete DMAP sequence must appear in the Executive Control Section. The Executive Control statements and examples of their use are described in the “File Management Statements” on page 31 of the MSC.Nastran Quick Reference Guide.

Case Control Commands (Required) The Case Control Section follows CEND and ends with the BEGIN BULK delimiter. It defines the subcase structure for the problem, defines sets of Bulk Data, and makes output requests for printing, punching, and plotting. A general discussion of the functions of the Case Control Section and a detailed description of the commands used in this section are given in the “Case Control Commands” on page 175 of the MSC.Nastran Quick Reference Guide . Those commands used most commonly in thermal analysis are complied in “Thermal Analysis Case Control Commands” on page 244. Also, the Case Control highlights for heat transfer are given here.

Steady State Heat Transfer - SOL 153 • A separate subcase must be defined for each unique combination of thermal loads (LOAD Case Control command), temperature constraints (SPC and MPC command), and nonlinear iteration strategy (NLPARM command).

• The LOAD Case Control command references the static thermal load entries: QVOL, QVECT, QHBDY, and QBDYi. Each subcase defines a set of loads that can then be subdivided into a number of increments for the nonlinear solution process (NLPARM Bulk Data entry).

Main Index

35

36

The load step is labeled by the cumulative load factor. The load factor varies from 0 to 1 in each subcase. Specifically, the load step ends with 1, 2, 3, etc. for the first, the second, and the third subcase, respectively. The data blocks containing solutions can be generated at each increment or at the end of each subcase, depending on the intermediate output option specified on the INTOUT field of the NLPARM Bulk Data entry. Data blocks are stored in the database for the output process and restarts.

• The SPC Case Control command references the temperature boundary conditions in the SPC Bulk Data entry. The applied temperature boundary condition is also subdivided in the subcase in an incremental fashion.

• The MPC Case Control command references the algebraic temperature constraints in the MPC Bulk Data entry. In heat transfer we can think of MPCs as perfect conductor networks.

• The TEMP(INIT) Case Control command references the initial temperatures that are required for all nonlinear analyses. An initialized temperature distribution must be defined using TEMP and/or TEMPD Bulk Data entries.

• Output requests for each subcase are processed independently. Requested output quantities for all the subcases are appended after the computational process for actual output operation. Available outputs are as follows: THERMAL

Temperatures for GRID points and SPOINTs.

FLUX

Inner element temperature gradients. Heat flows for CHBDYi elements.

OLOAD

Applied linear loads.

SPCF

Steady state heat of constraint for maintaining specified temperature boundary conditions.

• MSC.Nastran data may be output in either SORT1 or SORT2 formats. SORT1 output provides a tabular listing of all grid points or elements for each loading condition. SORT2 output is tabular listings of loading conditions for each grid point or element. SORT1 output is the steady state default format. SORT2 is generated by requesting XYPLOTS. See “Case Control Commands for Output” on page 25 of the MSC.Nastran Reference Guide for a discussion of SORT1 and SORT2 formats and their defaults.

• Restarts are controlled by the PARAMeters SUBID and LOOPID. The Case Control command THERMAL(PUNCH) can be used to generate temperature punch files suitable for restart initial conditions or thermal stress analysis loads.

Transient Heat Transfer - SOL 159 • Only one set of temperature constraints (via the MPC and SPC Case Control command) may be requested and must be specified above the subcase level. Any DMIG and/or TF used must also be selected above the subcase level.

• A subcase must be defined for each unique combination of transient thermal load Main Index

conditions (DLOAD command) and nonlinear iteration strategy (TSTEPNL command).

CHAPTER 3 Interface and File Communication

Each subcase defines a time interval starting from the last time step of the previous subcase, and the time interval requested is subdivided into the appropriate time steps. The data blocks containing solutions are generated at the end of each subcase to store in the database for output process and restarts.

• The DLOAD and/or NONLINEAR command must be used to specify time-dependent loading conditions. The static thermal load entries QVOL, QVECT, QHBDY, and QBDYi may be used in defining a dynamic load as specified by the TLOADi entry. The set identification number (SID) on the static load entries is specified in the DAREA field of the TLOADi entry. The TEMPBC (of TRAN type) Bulk Data entry may be requested in the same fashion. The input loading functions may be changed for each subcase or continued by repeating the same DLOAD request. However, it is recommended to use the same TLOADi Bulk Data entry for all subcases in order to maintain continuity, since the TLOADi entry defines the loading history as a function of cumulative time.

• Temperature initial conditions are requested above the subcase level with the IC Case Control command. Initial temperatures are specified on TEMP and/or TEMPD Bulk Data entries.

• Output requests for each subcase are processed independently. Requested output quantities for all the subcases are appended after the computational process for the actual output operation. The available output is as follows: ENTHALPY

Grid point enthalpies.

THERMAL

Grid point temperatures.

FLUX

Element gradient and fluxes.

OLOAD

Applied linear loads.

SPCF

Heat of constraint.

HDOT

Enthalpy gradient with respect to time.

• MSC.Nastran data may be output in either SORT1 or SORT2 output format. SORT1 output is a tabular listing of all grid points or elements for each time step in transient analysis. In transient analysis, SORT1 output is requested by placing a PARAM,CURVPLOT,+1 in the Bulk Data. See “Case Control Commands for Output” on page 25 of the MSC.Nastran Reference Guide for a discussion of SORT1 and SORT2 formats and their defaults. SORT2 is the default format for transient analysis.

• Restarts are controlled by the parameters STIME, LOOPID, and SLOOPID. See the MSC.Nastran Handbook for Nonlinear Analysis, Section 9.2.2 for a discussion of restarts for nonlinear transient analysis. The Case Control command THERMAL(PUNCH) can be used to generate temperature punch files suitable for restart initial conditions or for thermal stress analysis loads.

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38

Bulk Data Entries (Required) The Bulk Data Section follows BEGIN BULK and ends with the ENDDATA delimiter. It contains all of the details of the model and the conditions for the solution. BEGIN BULK and ENDDATA must be present even though no new Bulk Data is being introduced into the problem or if all of the Bulk Data is coming from an alternate source, such as user-generated input. The format of the BEGIN BULK entry is in free-field format. The ENDDATA delimiter must begin in column 1 or column 2. In general, only one model can be defined in the Bulk Data Section. However, some of the Bulk Data, such as the entries associated with loading conditions, direct input matrices, and transfer functions, may exist in multiple sets. Only sets selected in the Case Control Section are used in any particular solution. The Bulk Data entries associated primarily with thermal analysis are included in “Commonly Used Bulk Data Entries” in Appendix D.

Miscellaneous Input The input file might also include required resident operating system job control language (JCL) statements. The type and number of JCL statements varies with the particular computer installation. The input file may be formed by the insertion of other files with the INCLUDE statement. This INCLUDE statement may be specified in any of the five parts of the input file. Comments may be inserted in any of the parts of the input file. They are identified by a dollar sign ($) in column 1. Columns 2 through 72 may contain any desired text.

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CHAPTER 3 Interface and File Communication

3.4

Files Generated by MSC.Nastran Upon successful execution of an MSC.Nastran job, a variety of files are automatically created. These files have the following filename extensions and descriptions as shown below: .dat

The input file describing the model, the type of solution, the output requests, etc. Generated with a text editor or preprocessor.

.f06

The main output file containing the printed output such as temperature, temperature gradients, heat flows, etc.

.f04

A history of the assigned files, disk space usage, and modules used during the analysis. Useful for debugging.

.log

A summary of the command lines options used and the execution links.

.DBALL

A database containing the input files, assembled matrices, and solutions. Used for restarting the job for additional analysis.

.MASTER

The file containing the master directory of the files used by the run and the physical location of the files on the system. This file is also needed for a restart job.

.USRSOU

Used only for advanced DMAP applications. This file may be deleted after the run is finished. It is not needed for restarts.

.USROBJ

Used only for advanced DMAP applications. This file may be deleted after the run is finished. It is not needed for restarts.

.plt

Contains the plot information requested with the NASPLT command specified in the input file.

.pch

Contains the punch output as requested in the input file.

.xdb

Graphics database used by MSC.XL and MSC.Aries for postprocessing of the results.

miscellaneous scratch files

Several scratch files are generated during the analysis which MSC.Nastran automatically deletes upon completion of the run.

SCR (scratch) Command. If no restarts or database manipulations are planned, then the MASTER, DBALL, USRSOU, and USROBJ files can be automatically deleted (scratched) upon completion of the run by adding the statement SCR = YES to the execution command. For example, NASTRAN

EXAMPLE1

SCR=YES

Failure to delete these files may prohibit subsequent reruns of the same input file. The .dat, .f06, .f04, .log, and .pch files are ASCII files and can be viewed using any text editor. The remaining files are binary, and as such, cannot be viewed. The binary files are not intended to be used directly; they are used for additional analysis, such as restarts or postprocessing. If no

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40

restarts are planned, you may specify “scr = yes” when submitting the input file for execution. The .DBALL, .MASTER, .USROBJ, and .USRSOU files are placed on the scratch directory and are automatically deleted upon completion of the run. The .USEROBJ and .USRSOU files are intended only for DMAP users and may be deleted after the run is complete. The .plt file is a binary file that contains the plotting information generated by NASPLT, the MSC.Nastran internal plotting feature. If NASPLT is not used, the .plt file is deleted following the completion of the run. If punch output is specified, the .pch file is retained when the run is complete. The .xdb binary file is the graphic database used by MSC.XL, MSC.Aries, and other graphics pre- and postprocessors. It is requested using PARAM,POST in the Bulk Data Section. (Refer to the description of PARAM,POST in “Parameters” on page 601 of the MSC.Nastran Quick Reference Guide.)

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CHAPTER 3 Interface and File Communication

3.5

Plotting MSC.Nastran has the ability to generate structural plots or X-Y plots rom batch program executions. Such plots are requested by placing data commands at the end of the Case Control Section. Plot requests are separated from the Case Control by the OUTPUT(PLOT), OUTPUT(XYPLOT), or OUTPUT(XYOUT) commands. Data above this command is not recognized by the plotter. For virtually any type of plotter hardware, the plotter programs are executed by NASPLT ‘name.plt’ for a “CALCOMP-like” plot, or by TEKPLT ‘name.plt’ for a “TEKTRONIX-like” plot. The ‘name.plt’ is the filename of the plot file generated from MSC.Nastran. These programs are delivered with the utility files. The following discussion is limited to a description of all of the commands required to obtain undeformed structure, thermal contour, and X-Y plots in thermal analysis.

Structural Plotting In thermal analysis, structural plotting is applied to display the model geometry (undeformed structure plots) and the temperature distribution across the model (thermal contour plots). The structural plotting is requested in the Case Control Section by the plotting commands from an OUTPUT(PLOT) command to either a BEGIN BULK, OUTPUT(XYPLOT), or OUTPUT(XYOUT) command. Plot Set Selection. MSC.Nastran plots consist of element images. Grid points are identified by the intersection of the elements. Note that the surface elements CHBDYE, CONV, CONVM, and RADBC cannot be plotted. The SET command is required to specify sets of elements for plotting. Examples are as follows: SET 1 = ALL SET 2 = BAR, QUAD4, EXCEPT 10, 50 THRU 90 BY 20 SET 3 = 1, 5 THRU 10, 100 THRU 105, 210 SET 4 = ALL EXCEPT HBDY In these examples, SET 1 includes all elements, SET 2 includes all CBAR and CQUAD4 elements except elements 10, 50, 70, and 90, SET 3 includes a subset of elements selected by their ID numbers, and SET 4 includes all elements except CHBDYi surface elements. Only one set of elements can be selected for a particular plot. To request an undeformed structural plot, the following two commands are required: FIND SCALE, ORIGIN j, SET i PLOT SET i, ORIGIN j Main Index

41

42

where i identifies one of the sets described in the SET command and j defines an origin for the plot. If j is equal to i, the program finds the origin automatically and positions the plot in the center of the viewing window. If some other origin is desired, the ORIGIN command should be used. In particular, the ORIGIN command should be used if more than ten plot sets are requested.

Parameter Definition Commands The parameter definition commands are described in the MSC.Nastran Reference Manual. A set of commonly used commands is as follows:

• PLOTTER = {NAST} Selects plotter. The default is NAST.

• AXES R, S, T VIEW γ , β , α where: R, S, T = X or MX, Y or MY, Z or MZ (where “M” implies the negative axis) γ , β , α = three angles of rotation in degrees (Real) Defines the orientation of the object in relation to the observer. The observer’s coordinate system is defined as R, S, T, and the basic coordinate system of the object is defined as X, Y, Z. The angular relationship between the two systems is defined by the three angles α , β , and γ as follows: T

γ

β

S

α R

Main Index

Direction of View (Always in the negative Rdirection. The projection plane is always in, or parallel to, the S-T plane.)

CHAPTER 3 Interface and File Communication

The two coordinate systems are coincident (i.e., X is coincident with R, etc.) for γ = β = α = 0. The sequence in which the rotations are taken was arbitrarily chosen as: γ , the rotation about the T-axis; followed by β , the rotation about the S-axis; followed by α , the rotation about the R-axis. Normally, α is not used since it does not affect the appearance of the S-T projection, only its orientation on the page. The default values of the rotations are γ = 34.27°, β = 23.17°, and α = 0.0°, which produce a plot in which unit vectors on the X-, Y-, and Z-axes have equal lengths. The default view described above may be altered in two ways. The structural axes that coincide with the R-, S-, T-axes may be interchanged by means of the “AXES R, S, T” command, and the view angles can be rotated by the “VIEW γ , β , α ” command. The default forms of these commands are AXES X, Y, Z VIEW 34.27, 23.17, 0.0 To view the structure from the positive Y-axis, use the commands AXES Y, Z, X VIEW 0.0, 0.0, 0.0 that points the Z-axis toward the right and the X-axis upward in the plot, or use AXES Y, MX, Z VIEW 0.0, 0.0, 0.0 that points the X-axis toward the left (in this expression MX means that the minus Xaxis coincides with S) and points the Z-axis upward. Note that the expression AXES Y, X, Z provides a mirror image of the structure. In order to avoid a mirror image, the sequence of axes must obey the right-hand rule. The structure can be viewed from the position Z-axis by the expression AXES Z, X, Y VIEW 0.0, 0.0, 0.0 Other combinations of AXES and VIEW commands produce any desired views of the structure. For example, VIEW 45.0, 0.0, 0.0 provides a view midway between the positive X- and Y-axes of the basic coordinate system.   • CSCALE =  0.5 -------   cs 

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44

• Controls the spacing of the characters; the default value is 0.5. A value of 1.8 produces good spacing of output characters. The CSCALE command must immediately precede the PLOTTER selection command. If a second CSCALE command is used, a second PLOTTER selection command must also be used.

• PTITLE = {any legitimate character string} Title to be printed at the top of the plot on the line below the sequence number. The default value for the text is all blanks.

Undeformed Structural Plots Requests for undeformed plots take the following general form:  GRID POINTS  PLOT i 1 , i 2 THRU i 3 , i 4 , etc., SET j, ORIGIN k, LABEL  ELEMENTS   BOTH

    

The following entries are optional:

• i 1 , i 2 THRU i 3 , i 4 , etc. - List of subcases; the default is to plot all subcases.  GRID POINTS  • LABEL  ELEMENTS   BOTH

   - Label either the grid points and/or the  

elements with the ID numbers.

Thermal Contour Plots Requests for thermal contour plots are similar to requests for undeformed structural plots. All axes, view, and set commands are the same. The only changes are the addition of one CONTOUR command and one modification to the PLOT command. The CONTOUR command specifies that contour data is to be prepared for a subsequent plot command. For thermal analysis, this command has the form CONTOUR MAGNIT where “MAGNIT” is a mnemonic for a “magnitude” data request that satisfies the data processing requirement for thermal temperature contours. The CONTOUR command should be placed immediately before the associated PLOT execution command. A THERMAL Case Control command must appear for all grid points that are specified in the plot set definition of contour plots. The only change necessary to the PLOT command is the specification of CONTOUR plots. The PLOT command then appears as: Main Index

CHAPTER 3 Interface and File Communication

PLOT CONTOUR, SET i, OUTLINE The OUTLINE entry (optional) requests that only the outline of all the elements in the specified set be displayed. If this entry is not specified, all of the elements included in the specified set are displayed. To plot thermal contours at any time step of a transient analysis, the PLOT command must specify the desired time or time range. The PLOT command then takes the form PLOT CONTOUR, TIME t1 , t2 , SET i, OUTLINE Here the contour plot(s) is created for all parts of the model in SET i and at time steps within the range of t 1 and t 2 . If only t 1 is specified, the plot is generated at t = t 1 .

Examples of Structure Plot Requests The following examples are typical plot packets for thermal analysis. BEGIN BULK or OUTPUT(XYPLOT) command is shown as a reminder to the user to place the plot request packet properly in the Case Control Section, i.e., at the end of the Case Control Section or just before any X-Y output requests. Example The following sequence causes an undeformed structural plot to be selected for the entire model, using the default values for AXES and VIEW. OUTPUT (PLOT) SET 1 = ALL FIND SCALE, ORIGIN 1, SET 1 PLOT SET 1 BEGIN BULK Example The following sequence causes temperature contours over the entire model to be plotted using all default orientation view angles. OUTPUT (PLOT) SET 1 = ALL FIND SCALE, ORIGIN 1, SET 1 CONTOUR MAGNIT PLOT CONTOUR, SET 1 OUTPUT(XYPLOT) Example The following sequence causes three plots to be generated.

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OUTPUT (PLOT) SET 1 = ALL SET 2 = BAR, QUAD4 SET 3 = 14 THRU 44, 100 THRU 147, 210 $FIRST PLOT FIND SCALE, ORIGIN 1, SET 1 PLOT SET 1, ORIGIN 1 $SECOND PLOT AXES Z, X, Y VIEW 0.0, 0.0, 0.0 FIND SCALE, ORIGIN 2, SET 2 PLOT SET 2, ORIGIN 2 $THIRD PLOT FIND SCALE ORIGIN 3, SET 3 PLOT SET 3, ORIGIN 3, LABEL BOTH BEGIN BULK The first plot uses the default values for AXES and VIEW. The second plot uses the indicated overrides. The third plot uses the same view options as the previous plot, which is the default for multiple plots. It also uses the option to label both grid points and elements. Note that in all cases the FIND command immediately precedes the PLOT command and follows any AXES or VIEW commands that are explicitly present. Any other sequence for these commands results in improperly scaled plots. Example The following sequence generates three plots using more spacing of characters. OUTPUT (PLOT) CSCALE = 1.8 PLOTTER NAST SET 1 = ALL SET 2 = QUAD4 $FIRST PLOT PTITLE = BASIC MODEL FIND SCALE, ORIGIN 1, SET 1 PLOT SET 1, ORIGIN 1 $SECOND PLOT PTITLE = LABEL GRIDS FIND SCALE, ORIGIN 2, SET 2 PLOT SET 2 LABEL GRIDS $THIRD PLOT PTITLE = THERMAL CONTOURS CONTOUR MAGNIT PLOT CONTOUR, TIME 5.0, ORIGIN 1, SET 1, OUTLINE BEGIN BULK The first plot is a simple undeformed structural plot of the entire model and has the title “BASIC MODEL”. The second plot is the same type of plot for all CQUAD4 elements in the model. The plot title is “LABEL GRIDS”. This plot has its own scale and magnification factor as requested Main Index

CHAPTER 3 Interface and File Communication

by its unique FIND SCALE command. The third plot is a contour plot over the entire model for the temperatures at time 5.0. Since this plot does not have its own FIND SCALE command, the view has the same orientation as does the first plot. Its title is “THERMAL CONTOURS.”

X-Y Plotting In transient thermal analysis, X-Y plotting is used to track the temperature-time history or the heat flux/time history of grid points. It can also be applied in steady state analysis to plot temperature versus a set of grid points. In addition to the plots, X-Y tabular output may be printed or punched, and a summary of data (e.g., maximum and minimum values as well as the locations of these values) may be obtained for any X-Y output. The X-Y output is requested via a packet in the Case Control Section. This packet includes all of the commands between either OUTPUT(XYPLOT) or OUTPUT(XYOUT) and either BEGIN BULK or OUTPUT(PLOT).

X-Y Plotter Terminology A single set of plotted X-Y pairs is known as a “curve.” Curves are the entities that the user requests to be plotted. The surface (paper, microfilm frame, etc.) on which one or more curves is plotted is known as a “frame.” Curves may be plotted on a whole frame, an upper-half frame, or a lower-half frame. Grid lines, tic marks, axes, and axis labeling may be chosen by the user. The program selects defaults for parameters that are not selected by the user. Only two commands are required for an X-Y output request. They are

• X-Y output section delimiter - OUTPUT(XYPLOT) or OUTPUT(XYOUT). • At least one operation command. The terms OUTPUT(XYPLOT) and OUTPUT(XYOUT) are interchangeable and either form may be used for any of the X-Y output requests. If the output is limited to printing and/or punching, a plotter selection command is not required. The operation command(s) is used to request various forms of X-Y output. If only the required commands are used, the graphic control options assume all the default values. Curves using default parameters have the following general characteristics:

• Tic marks are drawn on all edges of the frame. Five spaces are provided on each edge of the frame.

• All tic marks are labeled with their values. • Linear scales are used. • Scales are selected such that all points fall within the frame. • The plotter points are connected with straight lines. • The plotted points are not identified with symbols.

Main Index

The above characteristics may be modified by inserting any number of parameter definition commands before the operation command(s). The following is an overview of the parameter definition commands and the operation commands for thermal analysis. A more complete description is contained in “X-Y PLOT Commands” on page 525 of the .

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48

Parameter Definition Commands The parameter definition commands are described in “X-Y Output Command Summary” on page 526 of the . A set of commonly used commands is listed as follows:

• PLOTTER = {NAST} Selects plotter. The default is NAST.

• CLEAR Causes all parameter values except titles (XTITLE, YTITLE, YTTITLE, YBTITLE, TCURVE) to revert to their default values.

• CSCALE = cs (Real) See the Parameter Definition Commands Section of Structural Plotting.

• CURVELINESYMBOL = cls (Integer) Request for points to be connected by lines (cls = 0), identified by symbol |cls| (cls < 0), or both (cls > 0); default value is 0. The following symbols are available: Symbol Number

Symbol

0

no symbol

1

¥

2

²

3

+

4

-

5 6 7 8 9 If more than one curve per frame is required, the symbol number is incremented by 1 for each curve.

• TCURVE = {any legitimate character string} Curve title.

• XTITLE = {any legitimate character string} Title to be used with the x-axis.

• YTITLE = {any legitimate character string} Title to be used with y-axis. This command pertains only to whole frame curves. Main Index

CHAPTER 3 Interface and File Communication

• XMIN = x1 (Real) XMAX = x2 (Real) Specifies the limits of the abscissa of the curve; the default values are chosen to accommodate all points.

• YMIN = y1 (Real) YMAX = y2 (Real) Specifies the limits of the ordinate of the curve; the default values are chosen to accommodate all points. This command pertains only to whole frame curves.  YES    NO 

• XGRID = 

Request for drawing in the grid lines parallel to the y-axis at locations requested for tic marks; the default value is NO. This command pertains only to whole frame curves.

 YES    NO 

• YGRID = 

Request for drawing in the grid lines parallel to the x-axis at locations requested for tic marks; the default value is NO. This command pertains only to whole frame curves.

Operation Commands When a command operation is encountered, one or more frames is generated using the current parameter specifications. The form of this command as applied in thermal analysis is

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Operation one or more (required)

Curve Type one only (required)

Subcase List (optional)

XYPLOT

FLUX

i 1, i 2, i 3 ,

XYPRINT

OLOAD

i 4 , THRU i 5 ,

XYPUNCH

SPCF

i 6 , etc.

XYPEAK

TEMP

XYPAPLOT

VELO

Curve Request(s) (required)

“frames”

Default is all subcases

Note: Continuation commands may not be used until the subcase list section is reached.

Operation The entries in the operation field have the following meanings: XYPLOT

Generates X-Y plots for the selected plotter.

XYPRINT

Generates tabular printer output for the X-Y pairs.

XYPUNCH

Generates punched command output for the X-Y pairs. Each command contains the following information:

x

X-Y pair sequence number.

x

X-value.

x

Y-value.

x

Command sequence number.

XYPEAK

Output is limited to the printed summary page for each curve. This page contains the maximum and minimum values of y for the range of x.

XYPAPLOT

Generates X-Y plots on the printer. The x-axis moves horizontally along the page and the y-axis moves vertically along the page. Symbol ‘*’ identifies the points associated with the first curve of a frame, then for successive curves on a frame the points are designated by symbols O, A, B, C, D, E, F, G, and H.

Curve Type Only one type of curve field may appear in a single operation command. However, there is no limit to the number of such commands. The entries in the curve type field have the following meaning:

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CHAPTER 3 Interface and File Communication

Curve Type FLUX OLOAD

Meaning Element flux output Load

SPCF

Single-point force of constraint

TEMP

Temperature in the physical set

VELO

Enthalpy in the physical set

Subcase List The subcase list generates output for the subcase numbers that are listed. The subcase list must be in ascending order. Default is all subcases for which solutions were obtained.

Curve Request(s) The word “frames” represents a series of curve identifiers of the following general form: /a1(b1,c1) ,a2(b2,c2),etc./d1(e1,f1) ,d2(e2,f2) ,etc./etc. The information between slashes (/) specifies curves that are to be drawn on the same frame. The symbol a1 identifies the grid point or element number associated with the first plot on the first frame. The symbol a2 identifies the grid point or element number associated with the second plot on the first frame. The symbols d1 and d2 identify similar items for plots on the second frame, etc. AII plot requests on one command are sorted by grid point or element ID to improve the efficiency of the plotting process. Symbols are assigned in order by grid points or element identification number. The symbols b1 and b2 are codes for the items to be plotted on the upper half of the first frame, and c1 and c2 are codes for the items to be plotted on the lower half of the first frame. If any of the symbols b1, c1, b2, or c2 are missing, the corresponding curve is not generated. If the comma (,) and c1 are absent along with the comma (,) and c2, full frame plots are prepared on the first frame for the items represented by b1 and b2. For any single frame, curve identifiers must all be of the whole frame type or all of the half frame type, i.e., the comma (,) following b1 and b2 must be present for all entries or absent for all entries in a single frame. The symbols e1, f1, e2, and f2 serve a similar purpose for the second frame, etc. If continuation commands are needed, the previous command may be terminated with any one of the slashes (/) or commas (,) in the general format. Item codes are fully described in “Item Codes” on page 777 of the MSC.Nastran Quick Reference Guide. For curve types OLOAD, SPCF, TEMP, and VELO in thermal analysis, use item code T1. For X-Y plots of heat fluxes (curve type FLUX), the item codes are

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Element Type Conductive Elements

CHBDYi Elements

Code

Item

4

x gradient

5

y gradient

6

z gradient

7

x flux

8

y flux

9

z flux

4

Applied load

5

Free convection

6

Forced convection

7

Radiation

8

Total

Examples of X-Y Output Request Packets The following examples are applied in transient thermal analysis to display the temperature or heat flux as a function of time. The BEGIN BULK or OUTPUT(PLOT) command is shown as a reminder to the user to place the X-Y output request packet properly in the Case Control Section, i.e., at the end of the Case Control Section or just ahead of any structure plot requests. Example The following sequence causes a single whole frame to be plotted for the temperature of grid point 5, using the default parameter values: OUTPUT(XYPLOT) XYPLOT TEMP/5 (T1) BEGIN BULK Example The following sequence causes a single frame (consisting of an upper half frame and a lower half frame) to be plotted using the default parameter values: OUTPUT(XYPLOT) XYPLOT FLUX/70 (7,9) ,80(7,9) OUTPUT (PLOT)

Each half frame contains two curves. The x-direction heat fluxes of the CHEXA element number 70 and the CPENTA element number 80 are plotted on the upper half frame. The z-direction heat fluxes are plotted on the lower half frame for these two elements.

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Example The following sequence causes three whole frames to be plotted using the default parameter values: OUTPUT(XYPLOT) XYPLOT VELO /11(T1),12(T1) XYPLOT OLOAD/21(T1),22(T1) XYPLOT SPCF /31(T1),32(T1) OUTPUT (PLOT) Each frame contains two curves. The first plot is the enthalpy at grid points 11 and 12. The second plot is the linear loads applied at grid points 21 and 22. The third plot is the single-point forces of constraint applied at grid points 31 and 32. Example The following sequence causes two whole frame plots to be generated, one for CHBDYi element numbers 10 and 20 and the other for CHBDYi element numbers 30 and 40: OUTPUT(XYPLOT) XTITLE = TIME IN SECONDS YTITLE = FREE CONVECTION AND RADIATION OF THE CHBDYi ELEMENTS XGRID = YES YGRID = YES CURVELINESYMB = 6 XYPLOT FLUX/10(5),10(7) ,20(5) ,20 (7) /30(5) ,30(7) ,40(5) ,40(7) BEGIN BULK

Each plot contains the free convection and radiation heat flows for two CHBDYi elements. The default parameters are modified to include titles and grid lines in both the x-direction and ydirection. Distinct symbols are used for each curve. The first curve is identified by circles ( ), the second curve by squares ( ), the third curve by diamonds ( ), and the fourth curve by triangles ( ). Example The following sequence causes three whole frames to be generated: OUTPUT(XYPLOT) XTITLE = TIME YTITLE = TEMPERATURE XGRID = YES YGRID = YES XYPLOT TEMP/1(T1),2(T1),3(T1) YTITLE = Y-FLUX OF THE QUAD4 ELEMENTS XYPLOT FLUX/10(8) YTITLE = FORCED CONVECTION OF THE CHBDYi ELEMENTS XYPLOT FLUX/31(6), 32(6) BEGIN BULK

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The first plot is the temperatures for grid points 1, 2, and 3. The second plot is the heat flux in the y-direction for CQUAD4 element number 10. The third plot is the forced convection heat flows for CHBDYi element numbers 31 and 32. The default parameters are modified to include titles and grid lines in both the x-direction and y-direction.

X-Y Plots for SORT1 Output It is often convenient to display the distribution of temperature versus a sequence of grid points. The identification numbers of the sequence of grid points to be plotted should be listed on a SET1 Bulk Data entry. The requests for X-Y plots appear in the Case Control Section in the standard form. For example, OUTPUT(XYPLOT) XTITLE = ZAXIS YTITLE = TEMPERATURE XGRID = YES YGRID = YES CURVELINESYMB = 6 XYPLOT TEMP/99(T1) BEGIN BULK . . . PARAM,CURVPLOT,1 PARAM,DOPT,3 SET1,99,1,THRU,10 This example generates an X-Y plot from grid point temperatures. The abscissa of the curve reflects the grid point IDs listed on the SET1 Bulk Data entry with an SID of 99, and the ordinate reflects the temperatures at these grid points. In the Bulk Data, PARAM,CURVPLOT,1 suppresses SORT2-type processing and requests that X-Y plots be made with the abscissas relating to grid point locations. Parameter DOPT controls the x spacing of these curves. The allowable values of this parameter are shown in the following table:

Main Index

Value of DOPT

Scaling for Abscissa

0 (default)

gj – gi

1

xj – xi

2

yj – yi

3

zj – zi

4

1

CHAPTER 3 Interface and File Communication

The default for DOPT is the length between grid points, with the first grid point listed on the referenced SET1 command at the origin. For DOPT values 1, 2, or 3, the spacing between adjacent points on the abscissa is proportional to one component of the distance between their grid points. DOPT = 4 spaces the grid points equally along the abscissa.

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Main Index

MSC.Nastran Thermal Analysis User’s Guide

CHAPTER

4

Method of Solution

■ Introduction to Solution Methods ■ Nonlinear Iteration Scheme ■ Steady State Analysis ■ Transient Analysis

Main Index

58

4.1

Introduction to Solution Methods This chapter describes the solution methods of MSC.Nastran thermal analysis. Two types of heat transfer problems, steady state analysis and transient analysis, are solved by MSC.Nastran. The solutions of these analysis types, their respective MSC.Nastran solution sequences, and iteration methods are discussed in the following sections.

Main Index

CHAPTER 4 Method of Solution

4.2

Nonlinear Iteration Scheme MSC.Nastran applies a Newton-Raphson iteration scheme to solve thermal (and structural) analysis problems. In finite element analysis, the general equilibrium equation is [K]{u} = {F}

Eq. 4-1

where: [ K ] = the conduction matrix (stiffness matrix) { u } = the unknown grid point temperature vector to be solved (displacement) { F } = the vector of known heat flows (forces) Applying Newton’s method involves the specification of a correction vector { ψ } = [ K]{ u } – { F }

Eq. 4-2

and the approximation of the vanished correction vector at the (i + 1)-th iteration, i.e., { ψ }i + 1 ≈ { ψ }i +

i

∂ψ { ∆u } i = 0 ------∂u

Eq. 4-3

where { ∆u } i = { u i + 1 – u i }

Eq. 4-4

is the i-th incremental displacement vector. The above equation can be rewritten as [ K T ] i { ∆u } i = { R } i

Eq. 4-5

where: [ KT ] =

∂ψ ------∂u

{ R } = –{ ψ }

= the tangential matrix which includes components related to conduction, convection advection, and radiation. = the residual vector

At each iteration, the left-hand side matrix [ K T ] i and the right-hand side vector { R } i are computed based on the temperature vector { u } i . By solving the unknown vector { ∆u } i , the displacement vector at the (i + 1)-th iteration can be calculated from { u } i + 1 = { u } i + { ∆u } i

Eq. 4-6

Since matrix decomposition is time consuming, MSC.Nastran does not update the left-hand side matrix at each iteration. The tangential matrix is updated only when the solution fails to converge or the iteration efficiency can be improved. However, the residual vector is updated at each iteration. In concert with Newton’s method, the following options are provided to improve the efficiency of the iteration: Main Index

59

60

• Tangential matrix update strategy. • Line search method. • Bisection of loads. • Quasi-Newton (BFGS) updates. These options are specified on NLPARM (steady state analysis) or TSTEPNL (transient analysis) Bulk Data entries. In general, if the solution diverges, a line search algorithm, a bisection of loads, and a quasi-Newton update are implemented in an effort to improve the solution. If the solution still fails to converge with all the above methods, the tangential stiffness is updated to resume the iteration. The user may refer to the MSC.Nastran Handbook for Nonlinear Analysis for detailed algorithms.

Main Index

CHAPTER 4 Method of Solution

4.3

Steady State Analysis Basic Equations. The steady state heat balance equation is 4

[ K ] { u } + [ ℜ ] { u + T abs } = { P } + { N }

Eq. 4-7

where: [ K ] = a heat conduction matrix [ ℜ ] = a radiation exchange matrix { P } = a vector of applied heat loads that are independent of temperature { N } = a vector of nonlinear heat loads that are temperature dependent { u } = a vector of grid point temperatures T abs = the absolute temperature scale adjustment required for radiation heat transfer exchange or radiation boundary conditions when all other temperatures and units are specified in deg-F or deg-C. The components of the applied heat flow vector { P } are associated either with surface heat transfer or with heat generated inside the volume heat conduction elements. The vector of nonlinear heat flows { N } results from boundary radiation, surface convection, and temperature-dependent thermal loads. The equilibrium equation is solved by a Newton iteration scheme where the tangential stiffness matrix is approximated by i

 ∂N  [ K T ] i ≈ [ K ] i + 4 [ ℜ ] i { u i + T abs } 3 –  ------   ∂u 

Eq. 4-8

and the residual vector is { R } i = { P } + { N } i – [ K ] i { u } i – [ ℜ ] i { u i + T abs } 4

Eq. 4-9

Steady State Analysis Solution Sequence In MSC.Nastran, steady state thermal analysis is solved by Solution Sequence 153. Since Solution 153 can be used for both structural (default) and thermal analyses, the user must include the command ANALYSIS = HEAT in the Case Control Section of the input data for thermal analysis. The input data file may then appear as:

Main Index

61

62

ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE ANALYSIS = HEAT NLPARM = 10 TEMP(INIT) = 20 . . BEGIN BULK NLPARM,10,.... . . TEMP,20,..... TEMPD,20,.... ENDDATA The NLPARM entry is required to control the incremental and iterative solution processes. For nonlinear problems, a set of temperatures should be provided for an initial guess. These temperatures are specified on TEMP and TEMPD Bulk Data entries and are selected by a TEMP(INIT) Case Control command.

Convergence Criteria The convergence criteria are characterized by the dimensionless error functions and the convergence tolerances. To ensure accuracy and efficiency, multiple criteria with errors measured about temperatures, loads, and energy are provided. 1. Temperature error function Since the error in temperatures is not known, a contraction factor q is introduced to formulate the temperature error function, which is defined as ui + 1 – ui ∆u i - = -----------------------q = ------------------------------ui – ui – 1 ∆u i – 1

Eq. 4-10

To avoid fluctuation and ill-conditioning, an averaging scheme is applied to compute the contraction factor 2 ∆u i 1 q i = --- ------------------------ + --- q i – 1 3 ∆u i – 1 3

Eq. 4-11

with an initial value q 0 = 0.99. If q is assumed to be constant with a value less than unity, the absolute error in temperatures can be estimated by

Main Index

CHAPTER 4 Method of Solution

u – ui + 1 ≤ u – ui + n + ui + n – ui + n – 1 + … + ui + 2 – ui + 1 ∆u i ( q n + q n – 1 + … + q )

=

=

Eq. 4-12

q ∆u i ------------1–q

The temperature error function is formulated by introducing the weighted normalization to the above equation, i.e.,

∑

ω j ∆u j

q ω ⋅ ∆u q j E u = ------------- ----------------------- = ------------- -------------------------1–q ω⋅u 1–q ∑ ωj uj

Eq. 4-13

j

where the weighting function { ω } is defined as the square root of the diagonal terms of the tangential matrix [ K T ] , i.e., ωj =

KT

Eq. 4-14

jj

2. Load error function The load error function is defined as

∑

Rj uj

R⋅u E p = -------------------- = ----------------------P' ⋅ u ∑ P'j u j j

Eq. 4-15

j

with { P' } = { P ld } + { ∆P ld }

Eq. 4-16

where { P ld } is the applied thermal load at the previous loading step, and { ∆P ld } is the incremental load. 3. Energy error function The energy (or work) error function is defined as

∑

R j ∆u j

R ⋅ ∆u j E w = ----------------------- ---------------------------P' ⋅ u ∑ P'j u j

Eq. 4-17

j

At every iteration, error functions are computed and printed in the convergence table under the headings EUI, EPI, and EWI. The convergence test is performed by comparing the error functions with the convergence tolerances, i.e., Main Index

63

64

E u < EPSU ( default = 10 – 3 ) E p < EPSP ( default = 10 – 3 ) E w < EPSW ( default = 10 – 7 ) where EPSU, EPSP, and EPSW are tolerances specified on the NLPARM Bulk Data entry. The solution has converged if these tests are satisfied. However, only those criteria selected by the user (specified in the CONV field of the NLPARM entry) are checked for convergence. Note that the tolerances should not be too tight to waste iteration time or too loose to affect accuracy. It is recommended that the default values be used until better values are found through iteration experience.

Iteration Control The incremental and iterative solution processes are controlled by the parameters specified on the NLPARM Bulk Data entry, with the data format and default values described as follows: 1

2

3

4

5

6

7

8

9

NLPARM

ID

NINC

DT

KMETHOD

KSTEP

MAXITER

CONV

INTOUT

AUTO

5

25

PW

NO

FSTRESS

LSTOL

NLPARM

+NP1

EPSU

EPSP

EPSW

MAXDIV

MAXQN

MAXLS

1.0E-3

1.0E-3

1.0E-7

3

MAXITER

4

MAXBIS +NP2

MAXR

0.5

10

+NP1

+NP2

RTOLB

5

In thermal analysis, the arc-length method (specified by NLPCI command) is disabled. The DT, FSTRESS, MAXR, and RTOLB fields are also ignored and should be left blank for heat transfer. The ID field specifies an integer selected by the Case Control request NLPARM. For each subcase, load and SPC temperature changes are processed incrementally with a number of equal subdivisions defined by the NINC value. The KMETHOD and KSTEP fields specify the tangential matrix update strategy. Three separate options for KMETHOD may be selected.

• AUTO The program automatically selects the most efficient strategy based on convergence rates. At each iteration, the number of steps required to converge as well as the computing time with and without matrix update are estimated. The tangential matrix is updated if (a) the estimated number of iterations to converge exceeds MAXITER,

Main Index

CHAPTER 4 Method of Solution

(b) the estimated time required for convergence with current matrix exceeds the estimated time to converge with matrix update, or (c) the solution diverges. The tangential matrix is also updated on convergence if KSTEP is less than the number of steps required for convergence with the current matrix.

• SEMI This option is identical to the AUTO option except that the program updates the tangential matrix after the first iteration.

• ITER The program updates the tangential matrix at every KSTEP iteration and on convergence if KSTEP < MAXITER. However, the tangential matrix is never updated if KSTEP > MAXITER. Note that the Newton-Raphson method is obtained if KSTEP = 1, and the modified Newton-Raphson method is selected by setting KSTEP = MAXITER. The number of iterations for a load increment is limited to MAXITER. If the solution does not converge in MAXITER iterations, the load increment is bisected and the analysis is repeated. If the load increment cannot be bisected (i.e., MAXBIS is reached or MAXBIS = 0) and MAXDIV is positive, the best attainable solution is computed, and the analysis is continued to the next load increment. If MAXDIV is negative, the analysis is terminated. The convergence criteria are defined through the test flags in the CONV field and the tolerances in the EPSU, EPSP, and EPSW fields. The requested criteria (combination of temperature error U, load error P, and energy error W) are satisfied upon convergence. The INTOUT controls the output requests for temperatures, heat fluxes, and heat flows. If the option ALL or YES is selected, the output requests specified in the Case Control Data are processed for every computed load increment. If the option is NO, the output requests are processed only for the last load step of the subcase. The MAXDIV limits the divergence conditions allowed for each iteration. The divergence rate E i is defined by the ratio of energy errors before and after the iteration, i.e., { ∆u i } T { R i } E i = ----------------------------------------{ ∆u i } T { R i – 1 }

Eq. 4-18

Depending on the divergence rate, the number of diverging iterations NDIV is incremented as follows: If E i ≥ 1 or E i < – 10 12, then NDIV = NDIV + 2 If – 10 12 < E i < – 1, then NDIV = NDIV + 1 The solution is assumed to diverge when NDIV > |MAXDIV|. If the solution diverges and the load increment cannot be bisected (i.e., MAXBIS is reached or MAXBIS = 0), the tangential matrix is updated and the analysis is continued. If the solution diverges again and MAXDIV is positive, the best attainable solution is computed, and the analysis is continued to the next load increment. If MAXDIV is negative, the analysis is terminated on the second divergence. Main Index

65

66

The BFGS update is performed if MAXQN > 0. As many as MAXQN quasi-Newton vectors can be accumulated. The BFGS update with these QN vectors provides a secant modulus in the search direction. If MAXQN is reached, the tangential matrix is updated, and the accumulated QN vectors are purged. The accumulation resumes at the next iteration. The line search is performed if MAXLS > 0. In the line search, the temperature increment is scaled to minimize the energy error. The line search is not performed if the absolute value of the relative energy error is less than the tolerance LSTOL or if the number of line searches reaches MAXLS. The number of bisections for a load increment is limited to |MAXBIS|. Different actions are taken when the solution diverges, depending on the sign of MAXBIS. If MAXBIS is positive, the tangential matrix is updated on the first divergence, and the load is bisected on the second divergence. If MAXBIS is negative, the load is bisected every time the solution diverges until the limit on bisection is reached. If the solution does not converge after |MAXBIS| bisections, the analysis is continued or terminated depending on the sign of MAXDIV.

Iteration Output At each iteration, the related output data is printed under the following heading: ITERATION

Iteration count i.

EUI

Relative error in terms of temperatures.

EPI

Relative error in terms of loads.

EWI

Relative error in terms of energy.

LAMBDA

Rate of convergence.

DLMAG

Absolute norm of the residual vector ( R l i ) .

FACTOR

Final value of the line search parameter.

E-FIRST

Divergence rate, initial error before line search.

E-FINAL

Error at the end of line search.

NQNV

Number of quasi-Newton vectors appended.

NLS

Number of line searches performed during the iteration.

ENIC

Expected number of iterations for convergence.

NDV

Number of occurrences of probable divergence during the iteration.

MDV

Number of occurrences of bisection conditions during the iteration.

The solver also prints diagnostic messages requested by DIAG 50 or 51 in the Executive Control Section. DIAG 50 only prints subcase status and NLPARM data, while DIAG 51 prints all data at each iteration. In general, the user should be cautioned against using DIAG 51, because it is used for debugging purposes and the volume of output is significant. It is recommended that DIAG 51 be used only for small test problems. The diagnostic output is summarized as follows: For each entry into NLITER, the following is produced: Main Index

CHAPTER 4 Method of Solution

• Subcase status data • NLPARM data • Core statistics (ICORE, etc.) • Problem statistics (g-size, etc.) • File control blocks • Input file status • External load increment for subcase: { ∆P ld } • Initial nonlinear force vector: { Fg } . In thermal analysis, { Fg } is the heat flow vector associated with nonlinear conduction, convection (CONV and CONVM), and boundary radiation (RADBC), i.e., { Fg } = [ Kg ] { ug } – { Ng } – { Ng } – { Ng } nl CONV CONVM RADBC

• Initial sum of nonlinear forces including follower forces: { Fl } . In heat transfer, { F l } is the heat flow vector associated with nonlinear conduction, convection, radiation, and nonlinear thermal loads (QBDY3, QVECT, and QVOL), i.e., { F l } = [ K l ] { u l } + [ ℜ l ] ( u l + T abs ) 4 – { N l } nl

• Initial temperature vector: { u l } • KFSNL • DELYS: [ K f ] T { ∆u s } s

• Initial residual vector: { R l } For each iteration, the following is produced:

• Temperature increment: { ∆u l } • Initial energy: { ∆u l } T { R l } • New temperature vector: { u g } • Nonlinear force vector: { F g } • Sum of nonlinear forces including follower forces: { F l } • New temperature vector: { u l } • New residual vector: { R l } • Denominator of EUI • Denominator of EPI • Contraction factor: q • Remaining time For each quasi-Newton vector set, the following is produced:

• Condition number: λ 2 • Quasi-Newton vector: δ Main Index

67

68

• Quasi-Newton vector: γ 1 • Energy error: z = --------T

δj γj

For each line search, the following is produced:

• Previous line search factor: α k • Previous error: E k • New line search factor: α k + 1

Recommendations The following are recommendations, designed to aid the user.

• Initial temperature estimate: For highly nonlinear problems, the iterative solution is sensitive to the initial temperature guess. It is recommended to overshoot (i.e., make a high initial guess) the estimated temperature vector in a radiation-dominated problem.

• Incremental load: Incremental loading reduces the imbalance of the equilibrium equation caused by applied loads. The single-point constraints (temperature specified by SPC in the Bulk Data) and the applied loads (specified by QBDY1, QBDY2, QBDY3, QHBDY, QVECT, and QVOL) can be incremented. If the solution takes more iterations than the default values of the maximum number of iterations allowed for convergence (MAXITER), the increment size should be decreased. For linear problems, no incremental load steps are required.

• Convergence criteria: At the beginning stages of a new analysis, it is recommended that the defaults be used on all options. However, the UPW option may be selected to improve the efficiency of convergence. For problems with poor convergence, the tolerances EPSU, EPSP, and EPSW can be increased within the limits of reasonable accuracy.

Main Index

CHAPTER 4 Method of Solution

4.4

Transient Analysis Basic Equations. The general equation solved in transient analysis has the form · [ B ] { u } + [ K ] { u } + { ℜ } { u + T abs } 4 = { P } + { N }

Eq. 4-19

To take phase change into consideration, the heat diffusion equation is converted into · { H } + [ K ] { u } + [ ℜ ] { u + T abs } 4 = { P } + { N }

Eq. 4-20

Note: In “” on page 69, H represents enthalpy, not the convection heat transfer coefficient. where: The equilibrium equation is solved by Newmark’s method with adaptive time stepping. [ B ] = a heat capacity matrix [ K ] = a heat conduction matrix [ ℜ ] = a radiation exchange matrix { P } = a vector of applied heat loads that are constant or functions of time, but not functions of temperature { N } = a vector of nonlinear heat loads that depend on temperature { H } = an enthalpy vector · { H } = { dH ⁄ dt } { u } = a vector of grid point temperature · { u } = { du ⁄ dt } T abs = the absolute temperature scale adjustment required for radiation heat transfer exchange or radiation boundary conditions when all other temperatures and units are specified in deg-F or deg-C. Based on this one-step integration scheme, the time derivative of the nodal temperatures at the (i + 1)-th iteration of the time step (n + 1) is expressed as  · 1 · 1  i+1 { u n + 1 } i + 1 = ---------  u n + 1 – u n  +  1 – --- { u n }   θ θ∆t  

Eq. 4-21

{ u n + 1 } i + 1 = { u n + 1 } i + { ∆u n + 1 } i

Eq. 4-22

1 --- = 2 – 2η θ

Eq. 4-23

where

and

Main Index

69

70

The parameter η is specified on the PARAM,NDAMP Bulk Data entry. When η = 0, ( θ = 0.5), no numerical damping is requested. In this case, Newmark’s method is equivalent to the CrankNicolson method. For the Newton-Raphson scheme, the iteration equation is 1  -------[B ] i + [ KT ] i { ∆u n + 1 } i = { R n + 1 } i  θ∆t- n + 1 n+1 

Eq. 4-24

The left-hand side matrices may be approximated by 1 1 ] i ≈ --------- [ B n ] + [ K T ] --------- [ B n + 1 ] i + [ K T θ∆t θ∆t n+1 n

Eq. 4-25

where [ K T ] is the tangential stiffness matrix evaluated at the previous time step, i.e., n  ∂N n  [ K T ] ≈ [ K n ] + 4 [ ℜ n ] { u n + T abs } 3 –  ----------  n  ∂u n 

Eq. 4-26

The residual vector is 1}

i

i i i i i = { Pn + 1 } + { Nn + 1 } – [ Kn + 1 ] { un + 1 } – [ ℜn + 1 ]  un + 1 + Ta 

1 +  --- – 1 ( { P n } + { N n } – [ K n ] { un } – [ ℜ n ] { un + T abs θ

Eq. 4-27

i 1 – --------- ( { H n + 1 } – { H n } ) θ∆t

At the first iteration, the initial conditions are 0

0

0

0

{ u n + 1 } = { u n }, [ K n + 1 ] = [ K n ], [ ℜ n + 1 ] = [ ℜ n ], and [ H n + 1 ] = { H n }

Eq. 4-28

Thus, the initial residual vector can be expressed as { Rn + 1 }

0

1 = { P n + 1 } + { N n + 1 } 0 +  --- – 1 ( { P n } + { N n } ) θ  4 1 – --- ( [ K n ] { u n } + [ ℜ n ] { u n + T abs } ) θ

Eq. 4-29

Transient Analysis Solution Sequence In MSC.Nastran, transient thermal analysis is solved by Solution Sequence 159. Since Solution 159 can be used for both structural (default) and thermal analyses, the user must include the command ANALYSIS = HEAT

Main Index

CHAPTER 4 Method of Solution

in the Case Control Section of the input data for thermal analysis. Additionally, the initial conditions (temperatures) and the time integration (solution time, time step size, convergence criteria) must be specified. The input data file may then appear as ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE ANALYSIS = HEAT TSTEPNL = 10 IC = 20 . . BEGIN BULK TSTEPNL,10,.... . . TEMP,20,..... TEMPD,20,.... ENDDATA The TSTEPNL entry is required to specify the initial time step and the iteration control. Initial temperatures are specified on TEMP and TEMPD Bulk Data entries and are selected by an “IC” Case Control command. As the solution progresses, the time steps are adjusted automatically by an adaptive time stepping scheme, which is described in the following section. It is up to the user to specify a reasonable initial time step size. A conservative estimate can be determined as follows. Let: 2

χ ∆t o ≅ --------------10 ⋅ α where: ∆t o = initial time step size χ = smallest element dimension in the model α = largest thermal diffusivity, α = k ⁄ ρC p and, k = thermal conductivity, ρ = density C p = specific heat

Main Index

Eq. 4-30

71

72

Automatic Time Stepping MSC.Nastran estimates optimal time stepsize and the stepsize evolves based on the convergence condition. The time step is doubled ( ∆t n + 1 = 2∆t n ) as { ∆u n } = { u n – u n – 1 } becomes small, i.e., · un ------------------ < UTOL ( default = 0.1 ) · u max

Eq. 4-31

· where u max is the maximum value of the norms computed from previous time steps and UTOL is a tolerance on the temperature increment specified on the TSTEPNL Bulk Data entry. If the temperature increment exceeds the tolerance, a proper time step size can be predicted from the following calculation where ωn is the inverse of the characteristic time. T

T { ∆u n } [ K T ] { ∆ u n } { ∆u n } { F n – F n – 1 } n ω n = ----------------------------------------------------- ~ --------------------------------------------------------T T { ∆u n } { ∆H n } { ∆u n } { ∆H n }

Eq. 4-32

In thermal analysis, { F n } is the heat flow vector associated with conduction, convection (CONV and CONVM), and radiation (RADBC and RADSET), i.e., 4

[ K n ] { un } + [ ℜ n ] { u n + T abs } – { N n }

CONV

– { Nn }

CONVM

– { Nn }

R

Eq. 4-33

The next time step is adjusted by ∆t n + 1 = f ( r )∆t n

Eq. 4-34

where r is a scaling factor defined as 1 1 2π r = --------------------  ------  -------- MSTEP  ω n  ∆t n

Eq. 4-35

with f = 0.25 for r < 0.5 • RB f = 0.5 for 0.5 • RB < r < RB f = 1.0 for RB < r < 2.0 f = 2.0 for 2.0 < r < 3.0/RB f = 4.0 for r > 3.0/RB Values of MSTEP and RB are specified on the TSTEPNL Bulk Data. If MSTEP is not specified, the default value is estimated by the stiffness ratio defined as T

{ ∆u n } { F n – F n – 1 } λ = -------------------------------------------------------T { ∆u n } [ K T ] { ∆ u n } n

Main Index

Eq. 4-36

CHAPTER 4 Method of Solution

The default value of MSTEP is determined based on the following criteria: λ* =

λ if λ ≥ 1

λ* =

1 --- if λ < 1 λ

Eq. 4-37

and MSTEP = 20 for λ * < 5 MSTEP = 40 for 5 ≤ λ * < 1000

Eq. 4-38

No Adjust for λ * ≥ 1000 The adjusted time step size is limited to the upper and lower bounds, i.e., DT DT MIN  ---------------------- , ------------------ ≤ ∆t ≤ MAXR ⋅ DT MAXBIS MAXR 2

Eq. 4-39

where DT is the user-specified time increment and MAXR and MAXBIS are user-defined entries specified on the TSTEPNL entry. The time step is set to the limit if it falls outside the bounds. When the time marches to a value close to the last time specified by the user, the adaptive stepping scheme stops for the current subcase. The termination criterion is N

∑

∆t N ∆t n + --------- ≤ DT ⋅ NDT 2

Eq. 4-40

n = 1

where DT ⋅ NDT is the user-specified time duration for the current subcase. The adjusted time step remains effective across the subcases.

Integration and Iteration Control The incremental and iterative solution processes are controlled by the parameters specified on the TSTEPNL Bulk Data entry with the data format and default values described as follows: 1

2

3

4

5

6

7

8

9

TSTEPNL

ID

NDT

DT

NO

METHOD

KSTEP

MAXITER

CONV

1

ADAPT

2

10

PW

FSTRESS

TSTEPNL

+TNL1

+TNL2

Main Index

EPSU

EPSP

EPSW

MAXDIV

MAXQN

MAXLS

1.0E-2

1.0E-3

1.0E-6

2

10

2

MAXBIS

ADJUST

MSTEP

RB

MAXR

UTOL

5

5

0

0.75

16.0

0.1

10

+TNL1

+TNL2

RTOLB

73

74

In thermal analysis, the options AUTO and TSTEP (specified in METHOD field) are disabled. The FSTRESS and RTOLB fields are also ignored and should be left blank for heat transfer. The ID field specifies an integer selected by the Case Control command TSTEPNL. The initial time increment and the number of time steps are specified by DT and NDT. Since the time increment is adjusted during the analysis, the actual number of time steps may not be equal to NDT. However, the total time duration is close to NDT ⋅ DT . For printing and plotting purposes, data recovery is performed at time steps O, NO, 2 • NO, ..., and the last converged step. The Case Control command OTIME may also be used to control the output times. Since both linear and nonlinear problems are solved by the same solution sequence, only the ADAPT option can be selected in the METHOD field for heat transfer. The ADAPT method automatically adjusts the incremental time and uses bisection. During the bisection process, the heat capacitance matrix and the tangential stiffness matrix are updated every KSTEP-th converged bisection solution. The number of iterations for a time step is limited to MAXITER. If MAXITER is negative, the analysis is terminated on the second divergence condition during the same time step or when the solution diverges for five consecutive time steps. If MAXITER is positive, the program computes the best solution and continues the analysis until divergence occurs again. If the solution does not converge in MAXITER iterations, the process is considered divergent. Either bisection or matrix update is activated when the process diverges. The convergence criteria are defined through the test flags in the CONV field and the tolerances in the EPSU, EPSP, and EPSW fields. The requested criteria (combination of temperature error U, load error P, and work error W) are satisfied upon convergence. Note that at least two iterations are required to check the temperature convergence criterion. MAXDIV limits the divergence conditions allowed for each iteration. Depending on the divergence rate, the number of diverging iteration NDIV is incremented as follows: NDIV = NDIV + 2 if NDIV = NDIV + 1 if

E 1i ≥ 1

or E 1i < – 10 12

– 10 12 < E 1i ≥ – 1

or E 2i > 1

Eq. 4-41

where: i

=

{ ∆u i } { R i } ------------------------------------{ ∆u i } { R i – 1 }

i

=

E pi -------------E pi – 1

E1

E2

T

The solution is assumed to diverge when NDIV reaches MAXDIV. If the bisection option is used, the time step is bisected upon divergence. Otherwise, the left-hand side matrices are updated, and the computation for the current time step is repeated. If NDIV reaches MAXDIV again within the same time step, the analysis is terminated. Main Index

CHAPTER 4 Method of Solution

The BFGS update and the line search process are performed in the same way as in steady state analysis. Nonzero values of MAXQN and MAXLS activate the quasi-Newton update and the line search process, respectively. The number of bisections for a load increment is limited to |MAXBIS|. Different actions are taken when the solution diverges, depending on the sign of MAXBIS. If MAXBIS is positive and the solution does not converge after MAXBIS bisections, the best solution is computed and the analysis is continued to the next time step. If MAXBIS is negative and the solution does not converge in |MAXBIS| bisections, the analysis is terminated. ADJUST controls the automatic time stepping in the following ways: 1. If ADJUST = 0, the automatic adjustment is deactivated. 2. If ADJUST > 0, the time increment is continually adjusted for the first few steps until a good value of ∆t is obtained. After this initial adjustment, the time increment is adjusted every ADJUST-th time step only. 3. If ADJUST is one order greater than NDT, the automatic adjustment is deactivated after the initial adjustment. Parameters MSTEP and RB are used to adjust the time increment. The upper and lower bounds of time step size are defined with MAXR. If the solution approaches steady state (checked by tolerance UTOL), the time step size is doubled. Detailed computations involving these parameters are described in the previous section.

Iteration Output At each iteration or time step, the related output data are printed under the following heading: TIME

Cumulative time for the duration of the analysis.

ITER

Iteration count for each time step.

DISP

Relative error in terms of temperatures defined as λi ui – ui – 1 E ui = -------------------------------------( 1 – λ i )u max

Eq. 4-42

where u max = max ( u 1 , u 2 , …, u n ) and λ i = E pi ⁄ E pi – 1 . LOAD

Relative error in terms of loads defined as R i E pi = -------------------------------------------------max ( F n , P t )

Eq. 4-43

n

where   are internal heat flows and external applied heat loads, { F n } and  P t  respectively.  n Main Index

75

76

In thermal analysis, { F n } is a heat flow vector defined in the Automatic Time Stepping section, and   is the total heat flow associated with conduction, convection, radiation,  P t  and applied loads, i.e.,  n    P t  = { P n } + { N n } ld – { F n }  n

Eq. 4-44

= { Nn } + { Nn } + { Nn } where { N n } ld QBDY3 QVECT QVOL WORK

Relative error in terms of work defined as { ui – ui – 1 }T{ R }i E wi = ------------------------------------------------------------------------------------   max  { u n } T { F n }, { u n } T  P t    n 

Eq. 4-45

LAMDBA(I)

Rate of convergence λ i ( = E pi ⁄ E pi – 1 ) .

DLMAG

Absolute norm of the residual vector ( R ) . The absolute convergence is defined using DLMAG by R < 10 – 12 .

FACTOR

Final value of the line search parameter.

E-FIRST

Divergence rate, initial error before line search.

E-FINAL

Error at the end of line search.

NQNV

Number of quasi-Newton vectors appended.

NLS

Number of line searches performed during the iteration.

ITR DIV

Number of occurrences of divergence detected during the adaptive iteration.

MAT DIV

Number of occurrences of bisection conditions during the iteration.

NO. BIS

Number of bisections executed for the current time interval.

ADJUST

Ratio of time step adjustment relative to DT.

Diagnostic messages are requested by DIAG 50 or 51 in the Executive Control Section. DIAG 50 only prints subcase status, TSTEPNL data, and iteration summary, while DIAG 51 prints all data at each iteration. In general, the user should be cautioned against using DIAG 51, because it is used for debugging purposes only and the volume of output is significant. It is recommended that DIAG 51 be used only for small test problems. The diagnostic output is summarized as follows: For each entry into NLTRD2, the following is produced:

• Subcase status data. Main Index

CHAPTER 4 Method of Solution

• TSTEPNL data. • Core statistics (ICORE, etc). • Problem statistics (g-size, etc.). • File control block. • Input file status. For each time step, the following is produced:

• NOLINi vector: { N d } • External load vector: { P d } • Load vector including follower forces and NOLINs: { P td } • Constant portion of residual vector: { R' d } • Total internal force: { F d } • Initial residual vector: { R d } For each iteration, the following is produced:

• Initial energy for line search: { ∆u d } T { R d } • Nonlinear internal force: { F g } , which is { Fg } = { Kg } { ug } – { Ng } – { Ng } – { Ng } nl CONV CONVM RADBC

Eq. 4-46

• Temperature vector: { u d } • Nonlinear internal force: { F d } nl , which is 4

l

= [ K d ] { ud } + [ ℜ d ] { u d + T abs } – { N d } – { Nd } – { Nd } nl CONV CONVM R

Eq. 4-47

• Total internal force: { F d } , which is { Fd } = [ Kd ] { ud } + { Fd } l nl

Eq. 4-48

• NOLINi vector: { N d } • Enthalpy vector: { H d } • Load vector including follower forces and NOLINs: { P td } , which is { P td } = { P d } + { N d } – { F d } ld = { Nd } + { Nd } + { Nd } where { N d } ld QBDY3 QVECT QVOL • Residual vector: { R d }

• Iteration summary (convergence factors, line search data, etc.) For each quasi-Newton vector set, the following is produced:

• Condition number: λ Main Index

2

• quasi-Newton vector: δ

Eq. 4-49

77

78

• quasi-Newton vector: γ 1 • Energy error: = --------T

δj γj

For each line search; the following is produced:

• Previous line search factor: α k • Previous error: E k • New line search factor: α k + 1 For each converged time step, the following is produced: · • Time derivative of temperature: { u d } For each time step adjustment, the following is produced: ·

• Magnitude of the time derivative of temperature: { u n } ·

• Magnitude of the new time derivative of temperature: { u n + 1 } T

• General conductance: DENOM1 = { ∆un } [ K T ] { ∆un } T

• General enthalpy: DENOM2 = { ∆un } { ∆H n }

n

T

• Work: { ∆u n } { ∆F n } • Inverse of Characteristic time: ω n • Conductance ratio: λ • Number of steps for the period of dominant frequency: MSTEP • Controlling ratio for time step adjustment: r

Recommendations The following are recommendations designed to aid the user.

• Time step size To avoid inaccurate or unstable results, a proper initial time step associated with spatial mesh size is suggested. The selection criterion is 1 2 ρc p ∆t = --- ∆x --------k n

Eq. 4-50

where ∆t is the time step, n is the modification number of the time scale, ∆x is the mesh size (smallest element dimension), ρ is the material density, c p is the specific heat, and k is the thermal conductivity. A suggested value of n is 10. For highly nonlinear problems, a small step size is recommended.

Main Index

CHAPTER 4 Method of Solution

• Numerical stability Numerical stability is controlled by the parameter η (specified on the PARAM,NDAMP Bulk Data entry). For linear problems, η = 0 (i.e., no numerical damping) is adequate, but for nonlinear problems a larger value of η may be advisable. Increasing the value of η improves numerical stability; however, the solution accuracy is reduced. The recommended range of values is from 0.0 to 0.1 (default value is 0.01).

• Initial temperatures and boundary temperatures The specification of initial temperatures and boundary condition temperatures should be consistent. For a given point, the initial temperature should be equal to the boundary condition temperature at t = 0.

• Convergence criteria At the beginning stages of a new analysis, it is recommended that the defaults be used on all options. However, the UPW option may be selected to improve the efficiency of convergence. For nonlinear problems with time-varying boundary conditions, the U option must be selected, because the large conductance (internally generated) affects the calculations of the PW error functions. For problems with poor convergence, the tolerances EPSU, EPSP, and EPSW can be increased within the limits of reasonable accuracy.

• Fixed time step If a fixed time step is desired, the adaptive time stepping can be deactivated by setting ADJUST = 0 on the TSTEPNL Bulk Data.

Main Index

79

80

Main Index

MSC.Nastran Thermal Analysis User’s Guide

CHAPTER

5

Examples

■ Steady State and Transient Analysis Examples ■ Example 1a - Linear Conduction ■ Example 1b - Nonlinear Free Convection Relationships ■ Example 1c - Temperature Dependent Heat Transfer Coefficient ■ Example 1d - Film Nodes for Free Convection ■ Example 1e - Radiation Boundary Condition ■ Example 2a - Nonlinear Internal Heating and Free Convection ■ Example 2b - Nonlinear Internal Heating and Control Nodes ■ Example 2c - Nonlinear Internal Heating and Film Nodes ■ Example 3 - Axisymmetric Elements and Boundary Conditions ■ Example 4a - Plate in Radiative Equilibrium, Nondirectional Solar Load with Radiation Boundary Condition ■ Example 4b - Plate in Radiative Equilibrium, Directional Solar Load with Radiation Boundary Condition ■ Example 4c - Plate in Radiative Equilibrium, Directional Solar Load, Spectral Surface Behavior ■ Example 5a - Single Cavity Enclosure Radiation with Shadowing ■ Example 5b - Single Cavity Enclosure Radiation with an Ambient Element Specification ■ Example 5c - Multiple Cavity Enclosure Radiation

Main Index

82

■ Example 6 - Forced Convection Tube Flow - Constant Property Flow ■ Example 7a - Transient Cool Down, Convection Boundary ■ Example 7b - Convection, Time Varying Ambient Temperature ■ Example 7c - Time Varying Loads ■ Example 7d - Time Varying Heat Transfer Coefficient ■ Example 7e - Temperature Dependent Free Convection Heat Transfer Coefficient ■ Example 7f - Phase Change ■ Example 8 - Temperature Boundary Conditions in Transient Analyses ■ Example 9a - Diurnal Thermal Cycles ■ Example 9b - Diurnal Thermal Cycles ■ Example 10 - Thermostat Control ■ Example 11 - Transient Forced Convection

Main Index

CHAPTER 5 Examples

5.1

Steady State and Transient Analysis Examples This chapter provides several examples of steady state and transient analysis. In each case, the general “demonstrated principals” are listed at the beginning, followed by an example discussion and concluding with a description of results. Where appropriate, plots and notes are provided.

Main Index

83

84

5.2

Example 1a - Linear Conduction Demonstrated Principles • Specifying Grid Point Geometry • Defining Element Connectivity • Describing Material Properties • Applying the “Load” • Accessing the Results

Discussion This simplest of examples demonstrates the organization of the MSC.Nastran input data file including the Executive, Case Control, and Bulk Data Sections for a typical heat transfer analysis. A complete description of all available input data is available in the MSC.Nastran Quick Reference Guide. The “Executive Control Section” on page 229, “Case Control Commands” on page 243, and “Bulk Data Entries” on page 275 of this User’s Guide describe the input data most commonly applied to heat transfer problems. CROD elements

o

T 1 = 1300 K 1

2

3

4

o

T 6 = 300 K 5

o

K = 204.0 W ⁄ m K A cross section = .007854 m 2 L = 0.5 m

Figure 5-1 Example 1a The MSC.Nastran input file is shown in Listing 5-1.

Main Index

6

CHAPTER 5 Examples

Listing 5-1 Example 1a Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 1a ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 BEGIN BULK NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.1,0.0,0.0 GRID,3,,0.2,0.0,0.0 GRID,4,,0.3,0.0,0.0 GRID,5,,0.4,0.0,0.0 GRID,6,,0.5,0.0,0.0 $ CROD,1,5,1,2 CROD,2,5,2,3 CROD,3,5,3,4 CROD,4,5,4,5 CROD,5,5,5,6 PROD,5,15,.0078540 MAT4,15,204.0 $ SPC,10,1,,1300.0 SPC,10,6,,300.0 TEMPD,20,1300.0 $ ENDDATA

Note: SPC and NLPARM are requested in the Case Control Section. SPCs are used to set the temperature boundary condition.

Results The abbreviated EX1A.f06 output file is shown in Listing 5-2. A plot of temperature versus distance is shown in Figure 5-2.

Main Index

85

86

Listing 5-2 Example 1a Results File EXAMPLE 1A

LOAD STEP =

NOVEMBER

POINT ID. 1 EXAMPLE 1A

TYPE S

LOAD STEP =

1.00000E+00

ID VALUE 1.300000E+03

ID+1 VALUE 1.100000E+03

F O R C E S POINT ID. 1 EXAMPLE 1A

TYPE S

LOAD STEP =

1.00000E+00 F I N I T E

Main Index

MSC/NASTRAN

11/ 1/93

PAGE

11

ID+4 VALUE ID+5 VALUE 5.000000E+02 3.000000E+02 2, 1993 MSC/NASTRAN 11/ 1/93

PAGE

12

PAGE

13

1.00000E+00 T E M P E R A T U R E

ELEMENT-ID 1 2 3 4 5

2, 1993

EL-TYPE ROD ROD ROD ROD ROD

ID VALUE 3.204432E+03

O F

X-GRADIENT -2.000000E+03 -2.000000E+03 -2.000000E+03 -2.000000E+03 -2.000000E+03

ID+2 VALUE 9.000000E+02

ID+3 VALUE 7.000000E+02 NOVEMBER

S I N G L E - P O I N T

ID+1 VALUE .0

E L E M E N T

V E C T O R

ID+2 VALUE .0

T E M P E R A T U R E Y-GRADIENT

C O N S T R A I N T

ID+3 VALUE .0 NOVEMBER

ID+4 VALUE ID+5 VALUE .0 -3.204432E+03 2, 1993 MSC/NASTRAN 11/ 1/93

G R A D I E N T S

Z-GRADIENT

A N D

X-FLUX 4.080000E+05 4.080000E+05 4.079999E+05 4.080000E+05 4.080001E+05

F L U X E S Y-FLUX

Z-FLUX

CHAPTER 5 Examples

Temperature (°K) 1400 1300

(0.0, 1300.)

1200

(0.1, 1100.)

1100 1000

(0.2, 900.)

900 800

(0.3, 700.)

700 600

(0.4, 500.)

500 400 300

(0.5, 300.)

200 100 0 0

0.1

0.2

0.3

Distance (meters) Figure 5-2 Temperature versus Distance

Main Index

0.4

0.5

87

88

5.3

Example 1b - Nonlinear Free Convection Relationships Demonstrated Principles • Surface Elements and Boundary Conditions • Free Convection Forms • Ambient Nodes

Discussion We introduce the CHBDY surface element for the purpose of applying free convection boundary conditions along the length of the rod. The Bulk Data entry CONV defines the convection character and the ambient grid points. To take advantage of empirical relationships for this type of flow field, a hand calculation is necessary to acquire the appropriate free convection heat transfer coefficient form. To facilitate this process, we will assume a fluid film temperature of 800 degrees and use the fluid properties for air at that temperature in our calculations. In “Example 1c - Temperature Dependent Heat Transfer Coefficient” on page 95 we will account for the variation of film temperature and corresponding fluid properties along the length of the rod. h AVG = 1.83 W ⁄ m 2

o

K

o

T ∞ = 300 K

o

T 1 = 1300 K 1

2

3

4

5

6

q CONV = h AVG ⋅ ( T – T ∞ ) .25 ⋅ ( T – T ∞ ) Figure 5-3 Example 1b

Calculating Heat Transfer Coefficients First we must calculate the input coefficients and convert to MSC.Nastran format. The symbols used in the description of the analysis are defined herein. C p Specific heat ν

Kinematic viscosity

k

Thermal conductivity

Pr Prandtl number Gr Grashof number Nu Nusselt number T w Wall temperature T ∞ Ambient temperature d Main Index

Diameter

CHAPTER 5 Examples

β

Volume coefficient of expansion (For an ideal gas β = ( 1 ⁄ T ) where T is the absolute temperature of the gas)

g

Acceleration due to gravity

Assume air properties at 800°K. Cp

=

ν

= .823 × 10 – 4 m 2 ⁄ s

k

=

Pr

= .689

Gr

=

=

o

1.098 KJ ⁄ Kg K

o

.058 W ⁄ m K gβd 3 ( T w – T ∞ ) -----------------------------------------ν2 o m 1 9.80 ----- ⋅ ------------------ ⋅ ( .10 ) 3 m 3 ⋅ 1000 K s 2 800 oK ------------------------------------------------------------------------------------------------------–4 m 4 ( .823 × 10 ) -------s2

= 1.8 × 10 6 Gr ⋅ Pr = 1.25 × 10 6 for 10 4 ≤ Gr ⋅ Pr ≤ 10 9

and for horizontal cylinders,

COEF = .53 (see J. P. Holman, Heat Transfer) m = .25 so m hd gβd 3 Nu = ------ = COEF  ------------- ⋅ Pr ⋅ ( T – T ∞ ) k ν2

or .25 .53 ( .058 )  9.80 ( 1 ⁄ 800 ) ( .10 ) 3 ( .689 )  h = -------------------------  -------------------------------------------------------------------  ( T – T ∞ ) .25 2 .10   ( .823 × 10 – 4 )

Note: The equation for h is nonlinear.

Main Index

89

90

therefore h ≅ 1.83 ( T – T ∞ ) .25 W ⁄ m 2

o

K

This form may be input on the PCONV and MAT4 Bulk Data entries. The MSC.Nastran input file is shown in Listing 5-3. Listing 5-3 Example 1b Input Files ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 1b ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 BEGIN BULK NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.1,0.0,0.0 GRID,3,,0.2,0.0,0.0 GRID,4,,0.3,0.0,0.0 GRID,5,,0.4,0.0,0.0 GRID,6,,0.5,0.0,0.0 GRID,99,,99.0,99.0,99.0 $ CROD,1,5,1,2 CROD,2,5,2,3 CROD,3,5,3,4 CROD,4,5,4,5 CROD,5,5,5,6 PROD,5,15,.0078540 MAT4,15,204.0,,,1.83 $ CHBDYP,10,25,LINE,,,1,2,,+CHP10 +CHP10,,,,,0.0,1.0,0.0 CHBDYP,20,25,LINE,,,2,3,,+CHP20 +CHP20,,,,,0.0,1.0,0.0 CHBDYP,30,25,LINE,,,3,4,,+CHP30

Main Index

CHAPTER 5 Examples

Listing 5-3 Example 1b Input Files (continued) +CHP30,,,,,0.0,1.0,0.0 CHBDYP,40,25,LINE,,,4,5,,+CHP40 +CHP40,,,,,0.0,1.0,0.0 CHBDYP,50,25,LINE,,,5,6,,+CHP50 +CHP50,,,,,0.0,1.0,0.0 PHBDY,25,.3141593 $ CONV,10,35,,,99,99 CONV,20,35,,,99,99 CONV,30,35,,,99,99 CONV,40,35,,,99,99 CONV,50,35,,,99,99 PCONV,35,15,0,0.25 $ SPC,10,1,,1300.0 SPC,10,99,,300.0 TEMPD,20,1300.0 $ ENDDATA

Note: COEF is given on the MAT4 entry. Exponent is given on the PCONV entry.

Main Index

91

92

Listing 5-4 ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 1b ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 BEGIN BULK NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.1,0.0,0.0 GRID,3,,0.2,0.0,0.0 GRID,4,,0.3,0.0,0.0 GRID,5,,0.4,0.0,0.0 GRID,6,,0.5,0.0,0.0 GRID,99,,99.0,99.0,99.0 $ CROD,1,5,1,2 CROD,2,5,2,3 CROD,3,5,3,4 CROD,4,5,4,5 CROD,5,5,5,6 PROD,5,15,.0078540 MAT4,15,204.0,,,1.83 $ CHBDYP,10,25,LINE,,,1,2,,+CHP10 +CHP10,,,,,0.0,1.0,0.0 CHBDYP,20,25,LINE,,,2,3,,+CHP20 +CHP20,,,,,0.0,1.0,0.0 CHBDYP,30,25,LINE,,,3,4,,+CHP30 +CHP30,,,,,0.0,1.0,0.0 CHBDYP,40,25,LINE,,,4,5,,+CHP40 +CHP40,,,,,0.0,1.0,0.0

Results The abbreviated EX1B.f06 output file is shown in Listing 5-5. Because this analysis is nonlinear, note the existence of numerical iteration until satifsfactory values of EPSP and EPSW (NLPARM entry defaults) have been attained. A plot of temperature versus distance is shown in Figure 5-4.

Main Index

CHAPTER 5 Examples

Listing 5-5 Example 1b Results File N O N - L I N E A R I T E R A T I O N M O D U L E O U T P U T STIFFNESS UPDATE TIME .49 SECONDS SUBCASE 1 ITERATION TIME .01 SECONDS LOAD FACTOR 1.000 - - - CONVERGENCE FACTORS - - - - - LINE SEARCH DATA - - ITERATION EUI EPI EWI LAMBDA DLMAG FACTOR E-FIRST E-FINAL NQNV NLS ENIC NDV MDV 1 1.0228E-13 9.7786E-02 9.9926E-17 1.0000E-01 2.9097E+02 1.0000E+00 0.0000E+00 0.0000E+00 0 0 0 1 2 1.6730E+01 1.9848E-02 3.6841E-03 1.5149E-01 6.5130E+01 1.0000E+00 -2.4629E-01 -2.4629E-01 0 0 0 1 3 2.7737E-02 1.3951E-04 3.4216E-06 7.9258E-02 4.3181E-01 1.0000E+00 4.7254E-03 4.7254E-03 1 0 0 0 1 4 2.9687E-05 3.3073E-06 4.8656E-10 5.1482E-02 1.0361E-02 1.0000E+00 -6.0088E-03 -6.0088E-03 2 0 -1 0 1 *** USER INFORMATION MESSAGE 6186, *** SOLUTION HAS CONVERGED *** SUBID 1 LOADINC 1 LOOPID 1 LOAD STEP 1.000 LOAD FACTOR 1.00000 ^^^ DMAP INFORMATION MESSAGE 9005 (NLSCSH) THE SOLUTION FOR LOOPID= 1 IS SAVED FOR RESTART EXAMPLE 1B NOVEMBER 2, 1993 MSC/NASTRAN 11/ 1/93 PAGE 10

EXAMPLE 1B

NOVEMBER

LOAD STEP =

POINT ID. 1 99 EXAMPLE 1B

TYPE S S

LOAD STEP =

1.00000E+00

ID VALUE 1.300000E+03 3.000000E+02

ID+1 VALUE 1.225588E+03

ID+2 VALUE 1.169515E+03

L O A D POINT ID. 99 EXAMPLE 1B

TYPE S

PAGE

11

PAGE

12

PAGE

13

11/ 1/93

PAGE

14

RADIATION TOTAL 0.000000E+00 -3.083314E+02 0.000000E+00 -2.824394E+02 0.000000E+00 -2.638446E+02 0.000000E+00 -2.518305E+02 0.000000E+00 -2.459362E+02 2, 1993 MSC/NASTRAN 11/ 1/93

PAGE

15

ID+3 VALUE 1.130402E+03

ID .0

LOAD STEP =

1.00000E+00

VALUE

ID+1 VALUE

F O R C E S POINT ID. 1 99 EXAMPLE 1B

TYPE S S

LOAD STEP =

1.00000E+00

O F

ID VALUE 1.352363E+03 -1.352382E+03

ID+2 VALUE

ID+3 VALUE

ELEMENT-ID 10 20 30 40 50

F L O W

ID+2 VALUE .0

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

I N T O

FREE-CONVECTION -3.083314E+02 -2.824394E+02 -2.638446E+02 -2.518305E+02 -2.459362E+02

EXAMPLE 1B

1.00000E+00 F I N I T E EL-TYPE ROD ROD ROD ROD ROD

E L E M E N T X-GRADIENT -7.441187E+02 -5.607344E+02 -3.911244E+02 -2.309877E+02 -7.638958E+01

H B D Y

2, 1993

11/ 1/93

ID+5 VALUE

MSC/NASTRAN

11/ 1/93

C O N S T R A I N T

ID+3 VALUE .0

ID+4 VALUE .0 2, 1993

E L E M E N T S

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 NOVEMBER

T E M P E R A T U R E Y-GRADIENT

MSC/NASTRAN

ID+4 VALUE

NOVEMBER

H E A T

ID+5 VALUE 1.099665E+03

V E C T O R

S I N G L E - P O I N T

ID+1 VALUE .0

ID+4 VALUE 1.107303E+03 2, 1993

NOVEMBER

ELEMENT-ID 1 2 3 4 5

11/ 1/93

V E C T O R

NOVEMBER

LOAD STEP =

MSC/NASTRAN

1.00000E+00 T E M P E R A T U R E

Main Index

2, 1993

MSC/NASTRAN

(CHBDY)

G R A D I E N T S

Z-GRADIENT

ID+5 VALUE .0

A N D

X-FLUX 1.518002E+05 1.143898E+05 7.978937E+04 4.712150E+04 1.558347E+04

F L U X E S Y-FLUX

Z-FLUX

93

94

Temperature (°K) 1400

1300

(0.0, 1300.) (0.1, 1226.)

1200

(0.2, 1170.) (0.3, 1130.)

(0.4, 1107.)

1100 (0.5, 1100.) 1000

900

800 0

0.1

0.2

0.3

0.4

Distance (meters)

Figure 5-4 Temperature versus Distance - Example 1b

Main Index

0.5

CHAPTER 5 Examples

5.4

Example 1c - Temperature Dependent Heat Transfer Coefficient Demonstrated Principles • Temperature dependent free convection heat transfer coefficient • Film node

Discussion This problem introduces the generalized method for representation of temperature dependent properties (MATT4,TABLEMi). In this case we wish to account for the fluid film temperature variation along the length of our rod and consider its effect on the local heat transfer coefficient. By default, the look-up temperature of the film node is the average temperature of the CHBDY surface and the ambient points. This temperature varies along the length of the rod. 2.5

(400., 2.27) (600., 2.03)

h( T)

2.0

W   ----------------- 2 o - K m

1.5

(800., 1.83)

1.0

400

600

800

o

T ( K)

h( T) o

T ∞ = 300 K

o

T 1 = 1300 K 1

2

3

4

5

6

q CONV = h ( T ) ⋅ ( T – T ∞ ) .25 ⋅ ( T – T ∞ ) Figure 5-5 Example 1c

Main Index

95

96

The MSC.Nastran input file is shown in Listing 5-6. Listing 5-6 Example 1c Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 1c ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 BEGIN BULK NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.1,0.0,0.0 GRID,3,,0.2,0.0,0.0 GRID,4,,0.3,0.0,0.0 GRID,5,,0.4,0.0,0.0 GRID,6,,0.5,0.0,0.0 GRID,99,,99.0,99.0,99.0 $ CROD,1,5,1,2 CROD,2,5,2,3 CROD,3,5,3,4 CROD,4,5,4,5 CROD,5,5,5,6 PROD,5,15,.0078540 MAT4,15,204.0,,,1.0 MATT4,15,,,,40 TABLEM2,40,0.0,,,,,,,+TBM +TBM,400.0,2.27,600.0,2.03,800.0,1.83,ENDT $ CHBDYP,10,25,LINE,,,1,2,,+CHP10 +CHP10,,,,,0.0,1.0,0.0 CHBDYP,20,25,LINE,,,2,3,,+CHP20 +CHP20,,,,,0.0,1.0,0.0 CHBDYP,30,25,LINE,,,3,4,,+CHP30 +CHP30,,,,,0.0,1.0,0.0 CHBDYP,40,25,LINE,,,4,5,,+CHP40 +CHP40,,,,,0.0,1.0,0.0 CHBDYP,50,25,LINE,,,5,6,,+CHP50 +CHP50,,,,,0.0,1.0,0.0 PHBDY,25,.3141593

Main Index

CHAPTER 5 Examples

Listing 5-6 Example 1c Input File (continued) CONV,10,35,,,99,99 CONV,20,35,,,99,99 CONV,30,35,,,99,99 CONV,40,35,,,99,99 CONV,50,35,,,99,99 PCONV,35,15,0,0.25 $ SPC,10,1,,1300.0 SPC,10,99,,300.0 TEMPD,20,1300.0 $ ENDDATA

Note: MAT4/MATT4/TABLEM2 supply the temperature dependence of the heat transfer coefficient.

Results The abbreviated EX1C.f06 output file is shown in Listing 5-7. A plot of temperature versus distance is shown in Figure 5-6.

Main Index

97

98

Listing 5-7 Example 1c Results File EXAMPLE 1C

NOVEMBER

LOAD STEP =

MSC/NASTRAN

11/ 1/93

PAGE

11

PAGE

12

PAGE

13

11/ 1/93

PAGE

14

RADIATION TOTAL 0.000000E+00 -3.110855E+02 0.000000E+00 -2.892279E+02 0.000000E+00 -2.729202E+02 0.000000E+00 -2.621092E+02 0.000000E+00 -2.567259E+02 2, 1993 MSC/NASTRAN 11/ 1/93

PAGE

15

1.00000E+00 T E M P E R A T U R E

POINT ID. 1 99 EXAMPLE 1C

TYPE S S

LOAD STEP =

1.00000E+00

ID VALUE 1.300000E+03 3.000000E+02

ID+1 VALUE 1.223213E+03

V E C T O R

ID+2 VALUE 1.165064E+03

ID+3 VALUE 1.124369E+03 NOVEMBER

L O A D POINT ID. 99 EXAMPLE 1C

TYPE S

LOAD STEP =

1.00000E+00

ID .0

VALUE

ID+1 VALUE

POINT ID. 1 99 EXAMPLE 1C

TYPE S S

LOAD STEP =

1.00000E+00

O F

ID VALUE 1.392052E+03 -1.392069E+03

ID+2 VALUE

ID+3 VALUE

ELEMENT-ID 10 20 30 40 50

F L O W

ID+2 VALUE .0

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

I N T O

FREE-CONVECTION -3.110855E+02 -2.892279E+02 -2.729202E+02 -2.621092E+02 -2.567259E+02

EXAMPLE 1C

LOAD STEP =

1.00000E+00 F I N I T E

ELEMENT-ID 1 2 3 4 5

EL-TYPE ROD ROD ROD ROD ROD

E L E M E N T X-GRADIENT -7.678735E+02 -5.814849E+02 -4.069491E+02 -2.408249E+02 -7.971770E+01

H B D Y

2, 1993

11/ 1/93

ID+5 VALUE

MSC/NASTRAN

11/ 1/93

C O N S T R A I N T

ID+3 VALUE .0

ID+4 VALUE .0 2, 1993

E L E M E N T S

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 NOVEMBER

T E M P E R A T U R E Y-GRADIENT

MSC/NASTRAN

ID+4 VALUE

NOVEMBER

H E A T

ID+5 VALUE 1.092315E+03

V E C T O R

S I N G L E - P O I N T

ID+1 VALUE .0

ID+4 VALUE 1.100287E+03 2, 1993

NOVEMBER

F O R C E S

Main Index

2, 1993

MSC/NASTRAN

(CHBDY)

G R A D I E N T S

Z-GRADIENT

ID+5 VALUE .0

A N D

X-FLUX 1.566462E+05 1.186229E+05 8.301761E+04 4.912827E+04 1.626241E+04

F L U X E S Y-FLUX

Z-FLUX

CHAPTER 5 Examples

Temperature (°K) 1400

1300

(0.0, 1300.) (0.1, 1223.)

1200

(0.2, 1165.) (0.3, 1124.)

(0.4, 1100.)

1100 (0.5, 1092.) 1000

900

800 0

0.1

0.2

0.3

0.4

Distance (meters) Figure 5-6 Temperature versus Distance - Example 1c

Main Index

0.5

99

100

5.5

Example 1d - Film Nodes for Free Convection Demonstrated Principles • Film nodes • MPCs

Discussion In the spirit of the previous example, we allow the free convection heat transfer coefficient to be temperature dependent; however, we extend the notion of the film node to provide a film temperature look-up value more heavily weighted toward the local surface temperatures than the ambient temperature. The MPC (multipoint constraint) relationship is available for this purpose. In this example, the film node temperatures become the average of the two CHBDY surface grid points each with a weight of 1.0, and the ambient temperature is also given a weighting of 1.0. Note that the default film node has a temperature which is the average of the average of the surface temperature and ambient point temperatures. For example, consider the first CHBDY element: Default calculation (see Listing 5-6): T∞ + T∞  T1 + T2 1 2 T FilmNode =  -------------------- + --------------------------- ⁄ 2 2 2   T 1 + T 2 + 2T ∞ = -------------------------------------4 MPC calculation: T1 + T2 + T∞ T Film Node = ----------------------------------3 The MSC.Nastran input file is shown in Listing 5-8.

Main Index

CHAPTER 5 Examples

Listing 5-8 Example 1d Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 1d ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 MPC = 30 NLPARM = 100 BEGIN BULK NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.1,0.0,0.0 GRID,3,,0.2,0.0,0.0 GRID,4,,0.3,0.0,0.0 GRID,5,,0.4,0.0,0.0 GRID,6,,0.5,0.0,0.0 GRID,91,,91.0,91.0,91.0 GRID,92,,92.0,92.0,92.0 GRID,93,,93.0,93.0,93.0 GRID,94,,94.0,94.0,94.0 GRID,95,,95.0,95.0,95.0 GRID,99,,99.0,99.0,99.0 $ CROD,1,5,1,2 CROD,2,5,2,3 CROD,3,5,3,4 CROD,4,5,4,5 CROD,5,5,5,6 PROD,5,15,.0078540 MAT4,15,204.0,,,1.0 MATT4,15,,,,40 TABLEM2,40,0.0,,,,,,,+TBM +TBM,400.0,2.27,600.0,2.03,800.0,1.83,ENDT $ CHBDYP,10,25,LINE,,,1,2,,+CHP10 +CHP10,,,,,0.0,1.0,0.0 CHBDYP,20,25,LINE,,,2,3,,+CHP20 +CHP20,,,,,0.0,1.0,0.0 CHBDYP,30,25,LINE,,,3,4,,+CHP30 +CHP30,,,,,0.0,1.0,0.0 CHBDYP,40,25,LINE,,,4,5,,+CHP40 +CHP40,,,,,0.0,1.0,0.0 CHBDYP,50,25,LINE,,,5,6,,+CHP50 +CHP50,,,,,0.0,1.0,0.0 PHBDY,25,.3141593 $ CONV,10,35,91,,99,99 CONV,20,35,92,,99,99 CONV,30,35,93,,99,99 CONV,40,35,94,,99,99 CONV,50,35,95,,99,99 PCONV,35,15,0,0.25 $

Main Index

101

102

Listing 5-8 Example 1d Input File MPC,30,91,,3.0,1,,-1.0,,+MPC91 +MPC91,,2,,-1.0,99,,-1.0 MPC,30,92,,3.0,2,,-1.0,,+MPC92 +MPC92,,3,,-1.0,99,,-1.0 MPC,30,93,,3.0,3,,-1.0,,+MPC93 +MPC93,,4,,-1.0,99,,-1.0 MPC,30,94,,3.0,4,,-1.0,,+MPC94 +MPC94,,5,,-1.0,99,,-1.0 MPC,30,95,,3.0,5,,-1.0,,+MPC95 +MPC95,,6,,-1.0,99,,-1.0 $ SPC,10,1,,1300.0 SPC,10,99,,300.0 TEMPD,20,1299.9 $ ENDDATA

Note: MPC must be requested in Case Control. GRID points 91-95 represent the film nodes.

Results The abbreviated EX1D.f06 output file is shown in Listing 5-9. A plot of temperature versus distance is shown in Figure 5-7.

Main Index

CHAPTER 5 Examples

Listing 5-9 Example 1d Results File EXAMPLE 1D

NOVEMBER

LOAD STEP =

POINT ID. 1 91 99 EXAMPLE 1D

TYPE S S S

LOAD STEP =

1.00000E+00

ID VALUE 1.300000E+03 9.427355E+02 3.000000E+02

ID+1 VALUE 1.228207E+03 9.005992E+02

ID+2 VALUE 1.173591E+03 8.696109E+02

L O A D POINT ID. 91 99 EXAMPLE 1D

TYPE S S

LOAD STEP =

1.00000E+00

ID .0 .0

VALUE

ID+1 VALUE .0

F O R C E S TYPE S S S

PAGE

16

PAGE

17

O F

ID VALUE 1.297968E+03 .0 -1.297969E+03

ID+2 VALUE .0

11/ 1/93

PAGE

18

RADIATION TOTAL 0.000000E+00 -2.847656E+02 0.000000E+00 -2.681580E+02 0.000000E+00 -2.554733E+02 0.000000E+00 -2.469317E+02 0.000000E+00 -2.426400E+02 2, 1993 MSC/NASTRAN 11/ 1/93

PAGE

19

ID+3 VALUE .0

S I N G L E - P O I N T

ID+1 VALUE .0 .0

ID+4 VALUE 1.112498E+03 8.391531E+02 2, 1993

ID+5 VALUE 1.104961E+03

MSC/NASTRAN

ID+4 VALUE .0

ID+2 VALUE .0 .0

2, 1993

11/ 1/93

ID+5 VALUE

MSC/NASTRAN

11/ 1/93

C O N S T R A I N T

ID+3 VALUE .0 .0

ID+4 VALUE .0 .0

NOVEMBER

2, 1993

ID+5 VALUE .0

MSC/NASTRAN

1.00000E+00 H E A T

ELEMENT-ID 10 20 30 40 50

F L O W

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

I N T O

FREE-CONVECTION -2.847656E+02 -2.681580E+02 -2.554733E+02 -2.469317E+02 -2.426400E+02

EXAMPLE 1D

ELEMENT-ID 1 2 3 4 5

15

V E C T O R

EXAMPLE 1D

LOAD STEP =

PAGE

ID+3 VALUE 1.135242E+03 8.492465E+02

NOVEMBER

LOAD STEP =

11/ 1/93

V E C T O R

NOVEMBER

POINT ID. 1 91 99

MSC/NASTRAN

1.00000E+00 T E M P E R A T U R E

Main Index

2, 1993

1.00000E+00 F I N I T E EL-TYPE ROD ROD ROD ROD ROD

E L E M E N T X-GRADIENT -7.179333E+02 -5.461558E+02 -3.834945E+02 -2.274367E+02 -7.536760E+01

H B D Y

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 NOVEMBER

T E M P E R A T U R E Y-GRADIENT

E L E M E N T S

G R A D I E N T S

(CHBDY)

Z-GRADIENT

A N D

X-FLUX 1.464584E+05 1.114158E+05 7.823288E+04 4.639708E+04 1.537499E+04

F L U X E S Y-FLUX

Z-FLUX

103

104

Temperature (°K) 1400

(0.0, 1300.)

1300

(0.1, 1228.) 1200

(0.2, 1174.) (0.3, 1135.)

(0.4, 1112.)

1100

(0.5, 1105.)

1000

900

800 0

0.1

0.2

0.3

0.4

Distance (meters) Figure 5-7 Temperature versus Distance

Main Index

0.5

CHAPTER 5 Examples

5.6

Example 1e - Radiation Boundary Condition Demonstrated Principles • Radiation Boundary Condition • Temperature Dependent Emissivity • Temperature Dependent Conductivity

Discussion Radiation heat transfer is added along the length of the rod from our previous examples. For this case we treat the problem as one in which radiant exchange occurs between the rod and an ambient environment at 300 °K. This can be modeled simply with a radiation boundary condition specification. Surface emissivity variation with temperature is also accounted for. Radiation exchange from the end of the rod has been included to illustrate the POINT type CHBDY element.

Main Index

105

106

o

T ∞ = 1300 K Radiation Boundary Condition

o

Radiation Boundary Condition

T 1 = 1300 K 1

2

3

4

5

6

0.8 (450., .75) 0.7 (700., .65) (800., .6)

0.6 ε(T)

(1100., .5)

0.5

0.4

(1500., .39)

(1900., .32)

0.3 250

500

750

1000

1250

1500

1750

2000

T (°K)

Figure 5-8 Example 1e - Emissivity as a Function of Temperature The MSC.Nastran input file is shown in Listing 5-10.

Main Index

CHAPTER 5 Examples

Listing 5-10 Example 1e Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 1e ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 BEGIN BULK NLPARM,100 PARAM,SIGMA,5.67E-8 PARAM,TABS,0.0 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.1,0.0,0.0 GRID,3,,0.2,0.0,0.0 GRID,4,,0.3,0.0,0.0 GRID,5,,0.4,0.0,0.0 GRID,6,,0.5,0.0,0.0 GRID,99,,99.0,99.0,99.0 $ CROD,1,5,1,2 CROD,2,5,2,3 CROD,3,5,3,4 CROD,4,5,4,5 CROD,5,5,5,6 PROD,5,15,.0078540 MAT4,15,1.0 MATT4,15,40 TABLEM2,40,0.0,,,,,,,+TBM1 +TBM1,173.16,215.0,273.16,202.0,373.16,206.0,473.16,215.0,+TBM2 +TBM2,573.16,228.0,673.16,249.0,ENDT $

Main Index

107

108

Listing 5-10 Example 1e Input File (continued) CHBDYP,10,25,LINE,,,1,2,,+CHP10 +CHP10,45,,,,0.0,1.0,0.0 CHBDYP,20,25,LINE,,,2,3,,+CHP20 +CHP20,45,,,,0.0,1.0,0.0 CHBDYP,30,25,LINE,,,3,4,,+CHP30 +CHP30,45,,,,0.0,1.0,0.0 CHBDYP,40,25,LINE,,,4,5,,+CHP40 +CHP40,45,,,,0.0,1.0,0.0 CHBDYP,50,25,LINE,,,5,6,,+CHP50 +CHP50,45,,,,0.0,1.0,0.0 CHBDYP,60,26,POINT,,,6,,,+CHP60 +CHP60,45,,,,1.0,0.0,0.0 PHBDY,25,.3141593 PHBDY,26,.0078540 $ RADBC,99,1.0,,10,THRU,60,BY,10 RADM,45,1.0,1.0 RADMT,45,41,41 TABLEM2,41,0.0,,,,,,,+TBM3 +TBM3,450.0,0.75,700.0,0.65,800.0,0.60,1100.0,0.50,+TBM4 +TBM4,1500.0,0.39,1900.0,0.32,ENDT $ SPC,10,1,,1300.0 SPC,10,99,,300.0 TEMPD,20,1300.0 $ ENDDATA

Note: Parameters SIGMA and TABS are required for any radiation problem. POINT type CHBDYP for radiation to space from the end of the rod.

Results The abbreviated EX1E.f06 output file is shown in Listing 5-11. A plot of temperature versus distance is shown in Figure 5-9.

Main Index

CHAPTER 5 Examples

Listing 5-11 Example 1e Results File EXAMPLE 1E

SEPTEMBER

LOAD STEP =

24, 1993

MSC/NASTRAN

9/23/93

PAGE

11

PAGE

12

PAGE

13

9/23/93

PAGE

14

RADIATION TOTAL -1.838179E+03 -1.838179E+03 -1.234006E+03 -1.234006E+03 -9.011517E+02 -9.011517E+02 -7.164666E+02 -7.164666E+02 -6.278596E+02 -6.278596E+02 -1.507721E+02 -1.507721E+02 24, 1993 MSC/NASTRAN 9/23/93

PAGE

15

1.00000E+00 T E M P E R A T U R E

POINT ID. 1 99 EXAMPLE 1E

TYPE S S

ID VALUE 1.300000E+03 3.000000E+02

LOAD STEP =

1.00000E+00

ID+1 VALUE 1.140835E+03

V E C T O R

ID+2 VALUE 1.026327E+03

ID+3 VALUE 9.476805E+02 SEPTEMBER

L O A D POINT ID. 99 EXAMPLE 1E

TYPE S

ID .0

LOAD STEP =

1.00000E+00

VALUE

ID+1 VALUE

24, 1993

POINT ID. 1 99 EXAMPLE 1E

TYPE S S

LOAD STEP =

1.00000E+00

O F

ID VALUE 5.468448E+03 .0

ID+2 VALUE

ID+3 VALUE

S I N G L E - P O I N T

ID+1 VALUE .0

ELEMENT-ID 10 20 30 40 50 60

F L O W

ID+2 VALUE .0

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

I N T O

FREE-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

EXAMPLE 1E

MSC/NASTRAN

ID+4 VALUE 24, 1993

9/23/93

H B D Y

ID+5 VALUE

MSC/NASTRAN

9/23/93

C O N S T R A I N T

ID+3 VALUE .0

ID+4 VALUE .0

SEPTEMBER

H E A T

ID+5 VALUE 8.795513E+02

V E C T O R

SEPTEMBER

F O R C E S

ID+4 VALUE 8.996806E+02

24, 1993

E L E M E N T S

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 SEPTEMBER

ID+5 VALUE .0

MSC/NASTRAN

(CHBDY)

NONLINEAR LOAD STEP =

1.00000E+00 F I N I T E

ELEMENT-ID 1 2 3 4 5

EL-TYPE ROD ROD ROD ROD ROD

Main Index

E L E M E N T X-GRADIENT -1.591654E+03 -1.145073E+03 -7.864676E+02 -4.799988E+02 -2.012931E+02

T E M P E R A T U R E Y-GRADIENT

G R A D I E N T S

Z-GRADIENT

A N D

X-FLUX 5.792411E+05 3.838152E+05 2.476643E+05 1.447721E+05 5.927191E+04

F L U X E S Y-FLUX

Z-FLUX

109

110

Temperature (°K) 1400

(0.0, 1300.)

1300

1200 (0.1, 1141.) 1100 (0.2, 1026.) 1000 (0.3, 948.) (0.4, 900.) 900 (0.5, 880.) 800 0

0.1

0.2

0.3

0.4

Distance (meters)

Figure 5-9 Temperature versus Distance

Main Index

0.5

CHAPTER

5.7

Example 2a - Nonlinear Internal Heating and Free Convection Demonstrated Principles • Heat Transfer “Loads” and their Descriptions • Temperature-Dependent Loads • AREA Type CHBDYs • Film Node • Free Convection Exponent

Discussion Examples 2a, 2b, and 2c describe MSC.Nastran heat transfer “loads”. While we tend to think of boundary conditions in regard to heat transfer, there are several surface conditions which we define as loads. In an MSC.Nastran sense, a load has the flexibility of being subcase selectable. This concept, an early carryover from structural analysis, allows the load vector to vary while the stiffness matrix and its decomposition remain unchanged. This provided an economical method for evaluating the effects of multiple loading states and superposition of loads. The load set/subcase capability is less significant for heat transfer since many boundary conditions have contributions to the coefficient matrix and are fundamentally nonlinear, eliminating any potential for superposition of loads. In this series of examples, a single CHEXA element is used to demonstrate the application of internal heat generation, free convection, control nodes, film nodes, and various nonlinear effects. The temperature dependence of the heat transfer coefficient and the heat generation rate illustrated are used. Example 2a - Nonlinear Internal Heating and Free Convection demonstrates the selection of the internal heat generation load QVOL. A control node, which is a member of the element grid point set, has been chosen to multiply the heat generation term as well as be the film node. We refer to this as local control. The free convection exponent, EXPF, is set to 0.0 (FORM = 0). The analytic expression for this example is given in Eq. 5-1. The basic energy balance can be expressed as:

Main Index

111

112

Y T ∞ = 0.0

Control Node and Film Node

QVOL = 1000.0

5

8

6

7 4

1

X

2 3 Z Temperature Dependent Tabular Inputs · Q(T )

h(T) 1000.

+

1000.

h=T

0 1000. Free Convection Heat Transfer Coefficient

· Q = 1000. – T

0

T

1000.

T

Internal Volumetric Heat Generation Rate

Figure 5-10 Example 2a

Analytic Solution of Example 2a L ⋅ U CN ⋅ HGEN ⋅ VOLUME = h ⋅ AREA ⋅ ( T – T ∞ ) ( 1000. ⋅ T ⋅ ( 1000. – T ) ⋅ 1.0 = T ⋅ 6.0 ⋅ T lting in, The MSC.Nastran input file is shown in Listing 5-12.

Main Index

EXPF

⋅ ( T – T∞ )

( EXPF = 0.0 ) ) o

T = 994.036 C

Eq. 5-1

CHAPTER

Listing 5-12 Example 2a Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 2a ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 LOAD = 200 BEGIN BULK NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0 GRID,4,,1.0,0.0,0.0 GRID,5,,0.0,1.0,0.0 GRID,6,,0.0,1.0,1.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,1.0,0.0 GRID,99,,99.0,99.0,99.0 $ CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,204.0,,,1.0,,1.0 MATT4,15,,,,40,,41 TABLEM2,40,0.0,,,,,,,+TBM40 +TBM40,0.0,0.0,1000.0,1000.0,ENDT TABLEM2,41,0.0,,,,,,,+TBM41 +TBM41,0.0,1000.0,1000.0,0.0,ENDT $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6 $

Main Index

113

114

Listing 5-12 Example 2a Input File (continued) $ CONV,10,35,1,,99 CONV,20,35,1,,99 CONV,30,35,1,,99 CONV,40,35,1,,99 CONV,50,35,1,,99 CONV,60,35,1,,99 PCONV,35,15,0,0.0 $ QVOL,200,1000.0,1,1 $ SPC,10,99,,0.0 TEMP,20,99,0.0 TEMPD,20,100.0 $ ENDDATA

Note: The load, in this case QVOL, must be requested in Case Control. The temperature dependence on internal heat generation is requested through HGEN on the MAT4/MATT4 entries.

Results The abbreviated EX2A.f06 output file is shown in Listing 5-13.

Main Index

CHAPTER

Listing 5-13 Example 2a Results File LOAD STEP =

1.00000E+00 T E M P E R A T U R E

POINT ID. 1 7 99 EXAMPLE 2A

TYPE S S S

ID VALUE 9.940355E+02 9.940355E+02 .0

LOAD STEP =

1.00000E+00

ID+1 VALUE 9.940355E+02 9.940355E+02

ID+2 VALUE 9.940355E+02

ID+3 VALUE 9.940355E+02

SEPTEMBER

L O A D POINT ID. 7 99 EXAMPLE 2A

TYPE S S

LOAD STEP =

1.00000E+00

ID .0 .0

VALUE

ID+1 VALUE .0

POINT ID. 7 99 EXAMPLE 2A

TYPE S S

LOAD STEP =

1.00000E+00

O F

ID VALUE .0 -5.928640E+06

ID+2 VALUE

ELEMENT-ID 10 20 30 40 50 60

F L O W

ID+2 VALUE

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

I N T O

FREE-CONVECTION -9.881066E+05 -9.881066E+05 -9.881066E+05 -9.881066E+05 -9.881066E+05 -9.881066E+05

EXAMPLE 2A

LOAD STEP =

1.00000E+00 F I N I T E

ELEMENT-ID 1

EL-TYPE HEXA

E L E M E N T X-GRADIENT -1.136868E-13

H B D Y

MSC/NASTRAN

12

PAGE

13

9/23/93

PAGE

14

RADIATION TOTAL 0.000000E+00 -9.881066E+05 0.000000E+00 -9.881066E+05 0.000000E+00 -9.881066E+05 0.000000E+00 -9.881066E+05 0.000000E+00 -9.881066E+05 0.000000E+00 -9.881066E+05 24, 1993 MSC/NASTRAN 9/23/93

PAGE

15

ID+4 VALUE

24, 1993

9/23/93

ID+5 VALUE

MSC/NASTRAN

9/23/93

C O N S T R A I N T

ID+3 VALUE

ID+4 VALUE

24, 1993

E L E M E N T S

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 SEPTEMBER

T E M P E R A T U R E Y-GRADIENT 1.136868E-13

PAGE

ID+3 VALUE

SEPTEMBER

H E A T

ID+5 VALUE 9.940355E+02

V E C T O R

S I N G L E - P O I N T

ID+1 VALUE .0

ID+4 VALUE 9.940355E+02

24, 1993

SEPTEMBER

F O R C E S

Main Index

V E C T O R

MSC/NASTRAN

(CHBDY)

G R A D I E N T S

Z-GRADIENT 5.684342E-14

ID+5 VALUE

A N D

X-FLUX 2.319211E-11

F L U X E S Y-FLUX -2.319211E-11

Z-FLUX -1.159606E-11

115

116

5.8

Example 2b - Nonlinear Internal Heating and Control Nodes Demonstrated Principles • Control Node Applied to Loads and Convection Boundaries • Free Convection Forms

Discussion of Variation 1 This problem extends Example 2a - Nonlinear Internal Heating and Free Convection in the implementation of local control for the internal heat generation control node and the film node for convection. However, the same control node is now used to multiply the convection heat transfer coefficient. The free convection exponent EXPF remains at 0.0 (FORM = 0). The basic energy balance can be expressed as: L ⋅ U CN ⋅ HGEN ⋅ VOLUME = h ⋅ AREA ⋅ ( T – T ∞ ) ⋅ ( T – T ∞ )

EXPF

⋅ U CN

( 1000 ⋅ T ⋅ ( 1000 – T ) ⋅ 1.0 = T ⋅ 6.0 ⋅ ( T – T ∞ ) ⋅ T o

lting in,

T = 333.33 C

The MSC.Nastran input file for Variation 1 is shown in Listing 5-14. Listing 5-14 Example 2b1 Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE2b1 ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 LOAD = 200 BEGIN BULK NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0

Main Index

Eq. 5-2

CHAPTER

Listing 5-14 Example 2b1 Input File (continued) GRID,4,,1.0,0.0,0.0 GRID,5,,0.0,1.0,0.0 GRID,6,,0.0,1.0,1.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,1.0,0.0 GRID,99,,99.0,99.0,99.0 $ CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,204.0,,,1.0,,1.0 MATT4,15,,,,40,,41 TABLEM2,40,0.0,,,,,,,+TBM40 +TBM40,0.0,0.0,1000.0,1000.0,ENDT TABLEM2,41,0.0,,,,,,,+TBM41 +TBM41,0.0,1000.0,1000.0,0.0,ENDT $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6 $ CONV,10,35,1,1,99 CONV,20,35,1,1,99 CONV,30,35,1,1,99 CONV,40,35,1,1,99 CONV,50,35,1,1,99 CONV,60,35,1,1,99 PCONV,35,15,0,0.0 $ QVOL,200,1000.0,1,1 $ SPC,10,99,,0.0 TEMP,20,99,0.0 TEMPD,20,100.0 $ ENDDATA

Results of Variation 1 The abbreviated EX2B1.f06 output file is shown in Listing 5-15.

Main Index

117

118

Listing 5-15 Example 2b1 Results File EXAMPLE 2B1

LOAD STEP =

SEPTEMBER

POINT ID. 1 7 99 EXAMPLE 2B1

TYPE S S S

LOAD STEP =

1.00000E+00

ID VALUE 3.333339E+02 3.333339E+02 .0

ID+1 VALUE 3.333339E+02 3.333339E+02

9/23/93

PAGE

11

PAGE

12

PAGE

13

9/23/93

PAGE

14

RADIATION TOTAL 0.000000E+00 -3.703721E+07 0.000000E+00 -3.703721E+07 0.000000E+00 -3.703721E+07 0.000000E+00 -3.703721E+07 0.000000E+00 -3.703721E+07 0.000000E+00 -3.703721E+07 24, 1993 MSC/NASTRAN 9/23/93

PAGE

15

V E C T O R

ID+2 VALUE 3.333339E+02

ID+3 VALUE 3.333339E+02

SEPTEMBER

L O A D POINT ID. 7 99 EXAMPLE 2B1

TYPE S S

LOAD STEP =

1.00000E+00

ID .0 .0

VALUE

ID+1 VALUE .0

POINT ID. 7 99 EXAMPLE 2B1

TYPE S S

LOAD STEP =

1.00000E+00

O F

ID VALUE .0 -2.222233E+08

ID+2 VALUE

ID+3 VALUE

ELEMENT-ID 10 20 30 40 50 60 EXAMPLE 2B1

1.00000E+00 F I N I T E EL-TYPE HEXA

F L O W

ID+2 VALUE

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

H B D Y

FREE-CONVECTION -3.703721E+07 -3.703721E+07 -3.703721E+07 -3.703721E+07 -3.703721E+07 -3.703721E+07

E L E M E N T X-GRADIENT 0.000000E+00

I N T O

MSC/NASTRAN

ID+4 VALUE

24, 1993

9/23/93

ID+3 VALUE

Y-GRADIENT 0.000000E+00

MSC/NASTRAN

ID+4 VALUE

24, 1993

E L E M E N T S

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 SEPTEMBER

T E M P E R A T U R E

ID+5 VALUE

9/23/93

C O N S T R A I N T

SEPTEMBER

H E A T

ID+5 VALUE 3.333339E+02

V E C T O R

S I N G L E - P O I N T

ID+1 VALUE .0

ID+4 VALUE 3.333339E+02

24, 1993

SEPTEMBER

F O R C E S

ELEMENT-ID 1

MSC/NASTRAN

1.00000E+00 T E M P E R A T U R E

LOAD STEP =

24, 1993

MSC/NASTRAN

(CHBDY)

G R A D I E N T S

Z-GRADIENT -2.842171E-14

ID+5 VALUE

A N D

X-FLUX 0.000000E+00

F L U X E S Y-FLUX 0.000000E+00

Z-FLUX 5.798029E-12

Discussion of Variation 2 A slight variation of Example 2a - Nonlinear Internal Heating and Free Convection is depicted in Eq. 5-3. The free convection relationship has been altered by introducing an EXPF value of 1.0 (FORM = 0). The basic energy balance can be written as: QVOL ⋅ U CN ⋅ HGEN ⋅ VOLUME = h ⋅ AREA ⋅ ( T – T ∞ ) or,

EXPF

⋅ ( T – T ∞ ) ⋅ U CN

( 1000 ⋅ T ⋅ ( 1000 – T ) ⋅ 1.0 = T ⋅ 6.0 ⋅ ( T – T ∞ ) ⋅ ( T – T ∞ ) ⋅ T )

Resulting in, The MSC.Nastran input file for Variation 2 is shown in Listing 5-16. Main Index

T = 54.02

Eq. 5-3

CHAPTER

Listing 5-16 Example 2b2 Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 2b2 ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 LOAD = 200 BEGIN BULK NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0 GRID,4,,1.0,0.0,0.0 GRID,5,,0.0,1.0,0.0 GRID,6,,0.0,1.0,1.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,1.0,0.0 GRID,99,,99.0,99.0,99.0 $ CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,204.0,,,1.0,,1.0 MATT4,15,,,,40,,41 TABLEM2,40,0.0,,,,,,,+TBM40 +TBM40,0.0,0.0,1000.0,1000.0,ENDT TABLEM2,41,0.0,,,,,,,+TBM41 +TBM41,0.0,1000.0,1000.0,0.0,ENDT $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6 $

Main Index

119

120

Listing 5-16 Example 2b2 Input File (continued) $ CONV,10,35,1,1,99 CONV,20,35,1,1,99 CONV,30,35,1,1,99 CONV,40,35,1,1,99 CONV,50,35,1,1,99 CONV,60,35,1,1,99 PCONV,35,15,0,1.0 $ QVOL,200,1000.0,1,1 $ SPC,10,99,,0.0 TEMP,20,99,0.0 TEMPD,20,100.0 $ ENDDATA

Results of Variation 2 The abbreviated EX2b2.f06 output file is shown in Listing 5-17.

Main Index

CHAPTER

Listing 5-17 Example 2b2 Results File EXAMPLE 2B2

LOAD STEP =

SEPTEMBER

POINT ID. 1 7 99 EXAMPLE 2B2

TYPE S S S

LOAD STEP =

1.00000E+00

ID VALUE 5.402279E+01 5.402279E+01 .0

ID+1 VALUE 5.402279E+01 5.402279E+01

ID+3 VALUE 5.402279E+01

SEPTEMBER

POINT ID. 7 99 EXAMPLE 2B2

TYPE S S

LOAD STEP =

1.00000E+00

ID .0 .0

VALUE

ID+1 VALUE .0

POINT ID. 7 99 EXAMPLE 2B2

TYPE S S

LOAD STEP =

1.00000E+00

O F

ID VALUE .0 -5.110450E+07

PAGE

11

PAGE

12

PAGE

13

PAGE

14

ID+2 VALUE

ID+3 VALUE

H E A T

F L O W

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

ID+2 VALUE

I N T O

FREE-CONVECTION -8.517416E+06 -8.517416E+06 -8.517416E+06 -8.517416E+06 -8.517416E+06 -8.517416E+06

H B D Y

24, 1993

ID+3 VALUE

PAGE

15

EL-TYPE HEXA

X-GRADIENT 0.000000E+00

T E M P E R A T U R E Y-GRADIENT 5.329071E-15

ID+5 VALUE

MSC/NASTRAN

ID+4 VALUE

24, 1993

E L E M E N T S

9/23/93

9/23/93

(CHBDY)

24, 1993

G R A D I E N T S

Z-GRADIENT 8.881784E-15

ID+5 VALUE

MSC/NASTRAN

RADIATION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

SEPTEMBER

E L E M E N T

9/23/93

C O N S T R A I N T

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

EXAMPLE 2B2

1.00000E+00 F I N I T E

MSC/NASTRAN

ID+4 VALUE

SEPTEMBER

ELEMENT-ID 10 20 30 40 50 60

ID+5 VALUE 5.402279E+01

V E C T O R

S I N G L E - P O I N T

ID+1 VALUE .0

ID+4 VALUE 5.402279E+01

24, 1993

SEPTEMBER

F O R C E S

Main Index

9/23/93

V E C T O R

ID+2 VALUE 5.402279E+01

L O A D

ELEMENT-ID 1

MSC/NASTRAN

1.00000E+00 T E M P E R A T U R E

LOAD STEP =

24, 1993

TOTAL -8.517416E+06 -8.517416E+06 -8.517416E+06 -8.517416E+06 -8.517416E+06 -8.517416E+06

MSC/NASTRAN

A N D

X-FLUX 0.000000E+00

9/23/93

F L U X E S Y-FLUX -1.087130E-12

Z-FLUX -1.811884E-12

121

122

5.9

Example 2c - Nonlinear Internal Heating and Film Nodes Demonstrated Principles • Free Convection Film Nodes • Free Convection Forms

Discussion of Variation 1 This problem provides another example of the use of film nodes. In our previous examples, the film node was chosen to be an element grid point, meaning that the TABLEM look-up temperature for the temperature dependent heat transfer coefficient was the actual body temperature. More often than not, the look-up temperature should be some weighted average of the surface temperature and ambient temperature. In this case, the default value (a blank entry) for the film node depicts that the average of the CHBDY surface element and the associated ambient point temperatures provide the TABLEM look up temperature (FORM = 0). The analytic expression for this case is given in Eq. 5-4: The basic energy balance can be expressed as: L ⋅ U CN ⋅ HGEN ⋅ VOLUME = h ⋅ AREA ⋅ ( T – T ∞ ) ⋅ U CN   1000 ⋅ T ⋅ ( 1000 – T ) =  T   --2- ⋅ 6.0 ⋅ ( T – T ∞ ) ⋅ T  lting in,

The MSC.Nastran input file for Variation 1 is shown in Listing 5-18. Listing 5-18 Example 2c1 Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 2c1 ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 LOAD = 200 BEGIN BULK NLPARM,100 $

Main Index

o

T = 434.26 C

Eq. 5-4

CHAPTER

Listing 5-18 Example 2c1 Input File (continued) GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0 GRID,4,,1.0,0.0,0.0 GRID,5,,0.0,1.0,0.0 GRID,6,,0.0,1.0,1.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,1.0,0.0 GRID,99,,99.0,99.0,99.0 $ CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,204.0,,,1.0,,1.0 MATT4,15,,,,40,,41 TABLEM2,40,0.0,,,,,,,+TBM40 +TBM40,0.0,0.0,1000.0,1000.0,ENDT TABLEM2,41,0.0,,,,,,,+TBM41 +TBM41,0.0,1000.0,1000.0,0.0,ENDT $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6 $ CONV,10,35,,1,99 CONV,20,35,,1,99 CONV,30,35,,1,99 CONV,40,35,,1,99 CONV,50,35,,1,99 CONV,60,35,,1,99 PCONV,35,15,0,0.0 $ QVOL,200,1000.0,1,1 $ SPC,10,99,,0.0 TEMP,20,99,0.0 TEMPD,20,100.0 $ ENDDATA

Results for Variation 1 The abbreviated EX2C1.f06 output file for Variation 1 is shown in Listing 5-19.

Main Index

123

124

Listing 5-19 Example 2c1 Results File EXAMPLE 2C1

LOAD STEP =

SEPTEMBER

POINT ID. 1 7 99 EXAMPLE 2C1

TYPE S S S

LOAD STEP =

1.00000E+00

ID VALUE 4.342588E+02 4.342588E+02 .0

ID+1 VALUE 4.342588E+02 4.342588E+02

9/23/93

PAGE

11

PAGE

12

PAGE

13

9/23/93

PAGE

14

RADIATION TOTAL 0.000000E+00 -4.094640E+07 0.000000E+00 -4.094640E+07 0.000000E+00 -4.094640E+07 0.000000E+00 -4.094640E+07 0.000000E+00 -4.094640E+07 0.000000E+00 -4.094640E+07 24, 1993 MSC/NASTRAN 9/23/93

PAGE

15

V E C T O R

ID+2 VALUE 4.342588E+02

ID+3 VALUE 4.342588E+02

SEPTEMBER

L O A D POINT ID. 7 99 EXAMPLE 2C1

TYPE S S

LOAD STEP =

1.00000E+00

ID .0 .0

VALUE

ID+1 VALUE .0

POINT ID. 7 99 EXAMPLE 2C1

TYPE S S

LOAD STEP =

1.00000E+00

O F

ID VALUE .0 -2.456784E+08

ID+2 VALUE

ID+3 VALUE

ELEMENT-ID 10 20 30 40 50 60 EXAMPLE 2C1

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

1.00000E+00 F I N I T E EL-TYPE HEXA

F L O W

ID+2 VALUE

H B D Y

FREE-CONVECTION -4.094640E+07 -4.094640E+07 -4.094640E+07 -4.094640E+07 -4.094640E+07 -4.094640E+07

E L E M E N T X-GRADIENT 0.000000E+00

I N T O

MSC/NASTRAN

ID+4 VALUE

24, 1993

9/23/93

ID+3 VALUE

Y-GRADIENT 0.000000E+00

MSC/NASTRAN

ID+4 VALUE

24, 1993

E L E M E N T S

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 SEPTEMBER

T E M P E R A T U R E

ID+5 VALUE

9/23/93

C O N S T R A I N T

SEPTEMBER

H E A T

ID+5 VALUE 4.342588E+02

V E C T O R

S I N G L E - P O I N T

ID+1 VALUE .0

ID+4 VALUE 4.342588E+02

24, 1993

SEPTEMBER

F O R C E S

ELEMENT-ID 1

MSC/NASTRAN

1.00000E+00 T E M P E R A T U R E

LOAD STEP =

24, 1993

MSC/NASTRAN

(CHBDY)

G R A D I E N T S

Z-GRADIENT -2.842171E-14

ID+5 VALUE

A N D

X-FLUX 0.000000E+00

F L U X E S Y-FLUX 0.000000E+00

Z-FLUX 5.798029E-12

Discussion of Variation 2 Eq. 5-5 describes a variation of this problem which has the control nodes removed and the value of 0.2 introduced for EXPF (FORM = 0). It should be noted that the elimination of the control nodes alone would have no effect on the analysis since they would have cancelled out of the prior equations. The basic energy balance can be expressed as: QVOL ⋅ HGEN ⋅ VOLUME = h ⋅ AREA ⋅ ( T – T ∞ ) or,

 

Resulting in, Main Index

.20

⋅ ( T – T∞ )

.20 T 1000 ⋅ ( 1000 – T ) =  --- ⋅ 6.0 ⋅ ( T ) ⋅ ( T )   2 o

T = 280. C

Eq. 5-5

CHAPTER

The MSC.Nastran input file for Variation 2 is shown in Listing 5-20. Listing 5-20 Example 2c2 Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 2c2 ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 LOAD = 200 BEGIN BULK NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0 GRID,4,,1.0,0.0,0.0 GRID,5,,0.0,1.0,0.0 GRID,6,,0.0,1.0,1.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,1.0,0.0 GRID,99,,99.0,99.0,99.0 $ CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,204.0,,,1.0,,1.0 MATT4,15,,,,40,,41 TABLEM2,40,0.0,,,,,,,+TBM40 +TBM40,0.0,0.0,1000.0,1000.0,ENDT TABLEM2,41,0.0,,,,,,,+TBM41 +TBM41,0.0,1000.0,1000.0,0.0,ENDT $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6 $ CONV,10,35,,1,99 CONV,20,35,,1,99 CONV,30,35,,1,99 CONV,40,35,,1,99 Main Index

125

126

Listing 5-20 Example 2c2 Input File (continued) CONV,50,35,,1,99 CONV,60,35,,1,99 PCONV,35,15,0,0.2 $ QVOL,200,1000.0,1,1 $ SPC,10,99,,0.0 TEMP,20,99,0.0 TEMPD,20,100.0 $ ENDDATA

Results of Variation 2 The abbreviated EX2c2.f06 output file for Variation 2 is shown in Listing 5-21. Listing 5-21 Example 2c2 Results File EXAMPLE 2C2

LOAD STEP =

SEPTEMBER

POINT ID. 1 7 99 EXAMPLE 2C2

TYPE S S S

LOAD STEP =

1.00000E+00

POINT ID. 7 99 EXAMPLE 2C2

TYPE S S

ID VALUE 2.791197E+02 2.791197E+02 .0

LOAD STEP =

1.00000E+00

ID+1 VALUE 2.791197E+02 2.791197E+02

PAGE

11

PAGE

12

PAGE

13

9/23/93

PAGE

14

RADIATION TOTAL 0.000000E+00 -3.353510E+07 0.000000E+00 -3.353510E+07 0.000000E+00 -3.353510E+07 0.000000E+00 -3.353510E+07 0.000000E+00 -3.353510E+07 0.000000E+00 -3.353510E+07 24, 1993 MSC/NASTRAN 9/23/93

PAGE

15

ID+3 VALUE 2.791197E+02

SEPTEMBER

ID .0 .0

VALUE

ID+1 VALUE .0

POINT ID. 7 99 EXAMPLE 2C2

TYPE S S

LOAD STEP =

1.00000E+00

O F

ID VALUE .0 -2.012106E+08

ID+3 VALUE

ELEMENT-ID 10 20 30 40 50 60 EXAMPLE 2C2

1.00000E+00 F I N I T E EL-TYPE HEXA

F L O W

ID+2 VALUE

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

FREE-CONVECTION -3.353510E+07 -3.353510E+07 -3.353510E+07 -3.353510E+07 -3.353510E+07 -3.353510E+07

E L E M E N T X-GRADIENT 0.000000E+00

I N T O

H B D Y

24, 1993

9/23/93

ID+5 VALUE

MSC/NASTRAN

9/23/93

C O N S T R A I N T

ID+3 VALUE

ID+4 VALUE

24, 1993

E L E M E N T S

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 SEPTEMBER

T E M P E R A T U R E Y-GRADIENT 0.000000E+00

MSC/NASTRAN

ID+4 VALUE

SEPTEMBER

H E A T

ID+5 VALUE 2.791197E+02

V E C T O R

ID+2 VALUE

S I N G L E - P O I N T

ID+1 VALUE .0

ID+4 VALUE 2.791197E+02

24, 1993

SEPTEMBER

F O R C E S

Main Index

9/23/93

V E C T O R

ID+2 VALUE 2.791197E+02

L O A D

ELEMENT-ID 1

MSC/NASTRAN

1.00000E+00 T E M P E R A T U R E

LOAD STEP =

24, 1993

MSC/NASTRAN

(CHBDY)

G R A D I E N T S

Z-GRADIENT -2.842171E-14

ID+5 VALUE

A N D

X-FLUX 0.000000E+00

F L U X E S Y-FLUX 0.000000E+00

Z-FLUX 5.798029E-12

CHAPTER

5.10

Example 3 - Axisymmetric Elements and Boundary Conditions Demonstrated Principles • Axisymmetric Modeling • Axisymmetric Surface Elements

Discussion Axisymmetric geometric models may be constructed using the CTRIAX6 element only. For this element, the grid point locations are input as R,THETA,Z where the axis of symmetry is the Z axis. The grid points lie in the RZ plane (THETA = 0.0). In this example we demonstrate the CHBDYE statement for identifying the surface element to which the boundary condition is to be applied. The surface type is automatically accounted for with this specification. If the CHBDYG had been used, a TYPE field of REV would be specified. For reference, any applied loads of a flux nature have a total load applied to the structure that is calculated based on the entire circumferential surface area. z R o = 2.0 m R i = 1.5 m 11 12 13 14 15 o

T = 300 K

6

10 1

C L

2

3

4

5 o

K = 204.0 W ⁄ m K Figure 5-11 Example 3

The MSC.Nastran input file is shown in Listing 5-22.

Main Index

h = 10.0 W ⁄ m 2 o

T ∞ = 1300 K

o

K

127

128

Listing 5-22 Example 3 Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 3 ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 BEGIN BULK NLPARM,100 $ GRID,1,,1.500,0.0,0.0 GRID,2,,1.625,0.0,0.0 GRID,3,,1.750,0.0,0.0 GRID,4,,1.875,0.0,0.0 GRID,5,,2.000,0.0,0.0 GRID,6,,1.500,0.0,0.125 GRID,7,,1.625,0.0,0.125 GRID,8,,1.750,0.0,0.125 GRID,9,,1.875,0.0,0.125 GRID,10,,2.000,0.0,0.125 GRID,11,,1.500,0.0,0.250 GRID,12,,1.625,0.0,0.250 GRID,13,,1.750,0.0,0.250 GRID,14,,1.875,0.0,0.250 GRID,15,,2.000,0.0,0.250 GRID,99,,99.0,99.0,99.0 $ CTRIAX6,1,15,1,2,3,8,13,7 CTRIAX6,2,15,11,12,13,7,1,6 CTRIAX6,3,15,3,4,5,10,15,9 CTRIAX6,4,15,13,14,15,9,3,8 MAT4,15,204.0,,,10.0 $ CHBDYE,10,3,2 CONV,10,35,,,99 PCONV,35,15,0,0.0 $ SPC,10,99,,1300.0 SPC,10,1,,300.0,6,,300.0 SPC,10,11,,300.0 TEMP,20,99,1300.0 TEMPD,20,300.0 $ ENDDATA Main Index

CHAPTER

Results The abbreviated EX3.f06 output file is shown in Listing 5-23. Listing 5-23 Example 3 Results File EXAMPLE 3

NOVEMBER

LOAD STEP =

POINT ID. 1 7 13 99 EXAMPLE 3

TYPE S S S S

LOAD STEP =

1.00000E+00

ID VALUE 3.000000E+02 3.076319E+02 3.146945E+02 1.300000E+03

ID+1 VALUE 3.076283E+02 3.146983E+02 3.212776E+02

ID+2 VALUE 3.147016E+02 3.212766E+02 3.274268E+02

L O A D POINT ID. 13 99 EXAMPLE 3

TYPE S S

LOAD STEP =

1.00000E+00

ID .0 .0

VALUE

ID+1 VALUE .0

PAGE

11

PAGE

12

PAGE

13

11/ 1/93

PAGE

14

RADIATION TOTAL 0.000000E+00 3.055420E+04 2, 1993 MSC/NASTRAN 11/ 1/93

PAGE

15

ID+3 VALUE 3.212750E+02 3.274309E+02

POINT ID. 1 7 13 99 EXAMPLE 3

TYPE S S S S

LOAD STEP =

1.00000E+00

O F

ID VALUE -5.102459E+03 .0 .0 3.055418E+04

ID+2 VALUE .0

ELEMENT-ID 10

F L O W

ID+2 VALUE .0 .0 .0

APPLIED-LOAD 0.000000E+00

I N T O

FREE-CONVECTION 3.055420E+04

EXAMPLE 3

1.00000E+00 F I N I T E EL-TYPE TRIAX6 TRIAX6 TRIAX6 TRIAX6

E L E M E N T X-GRADIENT 5.728976E+01 6.029604E+01 4.979697E+01 5.206061E+01

H B D Y

ID+3 VALUE .0 .0

MSC/NASTRAN

ID+4 VALUE

2, 1993

11/ 1/93

ID+5 VALUE

MSC/NASTRAN

ID+4 VALUE .0 -5.090287E+03

2, 1993

E L E M E N T S

FORCED-CONVECTION 0.000000E+00 NOVEMBER

T E M P E R A T U R E Y-GRADIENT 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

ID+5 VALUE 3.000000E+02 3.076353E+02

11/ 1/93

C O N S T R A I N T

NOVEMBER

H E A T

2, 1993

ID+3 VALUE

S I N G L E - P O I N T

ID+1 VALUE .0 .0 .0

ID+4 VALUE 3.274322E+02 3.000000E+02

V E C T O R

NOVEMBER

F O R C E S

Main Index

11/ 1/93

V E C T O R

NOVEMBER

ELEMENT-ID 1 2 3 4

MSC/NASTRAN

1.00000E+00 T E M P E R A T U R E

LOAD STEP =

2, 1993

MSC/NASTRAN

(CHBDY)

G R A D I E N T S

Z-GRADIENT 9.583211E-03 1.792225E-02 1.273317E-03 -4.323532E-03

ID+5 VALUE -2.036143E+04 .0

A N D

X-FLUX -1.168711E+04 -1.230039E+04 -1.015858E+04 -1.062036E+04

F L U X E S Y-FLUX 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

Z-FLUX -1.954975E+00 -3.656140E+00 -2.597566E-01 8.820006E-01

129

130

5.11

Example 4a - Plate in Radiative Equilibrium, Nondirectional Solar Load with Radiation Boundary Condition Demonstrated Principles • Flux Load Application • Radiation to Space

Discussion This series of radiative equilibrium problems illustrates various methods of flux load application and radiation exchange with space. The first example uses a nondirectional heat flux load to represent a solar source. A simple radiation boundary condition to space represents the loss mechanism. A blackbody surface is initially presumed. o

T ∞ = 0.0 R ε = α = 1.0

3 7 4

6 Q o = 442. Btu ⁄ hr ft 2 8

2

AREA = 1.0 ft 2

5 1 Figure 5-12 Example 4a The basic energy balance can be expressed as: 4) Q = σ A ε F ( T e4 – T ∞

or,

o

442. Btu ⁄ hr = .1714 × 10 – 8 Btu ⁄ hr ft 2 R 4 ⋅ 1.0 ft 2 ⋅ 1.0 ⋅ 1.0 ( T e4 – ( 460. ) 4 )

Resulting in, The MSC.Nastran input file is shown in Listing 5-24.

Main Index

o

T e ≅ 281.7 F

Eq. 5-6

CHAPTER

Listing 5-24 Example 4a Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 4a ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 LOAD = 200 BEGIN BULK PARAM,TABS,459.67 PARAM,SIGMA,.1714E-8 NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0 GRID,4,,1.0,0.0,0.0 GRID,5,,0.0,0.0,0.5 GRID,6,,0.5,0.0,1.0 GRID,7,,1.0,0.0,0.5 GRID,8,,0.5,0.0,0.0 GRID,99,,99.0,99.0,99.0 $ CQUAD8,1,5,1,2,3,4,5,6,+CQD8 +CQD8,7,8 PSHELL,5,15,0.1 MAT4,15,204.0 $ CHBDYG,10,,AREA8,,,45,,,+CHG10 +CHG10,1,2,3,4,5,6,7,8 $ RADM,45,1.0,1.0 RADBC,99,1.0,,10 $ QHBDY,200,AREA8,442.0,,1,2,3,4,+QHBDY +QHBDY,5,6,7,8 $ SPC,10,99,,0.0 TEMPD,20,0.0 $ ENDDATA

Main Index

131

132

Results The abbreviated EX4a.f06 output file is shown in Listing 5-25. Listing 5-25 Example 4a Results File EXAMPLE 4A

SEPTEMBER

LOAD STEP =

PAGE

11

POINT ID. 1 7 99 EXAMPLE 4A

TYPE S S S

LOAD STEP =

1.00000E+00

ID VALUE 2.819637E+02 2.819637E+02 .0

ID+1 VALUE 2.819637E+02 2.819637E+02

PAGE

12

PAGE

13

9/23/93

PAGE

14

FORCED-CONVECTION RADIATION TOTAL 0.000000E+00 -4.420000E+02 -4.420000E+02 SEPTEMBER 24, 1993 MSC/NASTRAN 9/23/93

PAGE

15

ID+2 VALUE 2.819637E+02

L O A D POINT ID. 1 7 99 EXAMPLE 4A

TYPE S S S

ID+3 VALUE 2.819637E+02

ID VALUE -3.683333E+01 1.473333E+02 .0

LOAD STEP =

1.00000E+00

ID+1 VALUE -3.683333E+01 1.473333E+02

F O R C E S POINT ID. 7 99 EXAMPLE 4A

TYPE S S

ID .0 .0

LOAD STEP =

1.00000E+00

O F

VALUE

ID+2 VALUE -3.683334E+01

ID+3 VALUE -3.683333E+01

ELEMENT-ID 10

F L O W

ID+2 VALUE

APPLIED-LOAD 0.000000E+00

I N T O

FREE-CONVECTION 0.000000E+00

EXAMPLE 4A

1.00000E+00 F I N I T E EL-TYPE QUAD8

E L E M E N T X-GRADIENT -5.454024E-08

H B D Y

T E M P E R A T U R E Y-GRADIENT 7.243386E-09

MSC/NASTRAN

ID+4 VALUE 1.473333E+02

24, 1993

9/23/93

ID+5 VALUE 1.473333E+02

MSC/NASTRAN

9/23/93

C O N S T R A I N T

ID+3 VALUE

ID+4 VALUE

SEPTEMBER

H E A T

ID+5 VALUE 2.819637E+02

V E C T O R

S I N G L E - P O I N T

ID+1 VALUE .0

ID+4 VALUE 2.819637E+02

24, 1993

SEPTEMBER

ELEMENT-ID 1

9/23/93

V E C T O R

SEPTEMBER

LOAD STEP =

MSC/NASTRAN

1.00000E+00 T E M P E R A T U R E

Main Index

24, 1993

24, 1993

E L E M E N T S

MSC/NASTRAN

(CHBDY)

G R A D I E N T S

Z-GRADIENT

ID+5 VALUE

A N D

X-FLUX 1.112621E-05

F L U X E S Y-FLUX -1.477651E-06

Z-FLUX

CHAPTER

5.12

Example 4b - Plate in Radiative Equilibrium, Directional Solar Load with Radiation Boundary Condition Demonstrated Principle • Directional Solar Heat Flux Loads

Discussion Heat loads from a distant source can be treated in a directional sense with the QVECT Bulk Data entry. The absorptivity is made available from a RADM Bulk Data entry. In this case, the radiation boundary condition also uses this absorptivity in its exchange relationship. For illustrative purposes, the angle of incidence was varied to create a plot of equilibrium temperature versus θ . nˆ

3 θ

4

Q0 2

1 Figure 5-13 Example 4b y x

QVECT Qy

Qx θ

 Q x = sin θ = E1   Q y = cos θ = E2  vary θ  Q Z = 0 = E3  

Q 0 = 442. Btu ⁄ hr ft 2 o

ε = α = 1.0, T ∞ = 0.0 F

Main Index

133

134

Table 5-1 Equilibrium Temperature versus Angle of Incident Radiation Direction Cosines θ (deg)

E2

282.0 0.0

-1.0

10

279.6 0.173648

-0.984808

20

272.2 0.342020

-0.939693

30

259.8 0.5

-0.866025

40

241.8 0.642788

-0.766044

50

217.6 0.766044

-0.642788

60

185.8 0.866025

-0.5

70

144.1 0.939693

-0.342020

80

87.2 0.984808

-0.173648

0.0 1.0

θ = 80° case is illustrated in the input file listing.

The MSC.Nastran input file is shown in Listing 5-26.

Main Index

E1

0

90

Note:

T plate (°F)

0.0

CHAPTER

Listing 5-26 Example 4b Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 4b ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 LOAD = 200 BEGIN BULK PARAM,TABS,459.67 PARAM,SIGMA,.1714E-8 NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0 GRID,4,,1.0,0.0,0.0 GRID,99,,99.0,99.0,99.0 $ CQUAD4,1,5,1,2,3,4 PSHELL,5,15,0.1 MAT4,15,204.0 RADM,45,1.0,1.0 $ CHBDYG,10,,AREA4,,,45,,,+CHG10 +CHG10,1,2,3,4 QVECT,200,442.0,,,.984808,-.173648,0.0,,+QVCT1 +QVCT1,10 RADBC,99,1.0,,10 $ SPC,10,99,,0.0 TEMPD,20,0.0 $ ENDDATA

Results The abbreviated EX4b.f06 output file is shown in Listing 5-27. Figure 5-14 describes equilibrium temperature versus angle of incident radiation.

Main Index

135

136

Listing 5-27 Example 4b Results File EXAMPLE 4B

SEPTEMBER

LOAD STEP =

PAGE

11

POINT ID. 1 99 EXAMPLE 4B

TYPE S S

LOAD STEP =

1.00000E+00

ID VALUE 8.717700E+01 .0

ID+1 VALUE 8.717700E+01

PAGE

12

PAGE

13

9/23/93

PAGE

14

FORCED-CONVECTION RADIATION TOTAL 0.000000E+00 -7.675240E+01 2.288818E-05 SEPTEMBER 24, 1993 MSC/NASTRAN 9/23/93

PAGE

15

ID+2 VALUE 8.717700E+01

L O A D POINT ID. 1 99 EXAMPLE 4B

TYPE S S

ID+3 VALUE 8.717700E+01

ID VALUE 1.918810E+01 .0

LOAD STEP =

1.00000E+00

ID+1 VALUE 1.918810E+01

F O R C E S POINT ID. 1 99 EXAMPLE 4B

TYPE S S

ID .0 .0

LOAD STEP =

1.00000E+00

O F

VALUE

ID+2 VALUE 1.918810E+01

ID+3 VALUE 1.918810E+01

ELEMENT-ID 10

F L O W

ID+2 VALUE .0

APPLIED-LOAD 7.675242E+01

I N T O

FREE-CONVECTION 0.000000E+00

EXAMPLE 4B

1.00000E+00 F I N I T E EL-TYPE QUAD4

E L E M E N T X-GRADIENT -7.105427E-15

H B D Y

T E M P E R A T U R E Y-GRADIENT 7.105427E-15

MSC/NASTRAN

ID+4 VALUE

24, 1993

9/23/93

ID+5 VALUE

MSC/NASTRAN

9/23/93

C O N S T R A I N T

ID+3 VALUE .0

ID+4 VALUE

SEPTEMBER

H E A T

ID+5 VALUE

V E C T O R

S I N G L E - P O I N T

ID+1 VALUE .0

ID+4 VALUE

24, 1993

SEPTEMBER

ELEMENT-ID 1

9/23/93

V E C T O R

SEPTEMBER

LOAD STEP =

MSC/NASTRAN

1.00000E+00 T E M P E R A T U R E

Main Index

24, 1993

24, 1993

E L E M E N T S

MSC/NASTRAN

(CHBDY)

G R A D I E N T S

Z-GRADIENT

ID+5 VALUE

A N D

X-FLUX 1.449507E-12

F L U X E S Y-FLUX -1.449507E-12

Z-FLUX

CHAPTER

Temperature (°F) 300

(10.0, 279.6) (20.0, 272.2) (30.0, 259.8) (0.0, 282.0) (40.0, 241.8)

250

(50.0, 217.6) 200 (60.0, 185.8)

150

(70.0, 144.1)

100 (80.0, 87.2) 50 (90.0, 0.0)

0 0

10

20

30

40

50

60

70

80

θ (degrees)

Figure 5-14 Temperature versus Angle of Incident Radiation

Main Index

90

137

138

5.13

Example 4c - Plate in Radiative Equilibrium, Directional Solar Load, Spectral Surface Behavior Demonstrated Principles • Solar Loads • Spectral Radiation Surface Behavior

Discussion Wavelength dependent surface properties can be incorporated in the radiation boundary condition or any radiation enclosure. For this simple radiative equilibrium problem, we demonstrate the principles by using a perfectly selective surface-a surface that behaves like a perfect blackbody ( ε = 1.0) below some finite cutoff wavelength and does not participate above that wavelength. Appendix G describes the mathematics underlying the waveband approximation to spectral radiation exchange. The RADBND Bulk Data entry supplies the wavelength break points and the RADM Bulk Data entry provides the band emissivities. The solar source (QVECT) for the analysis is treated as a blackbody at a temperature of 10400 °R . Qe 3

Qa

αλ ( λ )

2 4

1.0

1

λc

λ

Figure 5-15 Surface Absorptivity versus Wavelength - Example 4c

Main Index

CHAPTER

4000 (3275) 3000

(2760) (2410)

T eq (°R)

(2150)

2000

1000

The input listing corresponds to the λc = 0.6 µm condition.

(1890)

α = ε = 1.0, 0 ≤ λ ≤ ∞

713 0 0.4

0.6

0.8

1.0

1.2

1.4

1.6

λ c ( µm ) Figure 5-16 Radiative Equilibrium Temperature versus Cutoff Wavelength The MSC.Nastran input file is shown in Listing 5-28.

Main Index

139

140

Listing 5-28 Example 4c Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 4c ANALYSIS = HEAT THERMAL = ALL FLUX = ALL OLOAD = ALL SPCF = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 LOAD = 200 BEGIN BULK PARAM,TABS,0.0 PARAM,SIGMA,.1714E-8 NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,1.0,0.0,0.0 GRID,3,,1.0,1.0,0.0 GRID,4,,0.0,1.0,0.0 GRID,99,,99.0,99.0,99.0 $ CQUAD4,1,5,1,2,3,4 PSHELL,5,15,0.1 MAT4,15,204.0 $ CHBDYG,10,,AREA4,,,45,,,+CHG10 +CHG10,1,2,3,4 $ RADM,45,1.0,1.0,0.0 RADBND,3,25898.0,0.6,0.6 RADBC,99,1.0,,10 $ QVECT,200,442.0,10400.0,,0.0,0.0,-1.0,0,+QVECT +QVECT,10 $ SPC,10,99,,0.0 TEMP,20,99,0.0 TEMPD,20,2500.0 $ ENDDATA

Note: Only one RADBND may exist in any analysis. Main Index

CHAPTER

Results The abbreviated EX4c.f06 output file is shown in Listing 5-29. Listing 5-29 Example 4c Results File EXAMPLE 4C

DECEMBER

LOAD STEP =

1.00000E+00

POINT ID. 1 99 EXAMPLE 4C

TYPE S S

LOAD STEP =

1.00000E+00

T E M P E R A T U R E ID VALUE 3.275139E+03 .0

ID+1 VALUE 3.275139E+03

ID VALUE 4.153704E+01 .0

ID+1 VALUE 4.153704E+01

1.00000E+00

POINT ID. 1 99 EXAMPLE 4C

TYPE S S

LOAD STEP =

1.00000E+00

F O R C E S ID .0 .0

O F

VALUE

S I N G L E - P O I N T

ID+1 VALUE .0

H E A T

F L O W

APPLIED-LOAD 1.661482E+02

ID+2 VALUE .0

I N T O

FREE-CONVECTION 0.000000E+00

EXAMPLE 4C

ELEMENT-ID 1 EXAMPLE 4C

EXAMPLE 4C

Main Index

1.00000E+00 F I N I T E EL-TYPE QUAD4

E L E M E N T X-GRADIENT 0.000000E+00

PAGE

8

ID+5 VALUE

MSC/NASTRAN

12/ 9/93

PAGE

9

ID+4 VALUE

ID+5 VALUE

MSC/NASTRAN

12/ 9/93

PAGE

10

C O N S T R A I N T

ID+3 VALUE .0

ID+4 VALUE

PAGE

11

FORCED-CONVECTION RADIATION TOTAL 0.000000E+00 -1.661480E+02 1.678467E-04 DECEMBER 10, 1993 MSC/NASTRAN 12/ 9/93

PAGE

12

H B D Y

10, 1993

ID+5 VALUE

12/ 9/93

T E M P E R A T U R E Y-GRADIENT 0.000000E+00

10, 1993

10, 1993

DECEMBER

ELEMENT-ID 10

ID+4 VALUE

ID+3 VALUE 4.153704E+01

DECEMBER

LOAD STEP =

12/ 9/93

V E C T O R

ID+2 VALUE 4.153704E+01

EXAMPLE 4C

LOAD STEP =

ID+3 VALUE 3.275139E+03 DECEMBER

TYPE S S

MSC/NASTRAN

V E C T O R

ID+2 VALUE 3.275139E+03

L O A D POINT ID. 1 99

10, 1993

E L E M E N T S

MSC/NASTRAN

(CHBDY)

G R A D I E N T S

A N D

F L U X E S

Z-GRADIENT

X-FLUX Y-FLUX 0.000000E+00 0.000000E+00 DECEMBER 10, 1993 MSC/NASTRAN 12/ 9/93

DECEMBER

10, 1993

MSC/NASTRAN

12/ 9/93

Z-FLUX PAGE

13

PAGE

14

141

142

5.14

Example 5a - Single Cavity Enclosure Radiation with Shadowing Demonstrated Principles • Surface to Surface Radiation Exchange • Radiation Cavity / Enclosure • View Factor Calculation with Shadowing

Discussion A simple geometry composed of four plate elements is used to demonstrate radiant exchange in an enclosure. Every surface to participate in the exchange is identified with an CHBDYi Bulk Data entry surface element, in this case providing five surface elements. Only one RADCAV Bulk Data entry is defined in this example indicating that a single enclosure cavity has been defined. For this configuration, shadowing must be considered when calculating the view factors. The statements essential to the radiation solution process are described as follows: RADSET

Requests which cavities are to be included as radiation enclosures for the thermal analysis.

RADLST / RADMTX Provides the view factors required for generation of the radiation matrix. Since they are not provided by the user in this example, they are determined by use of the view module in the course of the analysis.

Main Index

RADCAV

Provides various global controls used for the calculation of view factors within the identified cavity.

VIEW

Provides the connection between a surface element and its assigned cavity and requests that view factors be calculated among those surface elements assigned to the same cavity.

VIEW3D

Requests that the view factors be calculated using the adaptive gaussian integration view factor routine as opposed to the default finite difference calculation.

CHBDYi

Describes the surface elements used in the enclosure, and associates them with the VIEW and RADM Bulk Data entries.

RADM

Provides the radiative surface properties (emissivity), in this case a constant value of 1.0.

CHAPTER

y 14

15

16

~

3

10

6

2

1

7

13 11 9

5 2000 °K

4 8

12

z

Figure 5-17 Example 5a. The MSC.Nastran input file is shown in Listing 5-30. Listing 5-30 Example 5a Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 5a ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 BEGIN BULK PARAM,TABS,0.0 PARAM,SIGMA,5.67E-08 NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,1.0,0.0 GRID,3,,0.0,1.0,1.0 GRID,4,,0.0,0.0,1.0 GRID,5,,1.0,0.0,0.0 GRID,6,,1.0,1.0,0.0 GRID,7,,1.0,1.0,1.0 Main Index

x

143

144

Listing 5-30 Example 5a Input File (continued) GRID,8,,1.0,0.0,1.0 GRID,9,,2.0,0.0,0.0 GRID,10,,2.0,1.0,0.0 GRID,11,,2.0,1.0,1.0 GRID,12,,2.0,0.0,1.0 GRID,13,,1.5,0.0,-1.0 GRID,14,,1.5,1.0,-1.0 GRID,15,,0.5,1.0,-1.0 GRID,16,,0.5,0.0,-1.0 $ CQUAD4,1,5,1,2,3,4 CQUAD4,2,5,5,6,7,8 CQUAD4,3,5,9,12,11,10 CQUAD4,4,5,13,14,15,16 PSHELL,5,15,0.1 MAT4,15,204.0 $ CHBDYG,10,,AREA4,55,,45,,,+CHG10 +CHG10,1,2,3,4 CHBDYG,20,,AREA4,56,,45,,,+CHG20 +CHG20,5,6,7,8 CHBDYG,21,,AREA4,56,,45,,,+CHG21 +CHG21,5,8,7,6 CHBDYG,30,,AREA4,55,,45,,,+CHG30 +CHG30,9,12,11,10 CHBDYG,40,,AREA4,57,,45,,,+CHG40 +CHG40,13,14,15,16 $ RADM,45,1.0,1.0 RADSET,65 RADCAV,65,,YES VIEW,55,65,KBSHD VIEW,56,65,KSHD VIEW,57,65,NONE VIEW3D,65,,,,,,,3 $ SPC,10,1,,2000.0,2,,2000.0 SPC,10,3,,2000.0,4,,2000.0 TEMPD,20,2000.0 $ ENDDATA

Note: The CQUAD4 element with an EID = 2 has two surface elements associated with it. The direction of the CHBDYG surface normals are important for any radiation exchange. Shadowing flags can save vast amounts of computation time for large problems.

Main Index

CHAPTER

Results The abbreviated EX5a.f06 output file is shown in Listing 5-31. Included in this output is a tabulation of the view factor calculation. The details of this output are discussed in“View Factor Calculation Methods” on page 409. Because the view factor summations are less than 1.0, there is considerable energy lost to space. The punch file of radiation view factors is shown in Listing 5-32.

Main Index

145

146

Listing 5-31 Example 5a Results File EXAMPLE 5A

SEPTEMBER

24, 1993

MSC/NASTRAN

9/23/93

PAGE

6

*** VIEW FACTOR MODULE *** OUTPUT DATA *** CAVITY ID = 65 *** ELEMENT TO ELEMENT VIEW FACTORS C* PARTIAL SURF-I SURF-J AREA-I AI*FIJ FIJ ERROR SHADING ERROR SCALE 10 21 1.0000E+00 1.97750E-01 1.97750E-01 2.5529E-01 NO YES 10 30 1.0000E+00 6.84135E-02 6.84135E-02 7.3895E-02 NO NO 10 40 1.0000E+00 4.08547E-02 4.08547E-02 6.6278E-02 NO NO 10 30 1.0000E+00 0.00000E+00 0.00000E+00 0/256 10 21 1.0000E+00 1.99944E-01 1.99944E-01 10 -SUM OF 2.40799E-01 2.40799E-01 20 30 1.0000E+00 1.97750E-01 1.97750E-01 2.5529E-01 NO YES 20 40 1.0000E+00 1.31841E-02 1.31841E-02 2.0133E-02 YES NO 20 40 1.0000E+00 1.16713E-02 1.16713E-02 20 30 1.0000E+00 1.99944E-01 1.99944E-01 20 -SUM OF 2.11616E-01 2.11616E-01 21 40 1.0000E+00 1.31841E-02 1.31841E-02 2.0133E-02 YES NO 21 40 1.0000E+00 1.16713E-02 1.16713E-02 21 -SUM OF 2.11616E-01 2.11616E-01 30 40 1.0000E+00 4.08547E-02 4.08547E-02 6.6278E-02 NO NO 30 -SUM OF 2.40799E-01 2.40799E-01 40 -SUM OF 1.05052E-01 1.05052E-01 ^^^ DMAP INFORMATION MESSAGE 9048 (NLSCSH) - LINEAR ELEMENTS ARE CONNECTED TO THE ANALYSIS SET (A-SET). *** USER INFORMATION MESSAGE 4534, 5 ELEMENTS HAVE A TOTAL VIEW FACTOR (FA/A) LESS THAN 0.99, ENERGY MAY BE LOST TO SPACE. LOAD STEP = 1.00000E+00 T E M P E R A T U R E V E C T O R POINT ID. 1 7 13 EXAMPLE 5A

LOAD STEP =

TYPE S S S

ID VALUE 2.000000E+03 1.132229E+03 9.168311E+02

ID+1 VALUE 2.000000E+03 1.132229E+03 9.168311E+02

ID+2 VALUE 2.000000E+03 7.732046E+02 9.168311E+02

POINT ID. 13 EXAMPLE 5A

TYPE S

LOAD STEP =

1.00000E+00

ID .0

VALUE

ID+1 VALUE .0

F O R C E S POINT ID. 1 13 EXAMPLE 5A

TYPE S S

LOAD STEP =

1.00000E+00

ID VALUE 2.217105E+05 .0

H E A T ELEMENT-ID 10 20 21 30 40

Main Index

24

9/23/93

PAGE

25

O F

ID+3 VALUE ID+4 VALUE ID+5 VALUE 2.217105E+05 .0 .0 .0 SEPTEMBER 24, 1993 MSC/NASTRAN 9/23/93

PAGE

26

ID+2 VALUE .0

ID+3 VALUE .0 SEPTEMBER

S I N G L E - P O I N T

ID+1 VALUE 2.217105E+05 .0

F L O W

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

V E C T O R

ID+2 VALUE 2.217105E+05 .0

I N T O

FREE-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

H B D Y

EL-TYPE QUAD4 QUAD4 QUAD4 QUAD4

E L E M E N T X-GRADIENT 0.000000E+00 2.273737E-13 0.000000E+00 -5.684342E-14

T E M P E R A T U R E Y-GRADIENT 0.000000E+00 1.136868E-13 0.000000E+00 0.000000E+00

24, 1993

E L E M E N T S

SEPTEMBER

1.00000E+00 F I N I T E

ID+4 VALUE

MSC/NASTRAN

(CHBDY)

RADIATION -8.868420E+05 -8.865096E+04 8.865097E+04 -3.671037E-04 6.051011E-03 24, 1993

G R A D I E N T S

Z-GRADIENT

ID+5 VALUE

C O N S T R A I N T

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

EXAMPLE 5A

ELEMENT-ID 1 2 3 4

PAGE

1.00000E+00 L O A D

LOAD STEP =

ID+3 VALUE ID+4 VALUE ID+5 VALUE 2.000000E+03 1.132229E+03 1.132229E+03 7.732046E+02 7.732046E+02 7.732046E+02 9.168311E+02 SEPTEMBER 24, 1993 MSC/NASTRAN 9/23/93

TOTAL -8.868420E+05 -8.865096E+04 8.865097E+04 -3.671037E-04 6.051011E-03

MSC/NASTRAN

A N D

X-FLUX 0.000000E+00 -4.638423E-11 0.000000E+00 1.159606E-11

9/23/93

PAGE

F L U X E S Y-FLUX 0.000000E+00 -2.319211E-11 0.000000E+00 0.000000E+00

Z-FLUX

27

CHAPTER

Listing 5-32 Example 5a Punch File (EX5a.pch) RADMTX RADMTX RADMTX RADMTX RADMTX RADLST

Main Index

65 65 65 65 65 65

1 2 3 4 5 1

0.0 0.0 0.0 0.0 0.0

0.0 .199944 0.0 .040855 0.0 .199944 .011671 0.0 .011671 .040855 10

20

21

30

40

147

148

5.15

Example 5b - Single Cavity Enclosure Radiation with an Ambient Element Specification Demonstrated Principles • Enclosure Radiation Exchange • Radiation Ambient Element

Discussion Example 5a involves four plates in radiative equilibrium which exhibit considerable energy loss to space since there is no defined exchange mechanism between them and their environment. This undefined environment behaves mathematically the same as blackbody space at a temperature of absolute zero. A convenient method for introducing an ambient environment into the problem capitalizes on the use of the ambient element as selected on the RADCAV Bulk Data entry. For any group of surface elements we wish to consider as a partial enclosure, we can define a single unique ambient element which will mathematically complete the enclosure. This surface element must have a specified temperature boundary condition. The ambient element concept relies on our knowledge that the individual elemental view factors must add up to a value of 1.0 for a complete enclosure. Any elemental surfaces which have a view factor sum of less than 1.0 as determined by the view module will automatically have the remainder assigned to the ambient element. This environmental view factor is not listed in the view module output, but is identified in the generated RADLST/RADMTX punch files. If the ambient element is to model space, it should be made appropriately large relative to the other elements in the enclosure. As discussed in “View Factor Calculation Methods” on page 409, whenever an ambient element is requested for a cavity, a symmetric conservative radiation matrix is generated. The MSC.Nastran input file is shown in Listing 5-33.

Main Index

CHAPTER

Listing 5-33 Example 5b Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 5b ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 BEGIN BULK PARAM,TABS,0.0 PARAM,SIGMA,5.67E-08 NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,1.0,0.0 GRID,3,,0.0,1.0,1.0 GRID,4,,0.0,0.0,1.0 GRID,5,,1.0,0.0,0.0 GRID,6,,1.0,1.0,0.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,0.0,1.0 GRID,9,,2.0,0.0,0.0 GRID,10,,2.0,1.0,0.0 GRID,11,,2.0,1.0,1.0 GRID,12,,2.0,0.0,1.0 GRID,13,,1.5,0.0,-1.0 GRID,14,,1.5,1.0,-1.0 GRID,15,,0.5,1.0,-1.0 GRID,16,,0.5,0.0,-1.0 GRID,17,,0.0,100.0,0.0 GRID,18,,100.0,100.0,0.0 GRID,19,,100.0,100.0,100.0 GRID,20,,0.0,100.0,100.0 $ CQUAD4,1,5,1,2,3,4 CQUAD4,2,5,5,6,7,8 CQUAD4,3,5,9,12,11,10 CQUAD4,4,5,13,14,15,16 CQUAD4,5,5,17,18,19,20 PSHELL,5,15,0.1 MAT4,15,204.0 $

Main Index

149

150

Listing 5-33 Example 5b Input File (continued) CHBDYG,10,,AREA4,55,,45,,,+CHG10 +CHG10,1,2,3,4 CHBDYG,20,,AREA4,56,,45,,,+CHG20 +CHG20,5,6,7,8 CHBDYG,21,,AREA4,56,,45,,,+CHG21 +CHG21,5,8,7,6 CHBDYG,30,,AREA4,55,,45,,,+CHG30 +CHG30,9,12,11,10 CHBDYG,40,,AREA4,57,,45,,,+CHG40 +CHG40,13,14,15,16 CHBDYG,99,,AREA4,,,45,,,+CHG99 +CHG99,17,18,19,20 $ RADM,45,1.0,1.0 RADSET,65 RADCAV,65,99,YES VIEW,55,65,KBSHD VIEW,56,65,KSHD VIEW,57,65,NONE VIEW3D,65,,,,,,,3 $ SPC,10,1,,2000.0,2,,2000.0 SPC,10,3,,2000.0,4,,2000.0 SPC,10,17,,500.0,18,,500.0 SPC,10,19,,500.0,20,,500.0 TEMPD,20,2000.0 $ ENDDATA

Note: Ambient element EID = 99 is defined with a large area to represent space.

Results The abbreviated EX5b.f06 output file is shown in Listing 5-34. Note that the ambient element does not appear in the view factor .f06 output. The punch file is shown in Listing 5-35, and does include the ambient element.

Main Index

CHAPTER

Listing 5-34 Example 5b Results File EXAMPLE 5B

FEBRUARY

*** VIEW FACTOR MODULE *** OUTPUT DATA *** CAVITY ID =

SURF-I

SURF-J

ELEMENT TO ELEMENT VIEW FACTORS C* AI*FIJ FIJ ERROR

AREA-I

10 21 1.0000E+00 10 30 1.0000E+00 10 40 1.0000E+00 10 30 1.0000E+00 10 21 1.0000E+00 10 -SUM OF 20 30 1.0000E+00 20 40 1.0000E+00 20 40 1.0000E+00 20 30 1.0000E+00 20 -SUM OF 21 40 1.0000E+00 21 40 1.0000E+00 21 -SUM OF 30 40 1.0000E+00 30 -SUM OF 40 -SUM OF LOAD STEP = 1.00000E+00

1.97750E-01 6.84135E-02 4.08547E-02 0.00000E+00 1.99944E-01 2.40799E-01 1.97750E-01 1.31841E-02 1.16713E-02 1.99944E-01 2.11616E-01 1.31841E-02 1.16713E-02 2.11616E-01 4.08547E-02 2.40799E-01 1.05052E-01

1.97750E-01 6.84135E-02 4.08547E-02 0.00000E+00 1.99944E-01 2.40799E-01 1.97750E-01 1.31841E-02 1.16713E-02 1.99944E-01 2.11616E-01 1.31841E-02 1.16713E-02 2.11616E-01 4.08547E-02 2.40799E-01 1.05052E-01

TYPE S S S S

ID VALUE 2.000000E+03 1.141790E+03 9.356503E+02 5.000000E+02

ID+1 VALUE 2.000000E+03 1.141790E+03 9.356503E+02 5.000000E+02

PARTIAL SHADING ERROR

2.5529E-01 7.3895E-02 6.6278E-02 0/256

NO NO NO

YES NO NO

2.5529E-01 2.0133E-02

NO YES

YES NO

2.0133E-02

YES

NO

6.6278E-02

NO

NO

ID+2 VALUE 2.000000E+03 8.044109E+02 9.356503E+02

TYPE S

ID .0

VALUE

ID+1 VALUE .0

LOAD STEP =

TYPE S S S

ID VALUE 2.208269E+05 .0 -2.208285E+05

ID+4 VALUE 1.141790E+03 8.044109E+02 5.000000E+02 14, 1994

ID+5 VALUE 1.141790E+03 8.044109E+02 5.000000E+02

MSC/NASTRAN

2/ 4/94

PAGE

11

PAGE

12

V E C T O R

ID+2 VALUE

ID+3 VALUE

O F

S I N G L E - P O I N T

ID+4 VALUE 14, 1994

ID+5 VALUE

MSC/NASTRAN

2/ 4/94

ID+1 VALUE 2.208269E+05 .0 -2.208285E+05

ID+2 VALUE 2.208269E+05 .0

C O N S T R A I N T

ID+3 VALUE 2.208269E+05 .0 FEBRUARY

ID+4 VALUE .0 -2.208285E+05

14, 1994

ID+5 VALUE .0 -2.208285E+05

MSC/NASTRAN

2/ 4/94

PAGE

13

PAGE

14

1.00000E+00 H E A T ELEMENT-ID 10 20 21 30 40 99

F L O W

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

I N T O

FREE-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

H B D Y

LOAD STEP =

ELEMENT-ID 1 2 3 4 5

E L E M E N T S

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

EXAMPLE 5B

Main Index

ID+3 VALUE 2.000000E+03 8.044109E+02 9.356503E+02

1.00000E+00 F O R C E S

POINT ID. 1 13 19 EXAMPLE 5B

7

V E C T O R

FEBRUARY

LOAD STEP =

PAGE

1.00000E+00 L O A D

POINT ID. 19 EXAMPLE 5B

2/ 4/94

SCALE

FEBRUARY

LOAD STEP =

MSC/NASTRAN

65 ***

T E M P E R A T U R E POINT ID. 1 7 13 19 EXAMPLE 5B

14, 1994

FEBRUARY

1.00000E+00 F I N I T E EL-TYPE QUAD4 QUAD4 QUAD4 QUAD4 QUAD4

E L E M E N T X-GRADIENT 0.000000E+00 0.000000E+00 -5.684342E-14 0.000000E+00 -5.204170E-17

T E M P E R A T U R E Y-GRADIENT 0.000000E+00 0.000000E+00 -1.136868E-13 0.000000E+00 5.204170E-17

RADIATION -8.833074E+05 -8.830299E+04 8.830428E+04 -7.230929E+00 -5.820249E-01 8.833141E+05 14, 1994

G R A D I E N T S

Z-GRADIENT

(CHBDY) TOTAL -8.833074E+05 -8.830299E+04 8.830428E+04 -7.230929E+00 -5.820249E-01 8.833141E+05

MSC/NASTRAN

A N D

X-FLUX 0.000000E+00 0.000000E+00 1.159606E-11 0.000000E+00 1.061651E-14

2/ 4/94

F L U X E S Y-FLUX 0.000000E+00 0.000000E+00 2.319211E-11 0.000000E+00 -1.061651E-14

Z-FLUX

151

152

Listing 5-35 Example 5b Punch File (EX5b.pch) RADMTX RADMTX RADMTX RADMTX RADMTX RADMTX RADLST

Main Index

65 65 65 65 65 65 65

1 2 3 4 5 6 4

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 .040855 .894948 10

20

.199944 0.0 .040855 .759201 .199944 .011671 .788384 .011671 .788384 .759201

21

30

40

99

CHAPTER

5.16

Example 5c - Multiple Cavity Enclosure Radiation Demonstrated Principles • Multiple Radiation Cavities • View Factor Calculation for Multiple Cavities

Discussion The concept of multiple radiation cavities is investigated in this problem. The primary use of this capability is to reduce the computation time associated with the identification and calculation of view factors when total separation exists between regions. If defined as a single enclosure, this problem would involve third body shadowing calculations, the most laborious and expensive part of any view factor calculation. As a three cavity problem, these calculations are eliminated. RADSET selects three cavities and the RADCAV entry for SHADOW is denoted as NO indicating that no third body shadowing calculations are to be performed within the individual cavities. The fields on the VIEW Bulk Data entry concerning SHADE are ignored when SHADOW is set to NO on the RADCAV Bulk Data entry. When hundreds or thousands of surfaces are involved, the savings may be crucial to the economics of the total analysis. y

2000 °K 6

2 3

11

7

~ 1 4

5 8

14

10 15

13

9 12

16

z Figure 5-18 Example 5c The MSC.Nastran input file is shown in Listing 5-36.

Main Index

x

153

154

Listing 5-36 Example 5c Input File ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 5c ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 BEGIN BULK PARAM,TABS,0.0 PARAM,SIGMA,5.67E-08 NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,1.0,0.0 GRID,3,,0.0,1.0,1.0 GRID,4,,0.0,0.0,1.0 GRID,5,,1.0,0.0,0.0 GRID,6,,1.0,1.0,0.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,0.0,1.0 GRID,9,,2.0,0.0,0.0 GRID,10,,2.0,1.0,0.0 GRID,11,,2.0,1.0,1.0 GRID,12,,2.0,0.0,1.0 GRID,13,,3.0,0.0,0.0 GRID,14,,3.0,1.0,0.0 GRID,15,,3.0,1.0,1.0 GRID,16,,3.0,0.0,1.0 $ CQUAD4,1,5,1,2,3,4 CQUAD4,2,5,5,6,7,8 CQUAD4,3,5,9,10,11,12 CQUAD4,4,5,13,16,15,14 PSHELL,5,15,0.1 MAT4,15,204.0 $

Main Index

CHAPTER

Listing 5-36 Example 5c Input File (continued) CHBDYG,10,,AREA4,55,,45,,,+CHG10 +CHG10,1,2,3,4 CHBDYG,20,,AREA4,55,,45,,,+CHG20 +CHG20,5,8,7,6 CHBDYG,30,,AREA4,56,,45,,,+CHG30 +CHG30,5,6,7,8 CHBDYG,40,,AREA4,56,,45,,,+CHG40 +CHG40,9,12,11,10 CHBDYG,50,,AREA4,57,,45,,,+CHG50 +CHG50,9,10,11,12 CHBDYG,60,,AREA4,57,,45,,,+CHG60 +CHG60,13,16,15,14 $ RADM,45,1.0,1.0 RADSET,65,75,85 RADCAV,65,,NO RADCAV,75,,NO RADCAV,85,,NO VIEW,55,65 VIEW,56,75 VIEW,57,85 VIEW3D,65,,,,,,,3 VIEW3D,75,,,,,,,3 VIEW3D,85,,,,,,,3 $ SPC,10,1,,2000.0,2,,2000.0 SPC,10,3,,2000.0,4,,2000.0 TEMPD,20,2000.0 $ ENDDATA

Results The abbreviated EX5c.f06 output file is shown in Listing 5-37. The punch file is shown in Listing 5-38. Note the multiple cavity information.

Main Index

155

156

Listing 5-37 Example 5c Results File EXAMPLE 5C SEPTEMBER 24, 1993 *** VIEW FACTOR MODULE *** OUTPUT DATA *** CAVITY ID = 65 *** ELEMENT TO ELEMENT VIEW FACTORS C* PARTIAL SURF-I SURF-J AREA-I AI*FIJ FIJ ERROR SHADING ERROR SCALE 10 20 1.0000E+00 1.97750E-01 1.97750E-01 2.5529E-01 NO YES 10 20 1.0000E+00 1.99944E-01 1.99944E-01 10 -SUM OF 1.99944E-01 1.99944E-01 20 -SUM OF 1.99944E-01 1.99944E-01 EXAMPLE 5C SEPTEMBER 24, 1993

*** VIEW FACTOR MODULE *** OUTPUT DATA *** CAVITY ID = 75 *** ELEMENT TO ELEMENT VIEW FACTORS C* PARTIAL SURF-I SURF-J AREA-I AI*FIJ FIJ ERROR SHADING ERROR SCALE 30 40 1.0000E+00 1.97750E-01 1.97750E-01 2.5529E-01 NO YES 30 40 1.0000E+00 1.99944E-01 1.99944E-01 30 -SUM OF 1.99944E-01 1.99944E-01 40 -SUM OF 1.99944E-01 1.99944E-01 EXAMPLE 5C SEPTEMBER 24, 1993

MSC/NASTRAN

9/23/93

PAGE

7

MSC/NASTRAN

9/23/93

PAGE

8

MSC/NASTRAN

9/23/93

PAGE

9

*** VIEW FACTOR MODULE *** OUTPUT DATA *** CAVITY ID = 85 *** ELEMENT TO ELEMENT VIEW FACTORS C* PARTIAL SURF-I SURF-J AREA-I AI*FIJ FIJ ERROR SHADING ERROR SCALE 50 60 1.0000E+00 1.97750E-01 1.97750E-01 2.5529E-01 NO YES 50 60 1.0000E+00 1.99944E-01 1.99944E-01 50 -SUM OF 1.99944E-01 1.99944E-01 60 -SUM OF 1.99944E-01 1.99944E-01 ^^^ DMAP INFORMATION MESSAGE 9048 (NLSCSH) - LINEAR ELEMENTS ARE CONNECTED TO THE ANALYSIS SET (A-SET). *** USER INFORMATION MESSAGE 4534, 2 ELEMENTS HAVE A TOTAL VIEW FACTOR (FA/A) LESS THAN 0.99, ENERGY MAY BE LOST TO SPACE. LOAD STEP = 1.00000E+00 T E M P E R A T U R E V E C T O R POINT ID. 1 7 13 EXAMPLE 5C

TYPE S S S

LOAD STEP =

ID VALUE 2.000000E+03 1.127462E+03 4.260592E+02

ID+1 VALUE 2.000000E+03 1.127462E+03 4.260592E+02

ID+2 VALUE 2.000000E+03 6.371667E+02 4.260592E+02

TYPE S

ID .0

VALUE

ID+1 VALUE .0

V E C T O R

ID+2 VALUE .0

EXAMPLE 5C

LOAD STEP =

TYPE S S

LOAD STEP =

ID VALUE 2.221976E+05 .0

ID+5 VALUE 9/23/93

PAGE

44

O F

S I N G L E - P O I N T

ID+1 VALUE 2.221976E+05 .0

ID+2 VALUE 2.221976E+05 .0

PAGE

45

C O N S T R A I N T

ID+3 VALUE ID+4 VALUE 2.221976E+05 .0 .0 SEPTEMBER 24, 1993 MSC/NASTRAN

ID+5 VALUE .0 9/23/93

1.00000E+00 H E A T

ELEMENT-ID 10 20 30 40 50 60

Main Index

ID+3 VALUE ID+4 VALUE .0 SEPTEMBER 24, 1993 MSC/NASTRAN

1.00000E+00 F O R C E S

POINT ID. 1 13 EXAMPLE 5C

43

1.00000E+00 L O A D

POINT ID. 13

ID+3 VALUE ID+4 VALUE ID+5 VALUE 2.000000E+03 1.127462E+03 1.127462E+03 6.371667E+02 6.371667E+02 6.371667E+02 4.260592E+02 SEPTEMBER 24, 1993 MSC/NASTRAN 9/23/93 PAGE

F L O W

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

I N T O

FREE-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

H B D Y

E L E M E N T S

FORCED-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

(CHBDY)

RADIATION -8.887904E+05 8.974247E+04 -8.974246E+04 8.970887E+03 -8.970880E+03 -5.437486E-04

TOTAL -8.887904E+05 8.974247E+04 -8.974246E+04 8.970887E+03 -8.970880E+03 -5.437486E-04

CHAPTER

Listing 5-37 Example 5c Results File (continued) EXAMPLE 5C

LOAD STEP =

ELEMENT-ID 1 2 3 4

SEPTEMBER

1.00000E+00 F I N I T E EL-TYPE QUAD4 QUAD4 QUAD4 QUAD4

E L E M E N T X-GRADIENT 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

T E M P E R A T U R E Y-GRADIENT 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

24, 1993

G R A D I E N T S

Z-GRADIENT

Main Index

65 65 65 75 75 75 85 85 85

1 2 1 1 2 1 1 2 1

0.0 .199944 0.0 10 20 0.0 .199944 0.0 30 40 0.0 .199944 0.0 50 60

A N D

X-FLUX 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

Listing 5-38 Example 5c Punch File RADMTX RADMTX RADLST RADMTX RADMTX RADLST RADMTX RADMTX RADLST

MSC/NASTRAN

9/23/93

PAGE

46

F L U X E S Y-FLUX 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

Z-FLUX

157

158

5.17

Example 6 - Forced Convection Tube Flow - Constant Property Flow Demonstrated Principles • Forced Convection Fluid Elements • Control Node for Mass Flow Rate • Relationships for Tube Flows • Film Nodes for Forced Convection • Constant Heat Transfer Coefficient

Discussion A forced convection element (CONVM) is available for the simulation of 1-D fluid flow networks. The formulation takes into account conduction and convection in the streamwise direction as well as the convection resistance between the fluid and the adjoining structure or environment. The mass flow rate is specified by the value of the control node (CNTMDOT). Fluid properties which vary with temperature are available through the MAT4/MATT4 entries for conductivity, specific heat, and dynamic viscosity. In this example, the forced convection 2 heat transfer coefficient has been input at a constant value of 200. ⁄ m °C . For tube flow, the heat transfer coefficient could easily have been calculated internally based on the relationships available through the CONVM/PCONVM. It may be desirable to consider a fluid flow problem in an evolutionary sense. This allows for a much broader interpretation of load incrementing through time stepping, as well introducing the stabilizing effects associated with heat capacitance and implicit time integration. The steady state solution may then be likened to the long time solution from a transient analysis. o

Tw = 0 C

o

T in = 100 C 1

T exit 2

3

4

5

6

7

5.0 m Figure 5-19 Example 6 Working Fluid = Water: K =

o

.065 W ⁄ m C

C p = 4200. J ⁄ kg oC ρ = 1000.kg ⁄ m 3 Main Index

8

9

10

11

CHAPTER

µ = 1.0 × 10 – 3 kg ⁄ m sec h =

200. W ⁄ m

2 o

C = constant

· = 0.1 kg ⁄ sec m DIA = .05 m The MSC.Nastran input file is shown in Listing 5-39. · Listing 5-39 Example 6 Input File, m = .10 ID MSC-NASTRAN V68 SOL 153 TIME 10 CEND TITLE = EXAMPLE 6 ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 TEMP(INIT) = 20 NLPARM = 100 BEGIN BULK NLPARM,100 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.5,0.0,0.0 GRID,3,,1.0,0.0,0.0 GRID,4,,1.5,0.0,0.0 GRID,5,,2.0,0.0,0.0 GRID,6,,2.5,0.0,0.0 GRID,7,,3.0,0.0,0.0 GRID,8,,3.5,0.0,0.0 GRID,9,,4.0,0.0,0.0 GRID,10,,4.5,0.0,0.0 GRID,11,,5.0,0.0,0.0 GRID,50,,50.0,50.0,50.0 GRID,99,,99.0,99.0,99.0 $

Main Index

159

160

· Listing 5-39 Example 6 Input File, m = .10 (continued) CHBDYP,10,25,FTUBE,,,1,2 CHBDYP,20,25,FTUBE,,,2,3 CHBDYP,30,25,FTUBE,,,3,4 CHBDYP,40,25,FTUBE,,,4,5 CHBDYP,50,25,FTUBE,,,5,6 CHBDYP,60,25,FTUBE,,,6,7 CHBDYP,70,25,FTUBE,,,7,8 CHBDYP,80,25,FTUBE,,,8,9 CHBDYP,90,25,FTUBE,,,9,10 CHBDYP,100,25,FTUBE,,,10,11 PHBDY,25,,0.05,0.05 $ CONVM,10,95,,50,99 CONVM,20,95,,50,99 CONVM,30,95,,50,99 CONVM,40,95,,50,99 CONVM,50,95,,50,99 CONVM,60,95,,50,99 CONVM,70,95,,50,99 CONVM,80,95,,50,99 CONVM,90,95,,50,99 CONVM,100,95,,50,99 $ PCONVM,95,15,0,1,200.0,0.0,0.0,0.0 MAT4,15,0.65,4200.0,1000.0,,1.0E-03 $ SPC,10,1,,100.0 SPC,10,99,,0.0 SPC,10,50,,0.1 $ TEMP,20,1,100.0 TEMP,20,99,0.0 TEMP,20,50,0.1 TEMPD,20,100.0 $ ENDDATA

· Note: The input file reflects a mass flow rate of m = .10 kg/sec.

Results The abbreviated EX6.f06 output file is shown in Listing 5-40. A plot of temperature versus mass flow rate is shown in Figure 5-20.

Main Index

CHAPTER

· Listing 5-40 Example 6 Results File, m = .10 Case EXAMPLE 6

DECEMBER

LOAD STEP =

TYPE S S S S

ID VALUE 1.000000E+02 8.022740E+01 1.000000E-01 .0

ID+1 VALUE 9.639484E+01 7.733508E+01

ID+2 VALUE 9.291965E+01 7.454703E+01

EXAMPLE 6

TYPE S S S

ID .0 .0 .0

VALUE

ID+1 VALUE .0

POINT ID. 7 50 99 EXAMPLE 6

TYPE S S S

ID+4 VALUE 8.634062E+01 6.926884E+01

3, 1993

MSC/NASTRAN

PAGE

9

ID+5 VALUE 8.322791E+01

12/ 2/93

V E C T O R

ID+2 VALUE .0

ID+3 VALUE .0

O F

ID VALUE .0 .0 -1.338981E+04

S I N G L E - P O I N T

ID+4 VALUE .0

3, 1993

ID+5 VALUE

MSC/NASTRAN

12/ 2/93

PAGE

10

ID+1 VALUE .0

ID+2 VALUE .0

PAGE

11

C O N S T R A I N T

ID+3 VALUE .0

DECEMBER

LOAD STEP =

8

1.00000E+00 F O R C E S

ID+4 VALUE .0

3, 1993

ID+5 VALUE

MSC/NASTRAN

12/ 2/93

1.00000E+00 H E A T

ELEMENT-ID 10 20 30 40 50 60 70 80 90 100

Main Index

ID+3 VALUE 8.956976E+01 7.185950E+01

DECEMBER

LOAD STEP =

PAGE

1.00000E+00 L O A D

POINT ID. 7 50 99 EXAMPLE 6

12/ 2/93

V E C T O R

DECEMBER

LOAD STEP =

MSC/NASTRAN

1.00000E+00 T E M P E R A T U R E

POINT ID. 1 7 50 99

3, 1993

F L O W

APPLIED-LOAD 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

I N T O

FREE-CONVECTION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

H B D Y

E L E M E N T S

FORCED-CONVECTION -1.542481E+03 -1.486873E+03 -1.433269E+03 -1.381597E+03 -1.331788E+03 -1.283775E+03 -1.237493E+03 -1.192879E+03 -1.149874E+03 -1.108419E+03

(CHBDY)

RADIATION 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

TOTAL -1.542481E+03 -1.486873E+03 -1.433269E+03 -1.381597E+03 -1.331788E+03 -1.283775E+03 -1.237493E+03 -1.192879E+03 -1.149874E+03 -1.108419E+03

161

162

100

(0.40, 91.1) (0.50, 92.8) (0.30, 88.3)

90

(0.25, 86.2)

(0.20, 83.1) 80

T exit

(0.45, 92.1) (0.35, 90.0)

(0.15, 78.2)

70

(0.10, 69.3)

o

( C) 60

50

(0.05, 48.6)

40 0

0.1

0.2

0.3

0.4

· m ( kg ⁄ sec ) Figure 5-20 Exit Temperature versus Mass Flow Rate

Main Index

0.5

CHAPTER

5.18

Example 7a - Transient Cool Down, Convection Boundary Demonstrated Principles • Transient Solution Sequence • Transient Solution Control • Transient Temperature Specification • Initial Conditions • Transient Plots

Discussion This example demonstrates the simplest of transient thermal responses. A single CHEXA element at an initial temperature of 1000. °C is exposed to a free convection environment maintained at 0.0 °C. Transient analysis involves the time-dependent storage as well as transport of thermal energy. Therefore, relative to steady state analysis, the heat capacitance (storage) must be accounted for as well as any time dependencies on loads and boundary conditions. A starting point or initial condition is required and a solution duration is specified. There are various techniques available for specifying temperature boundary conditions or ambient node temperatures for transient analyses. If the temperature is to remain constant throughout the analysis, an SPC should be used to set the boundary condition just as in steady state analysis. Fundamental MSC.Nastran X-Y plotting is demonstrated here for simple transient plots. “Interface and File Communication” on page 31 discusses this capability in more detail. The MSC.Nastran input file is shown in Listing 5-41. Listing 5-41 Example 7a Input File ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 7A ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 IC = 20 TSTEPNL = 100 OUTPUT(XYPLOT)

Main Index

163

164

Listing 5-41 Example 7a Input File (continued) XTITLE = TIME, SECONDS YTITLE = TEMPERATURE DEGREES CELSIUS TCURVE = TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) BEGIN BULK TSTEPNL,100,1500,100.0,1 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0 GRID,4,,1.0,0.0,0.0 GRID,5,,0.0,1.0,0.0 GRID,6,,0.0,1.0,1.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,1.0,0.0 GRID,99,,99.0,99.0,99.0 $ CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,204.0,896.0,2707.0,10.0 $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6 $ CONV,10,35,,,99 CONV,20,35,,,99 CONV,30,35,,,99 CONV,40,35,,,99 CONV,50,35,,,99 CONV,60,35,,,99 PCONV,35,15,0,0.0 $ SPC,10,99,,0.0 TEMP,20,99,0.0 TEMPD,20,1000.0 $ ENDDATA

Note: TSTEPNL is identified in the Case Control Section, as are the NASPLT plot requests. TSTEPNL provides the solution timing information in the Bulk Data Section. MAT4 must have density and specific heat field data for transient analysis. Main Index

CHAPTER

Results An MSC.Nastran X-Y plot of temperature versus time is shown in Figure 5-21. These plots were examined by typing NASPLT EX7A.plt subsequent to the analysis. The EX7A.f06 file has large lists of temperature vs. time for each grid point, and have been omitted here for the sake of brevity.

Figure 5-21 Temperature versus Time

Main Index

165

166

5.19

Example 7b - Convection, Time Varying Ambient Temperature Demonstrated Principles • General Time Varying Methodology • Time-Varying Ambient Temperature

Discussion The simple CHEXA element example is extended to illustrate convection with a time-varying ambient temperature. In this case, the nonconstant temperature disallows the use of an SPC for this specification. The transient form of the TEMPBC Bulk Data entry is demonstrated. The TEMPBC is treated with the same methodology as a thermal load for transient analysis (see Figure 5-22 for input schematic). Note the Case Control request for DLOAD = SID. y

h = 100. W ⁄ m

5

T∞ = f ( t )

8

2 o

C

(see Figure 5-23) o

T element ( t = 0.0 ) = 0 C 7

6

4

1

2

x

3

z Figure 5-22 Example 7b

Main Index

CHAPTER

500.

T∞ ( t )

1000.

2000.

3000.

t ( sec ) Figure 5-23 T ∞ versus Time CASE CONTROL DLOAD = SID

TLOADn

SID

DAREA

DELAY

TYPE

TID

“LOAD”

SID

DELAY

SID

P1

C1

T1

P2

C2

T2

TABLEDi

ID

X1

x1

y1

x2

y2

x3

y3

x4

Figure 5-24 General Transient Load Methodology The MSC.Nastran input file is shown in Listing 5-42.

Main Index

y4

167

168

Listing 5-42 Example 7b Input File ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 7B ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL IC = 20 TSTEPNL = 100 DLOAD = 200 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS YTITLE = GRID 1 TEMPERATURE DEGREES CELSIUS TCURVE = GRID 1 TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) XTITLE = TIME, SECONDS YTITLE = AMBIENT TEMPERATURE DEGREES CELSIUS TCURVE = AMBIENT TEMPERATURE VS. TIME XYPLOT TEMP/99(T1) BEGIN BULK TSTEPNL,100,7500,1.0,1,,,,U $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0 GRID,4,,1.0,0.0,0.0 GRID,5,,0.0,1.0,0.0 GRID,6,,0.0,1.0,1.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,1.0,0.0 GRID,99,,99.0,99.0,99.0 $ CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,204.0,896.0,2707.0,100.0 $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6

Main Index

CHAPTER

Listing 5-42 Example 7b Input File (continued) $ CONV,10,35,,,99 CONV,20,35,,,99 CONV,30,35,,,99 CONV,40,35,,,99 CONV,50,35,,,99 CONV,60,35,,,99 PCONV,35,15,0,0.0 $ TLOAD1,200,300,,,400 TABLED1,400,,,,,,,,+TBD1 +TBD1,0.0,0.0,1000.0,1.0,2000.0,1.0,3000.0,0.0,+TBD2 +TBD2,4000.0,0.0,ENDT TEMPBC,300,TRAN,500.0,99 TEMP,20,99,0.0 TEMPD,20,0.0 $ ENDDATA

Results An MSC.Nastran X-Y plot of ambient temperature versus time is shown in Figure 5-25. An MSC.Nastran X-Y plot of grid 1 temperature versus time is shown in Figure 5-26.

Main Index

169

170

Figure 5-25 Ambient Temperature versus Time

Main Index

CHAPTER

Figure 5-26 Grid 1 Temperature versus Time

Main Index

171

172

5.20

Example 7c - Time Varying Loads Demonstrated Principle • Time-Varying Loads

Discussion As discussed in regard to steady state analysis (see “Thermal Loads” on page 12), internal heat generation is considered to be a thermal load and as such is Case Control selectable. In a transient analysis, this allows for using the time loading scheme illustrated in the previous example (see Figure 5-24). This methodology can be applied to any SID selectable load. h = 100. W ⁄ m

y

2 o

C

HGEN = 10. 5

o

T ∞ = 0. C

8

o

T element ( t = 0.0 ) = 0. C 6

7 4

1

2

x

3

z Figure 5-27 Example 7c

10,000. QVOL 3

(W ⁄ m )

1000.

2000. t ( sec )

Figure 5-28 Internal Heat Generation Rate versus Time Main Index

CHAPTER

The MSC.Nastran input file is shown in Listing 5-43. Listing 5-43 Example 7c Input File ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 7C ANALYSIS = HEAT THERMAL = ALL SPC = 10 IC = 20 TSTEPNL = 100 DLOAD = 200 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS YTITLE = GRID 1 TEMPERATURE DEGREES CELSIUS TCURVE = GRID 1 TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) BEGIN BULK TSTEPNL,100,5900,1.0,1 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0 GRID,4,,1.0,0.0,0.0 GRID,5,,0.0,1.0,0.0 GRID,6,,0.0,1.0,1.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,1.0,0.0 GRID,99,,99.0,99.0,99.0 $

Main Index

173

174

Listing 5-43 Example 7c Input File (continued) CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,204.0,896.0,2707.0,100.0,,10.0 $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6 $ CONV,10,35,,,99 CONV,20,35,,,99 CONV,30,35,,,99 CONV,40,35,,,99 CONV,50,35,,,99 CONV,60,35,,,99 PCONV,35,15,0,0.0 $ TLOAD1,200,300,,,400 TABLED1,400,,,,,,,,+TBD1 +TBD1,0.0,0.0,1000.0,1.0,2000.0,0.0,3000.0,0.0,+TBD2 +TBD2,ENDT QVOL,300,10000.0,,1 $ SPC,10,99,,0.0 TEMP,20,99,0.0 TEMPD,20,0.0 $ ENDDATA

Note: HGEN field on MAT4 is 10.0. It multiplies the QVOL entry.

Results An MSC.Nastran X-Y plot of grid 1 temperature versus time is shown in Figure 5-29.

Main Index

CHAPTER

Figure 5-29 Grid 1 Temperature versus Time

Main Index

175

176

5.21

Example 7d - Time Varying Heat Transfer Coefficient Demonstrated Principles • Specification of Multiple Loads.

Discussion There are a number of boundary conditions which are not defined as loads (“Thermal Capabilities” on page 5) and as a result cannot be made time varying in the same fashion as described in “Example 7c - Time Varying Loads” on page 172. In most cases, transient behavior can be introduced into the boundary condition (convection or radiation) through specification of a control node. The control node can be a simple free grid point, an SPOINT, or an active degree of freedom in the system. In this example we drive the value of the control node explicitly via TEMPBC and related TLOAD1 and TABLED1 statements to produce a free convection heat transfer coefficient which varies with time. We also demonstrate the use of the DLOAD statement in the Bulk Data for applying more than one TLOADi in the same analysis. y

o

h = 1000. W ⁄ m 2 C o

T ∞ = 0. C (grid point 99) Q 0 = 6. ⋅ (50,000.) W o

T element ( t = 0.0 ) = 0. C

5

8

6

7 1

2

4

3

z Figure 5-30 Example 7d

Main Index

x

CHAPTER

1.0

U CN

0.0 1000.

2000. t ( sec )

Figure 5-31 Control Node (Grid Point 50) for Free Convection Boundary Condition The MSC.Nastran input file is shown in Listing 5-44. Listing 5-44 Example 7d Input File ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 7D ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 IC = 20 TSTEPNL = 100 DLOAD = 200 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS YTITLE = GRID 1 TEMPERATURE DEGREES CELSIUS TCURVE = GRID 1 TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) XTITLE = TIME, SECONDS YTITLE = GRID 50 TEMPERATURE DEGREES CELSIUS TCURVE = GRID 50 TEMPERATURE VS. TIME XYPLOT TEMP/50(T1) BEGIN BULK TSTEPNL,100,490,10.0,,,,U $

Main Index

177

178

Listing 5-44 Example 7d Input File (continued) GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0 GRID,4,,1.0,0.0,0.0 GRID,5,,0.0,1.0,0.0 GRID,6,,0.0,1.0,1.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,1.0,0.0 GRID,50,,50.0,50.0,50.0 GRID,99,,99.0,99.0,99.0 $ CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,204.0,896.0,2707.0,1000.0 $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6 $ CONV,10,35,,50,99 CONV,20,35,,50,99 CONV,30,35,,50,99 CONV,40,35,,50,99 CONV,50,35,,50,99 CONV,60,35,,50,99 PCONV,35,15,0,0.0 $ DLOAD,200,1.0,1.0,300,1.0,400 $ TLOAD1,300,500,,,700 TABLED1,700,,,,,,,,+TBD700 +TBD700,0.0,1.0,1000.0,1.0,ENDT QBDY3,500,50000.0,,10,THRU,60,BY,10 $ TLOAD1,400,600,,,800 TABLED1,800,,,,,,,,+TBD800 +TBD800,0.0,0.0,1000.0,0.0,2000.0,1.0,5000.0,1.0,+TBD801 +TBD801,ENDT TEMPBC,600,TRAN,1.0,50 SPC,10,99,,0.0 TEMP,20,99,0.0 TEMPD,20,0.0 $ ENDDATA

Main Index

CHAPTER

Results An MSC.Nastran X-Y plot of the control node, grid point 50, temperature versus time is shown in Figure 5-32. An MSC.Nastran X-Y plot of grid point 1 temperature versus time is shown in Figure 5-33.

Figure 5-32 Grid 50 Temperature versus Time

Main Index

179

180

Figure 5-33 Grid 1 Temperature versus Time Examples

Main Index

CHAPTER

5.22

Example 7e - Temperature Dependent Free Convection Heat Transfer Coefficient Demonstrated Principle • Temperature Dependent Heat Transfer Coefficient

Discussion The extension of the temperature dependent free convection heat transfer coefficient is demonstrated for transient analysis. The user specification of this capability is treated the same as in the steady state case, but due to the evolutionary nature of the transient problem, the heat transfer coefficient becomes an implicit function of time. o

o

h ( T ) = 0. W ⁄ m 2 C

( T ≤ 100. C ) o

h ( T ) = 10. ⋅ T – 1000. W ⁄ m 2 C o

( T ≥ 200. C )

o

T ∞ = 0. C (grid point 99) Q 0 = 6. ⋅ (50,000.) W o

T element ( t = 0.0 ) = 0. C 5

8

6

7 x

4

1

2

3

z Figure 5-34 Example 7e

Main Index

o

o

h ( T ) = 1000. W ⁄ m 2 C y

o

( 100. C > T > 200. C )

181

182

1000. h( T) o

( W ⁄ m2 C )

100.

200. o

T ( C) Figure 5-35 h(T) versus T The MSC.Nastran input file is shown in Listing 5-45. Listing 5-45 Example 7e Input File ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 7E ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 IC = 20 TSTEPNL = 100 DLOAD = 300 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS YTITLE = GRID 1 TEMPERATURE DEGREES CELSIUS TCURVE = GRID 1 TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) BEGIN BULK TSTEPNL,100,390,10.0,1 $

Main Index

CHAPTER

Listing 5-45 Example 7e Input File (continued) GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,1.0 GRID,3,,1.0,0.0,1.0 GRID,4,,1.0,0.0,0.0 GRID,5,,0.0,1.0,0.0 GRID,6,,0.0,1.0,1.0 GRID,7,,1.0,1.0,1.0 GRID,8,,1.0,1.0,0.0 GRID,99,,99.0,99.0,99.0 $ CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,204.0,896.0,2707.0,1000.0 MATT4,15,,,,40 TABLEM2,40,0.0,,,,,,,+TBM1 +TBM1,0.0,0.0,100.0,0.0,200.0,1.0,1000.0,1.0,+TBM2 +TBM2,ENDT $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6 $ CONV,10,35,,,99 CONV,20,35,,,99 CONV,30,35,,,99 CONV,40,35,,,99 CONV,50,35,,,99 CONV,60,35,,,99 PCONV,35,15,0,0.0 $ TLOAD1,300,500,,,700 TABLED1,700,,,,,,,,+TBD700 +TBD700,0.0,1.0,1000.0,1.0,ENDT QBDY3,500,50000.0,,10,THRU,60,BY,10 $ SPC,10,99,,0.0 TEMP,20,99,0.0 TEMPD,20,0.0 $ ENDDATA

Results An MSC.Nastran X-Y plot of grid 1 temperature versus time is shown in Figure 5-36.

Main Index

183

184

Figure 5-36 Grid 1 Temperature versus Time

Main Index

CHAPTER

5.23

Example 7f - Phase Change Demonstrated Principles • Capturing Latent Heat Effects • Appropriate Convergence Criteria • Numerical Damping • Consistent Units • Enthalpy

Discussion Latent heat effects can be captured by specifying phase change material properties on the MAT4 Bulk Data entry. The information required includes the latent heat and a finite temperature range over which the phase change is to occur. For pure materials, this range can physically be quite small whereas for solutions or alloys the range can be quite large. Numerically, the wider the range the better. It is not recommended to make this range less than a few degrees. Phase change involves the release of considerable amounts of heat while the temperature remains nearly constant. In this case, it is beneficial to consider the change in enthalpy as illustrated in Figure 5-37. The calculated enthalpies are available with the use of DIAG 50, 51, or by the Case Control command ENTHALPY = ALL. The solution sequence for the phase change specific algorithm is discussed in “Method of Solution” on page 57. In the cases that follow, the first variation illustrates freezing. Variation 2 demonstrates melting.

Main Index

185

186

o

h = 100. W ⁄ m 2 C

y

QLAT = 3.34 × 10 5 J ⁄ kg o

TCH = 0. C o

TDELTA = 2. C 5

8

o

T ∞ = – 20. C o

T element ( t = 0 ) = – 20. C 6

7 4

1

2

x

3

z Figure 5-37 Example 7f1 Variation 1 The MSC.Nastran input file is shown in Listing 5-46. Listing 5-46 Example 7f1 Variation 1 Input File ID MSC-NASTRAN V68 SOL 159 DIAG 51 TIME 10 CEND $ TITLE = EXAMPLE 7F1 ANALYSIS = HEAT THERMAL = ALL FLUX = ALL ENTHALPY = ALL SPCF = ALL OLOAD = ALL SPC = 10 IC = 20 TSTEPNL = 100 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS

Main Index

CHAPTER

Listing 5-46 Example 7f1 Variation 1 Input File (continued) YTITLE = TEMPERATURE DEGREES CELSIUS TCURVE = TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) BEGIN BULK PARAM,NDAMP,0.1 TSTEPNL,100,980,5.0,1,,,,,+TSTP +TSTP,0.001 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,0.1 GRID,3,,0.1,0.0,0.1 GRID,4,,0.1,0.0,0.0 GRID,5,,0.0,0.1,0.0 GRID,6,,0.0,0.1,0.1 GRID,7,,0.1,0.1,0.1 GRID,8,,0.1,0.1,0.0 GRID,99,,99.0,99.0,99.0 $ CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,0.569,4217.0,1000.0,100.0,,,0.0,+MAT4 +MAT4,0.0,2.0,3.34E5 $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6 $ CONV,10,35,,,99 CONV,20,35,,,99 CONV,30,35,,,99 CONV,40,35,,,99 CONV,50,35,,,99 CONV,60,35,,,99 PCONV,35,15,0,0.0 $ SPC,10,99,,-20.0 TEMP,20,99,-20.0 TEMPD,20,20.0 $ ENDDATA

Note: NDAMP provides numerical damping for the phase change phenomenon.

Main Index

187

188

Results - Variation 1 An MSC.Nastran X-Y plot of temperature versus time is shown in Figure 5-38.

Figure 5-38 Temperature versus Time (Variation 1)

Main Index

CHAPTER

Variation 2 o

h = 100. W ⁄ m 2 C y

QLAT = 3.34 × 10 5 J ⁄ kg o

TCH = 0. C o

TDELTA = 2. C o

5

8

T ∞ = – 20. C o

T element ( t = 0 ) = 20. C 6

7 1

2

4

3

z Figure 5-39 Example 7f2 Variation 2

Main Index

x

189

190

Listing 5-47 Example 7f2 Variation 2 Input File ID MSC-NASTRAN V68 SOL 159 DIAG 51 TIME 10 CEND $ TITLE = EXAMPLE 7F2 ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 IC = 20 TSTEPNL = 100 OUTPUT(XYPLOT)

Main Index

CHAPTER

Listing 5-47 Example 7f2 Variation 2 Input File (continued) XTITLE = TIME, SECONDS YTITLE = TEMPERATURE DEGREES CELSIUS TCURVE = TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) BEGIN BULK PARAM,NDAMP,0.1 TSTEPNL,100,980,5.0,1,,,,U,+TSTP +TSTP,0.001 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.0,0.0,0.1 GRID,3,,0.1,0.0,0.1 GRID,4,,0.1,0.0,0.0 GRID,5,,0.0,0.1,0.0 GRID,6,,0.0,0.1,0.1 GRID,7,,0.1,0.1,0.1 GRID,8,,0.1,0.1,0.0 GRID,99,,99.0,99.0,99.0 $ CHEXA,1,5,1,2,3,4,5,6,+CHX1 +CHX1,7,8 PSOLID,5,15 MAT4,15,1.88,2040.0,920.0,100.0,,,0.0,+MAT4 +MAT4,0.0,2.0,3.34E5 $ CHBDYE,10,1,1 CHBDYE,20,1,2 CHBDYE,30,1,3 CHBDYE,40,1,4 CHBDYE,50,1,5 CHBDYE,60,1,6 $ CONV,10,35,,,99 CONV,20,35,,,99 CONV,30,35,,,99 CONV,40,35,,,99 CONV,50,35,,,99 CONV,60,35,,,99 PCONV,35,15,0,0.0 $ SPC,10,99,,20.0 TEMP,20,99,20.0 TEMPD,20,-20.0 $ ENDDATA

Main Index

191

192

Results - Variation 2 An MSC.Nastran X-Y plot of temperature versus time is shown in Figure 5-40.

Figure 5-40 Temperature versus Time (Variation 2)

Main Index

CHAPTER

5.24

Example 8 - Temperature Boundary Conditions in Transient Analyses Demonstrated Principles • SPC for Transient Analysis • TEMPBC for Transient Analysis • SLOAD and CELASi for Transient Analysis • Nodal Lumped Heat Capacitance • POINT type CHBDYi

Discussion A radiative equilibrium analysis is used to demonstrate different methods of temperature specification for transient analyses. As discussed in “Thermal Capabilities” on page 5, an SPC is used when the temperature is to remain constant for the duration of the analysis (Variation 1). When the temperature is to vary during the analysis, two methods are available. A TEMPBC of type TRAN, or a CELASi with applied SLOAD can be used. When a TEMPBC is implemented (Variation 2), a thermal conductivity matrix element of magnitude of 1.0E+10 is imposed internally in the form of a penalty method. For many problems this will be adequate for maintaining the grid point temperature while facilitating convergence. In some cases, however, the size of this conductance can be overwhelming with respect to those of the rest of the model. In such a case, it may be difficult to satisfy the convergence criteria due to the dominance of one matrix conductance value. The alternative approach to this problem is to use a CELASi element and specify a consistent conductance or stiffness value for the model in question (Variation 3). The QHBDY power level can be adjusted to maintain the desired temperature. RADBC

o

T ∞ = 300 C o

T element ( t = 0 ) = 0 K

QHBDY Q 0 = 10,000. W ⁄ m 2

Area = 1.0 m 2 ε = α = 1.0 m = 10. kg Figure 5-41 Example 8

The MSC.Nastran input file is shown in Listing 5-48.

Main Index

193

194

Listing 5-48 Example 8a Input File ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 8A ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 IC = 20 TSTEPNL = 100 DLOAD = 200 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS YTITLE = GRID 1 TEMPERATURE KELVIN TCURVE = GRID 1 TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) BEGIN BULK PARAM,TABS,0.0 PARAM,SIGMA,5.67E-8 TSTEPNL,100,1500,1.0,1 $ GRID,1,,0.0,0.0,0.0 GRID,99,,99.0,99.0,99.0 $ CDAMP5,1,5,1 PDAMP5,5,15,10.0 MAT4,15,204.0,896.0 $ CHBDYP,10,25,POINT,,,1,,,+CHP10 +CHP10,45,,,,1.0,0.0,0.0 PHBDY,25,1.0 $ RADM,45,1.0,1.0 RADBC,99,1.0,,10 $ TLOAD1,200,300,,,400 TABLED1,400,,,,,,,,+TBD400 +TBD400,0.0,1.0,1000.0,1.0,ENDT QHBDY,300,POINT,10000.0,1.0,1 $ SPC,10,99,,300.0 TEMP,20,99,300.0 TEMPD,20,0.0 $ ENDDATA

Main Index

CHAPTER

An MSC.Nastran X-Y plot of grid 1 temperature versus time is shown in Figure 5-42.

Figure 5-42 Grid 1 Temperature versus Time

Main Index

195

196

Listing 5-49 Example 8b Input File ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 8B ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL IC = 20 TSTEPNL = 100 DLOAD = 700 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS YTITLE = GRID 1 TEMPERATURE KELVIN TCURVE = GRID 1 TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) BEGIN BULK PARAM,TABS,0.0 PARAM,SIGMA,5.67E-8 TSTEPNL,100,1500,1.0,1,,,,U $ GRID,1,,0.0,0.0,0.0 GRID,99,,99.0,99.0,99.0 $ CDAMP5,1,5,1 PDAMP5,5,15,10.0 MAT4,15,204.0,896.0 $ CHBDYP,10,25,POINT,,,1,,,+CHP10 +CHP10,45,,,,1.0,0.0,0.0 PHBDY,25,1.0 $ RADM,45,1.0,1.0 RADBC,99,1.0,,10 $ DLOAD,700,1.0,1.0,200,1.0,500 TABLED1,400,,,,,,,,+TBD400 +TBD400,0.0,1.0,1000.0,1.0,ENDT $ TLOAD1,200,300,,,400 QHBDY,300,POINT,10000.0,1.0,1 $ TLOAD1,500,600,,,400 TEMPBC,600,TRAN,300.0,99 TEMP,20,99,300.0 TEMPD,20,0.0 $ ENDDATA Main Index

CHAPTER

Figure 5-43 Grid 1 Temperature versus Time

Main Index

197

198

Listing 5-50 Example 8c Input File ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 8C ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL IC = 20 TSTEPNL = 100 DLOAD = 700 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS YTITLE = GRID 1 TEMPERATURE KELVIN TCURVE = GRID 1 TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) BEGIN BULK PARAM,TABS,0.0 PARAM,SIGMA,5.67E-8 TSTEPNL,100,1500,1.0,1 $ GRID,1,,0.0,0.0,0.0 GRID,99,,99.0,99.0,99.0 $ CDAMP5,1,5,1 PDAMP5,5,15,10.0 MAT4,15,204.0,896.0 $ CHBDYP,10,25,POINT,,,1,,,+CHP10 +CHP10,45,,,,1.0,0.0,0.0 PHBDY,25,1.0 $ RADM,45,1.0,1.0 RADBC,99,1.0,,10 $ DLOAD,700,1.0,1.0,200,1.0,500 TABLED1,400,,,,,,,,+TBD400 +TBD400,0.0,1.0,1000.0,1.0,ENDT $ TLOAD1,200,300,,,400 QHBDY,300,POINT,10000.0,1.0,1 $ TLOAD1,500,600,,,400 CELAS2,999,1.0E5,99,1 SLOAD,600,99,300.0E5 TEMP,20,99,300.0 TEMPD,20,0.0 $ ENDDATA

Main Index

CHAPTER

Figure 5-44 Grid 1 Temperature versus Time

Main Index

199

200

5.25

Example 9a - Diurnal Thermal Cycles Demonstrated Principles • Diurnal Heat Loads • Multiple Loads / Multiple CHBDYi’s

Discussion A diurnal heat transfer analysis is performed over a two day cycle. The TLOAD2 Bulk Data entry is used to specify the load function (QVECT) in convenient sinusoidal format. A radiation boundary condition provides the heat loss mechanism to an ambient environment at 300 degrees. In Example 9a, the absorptivity and emissivity are constant and the loading is a function of time based on the load magnitude which reflects a projected area without treating the QVECT as a vector load. In “Example 9b - Diurnal Thermal Cycles” on page 204, the variation of absorptivity with respect to time is added to the problem. Period T = 24 hr = 86,400 sec

QVECT

3 4

1 Frequency F = --- = 1.157 × 10 – 5 Hz T

RADBC 2 1

750.0 QVECT ( W ⁄ m2 )

0

21,600

43,200

64,800

86,400 108,000 129,600 151,200

Day 1

172,800

t ( sec )

Day 2

Day 1

Day 2

Sunrise

t=0

t = 86,400

Noon

t = 21,600

t = 108,000

Sunset

t = 43,200

t = 129,600

Night

43,200 < t < 86,400

129,600 < t < 172,800

Figure 5-45 Example 9a

• Sun heating aluminum plate over two days. • Solar flux = 750 W/m2 at noon. Plate is one square meter and 0.005 meters thick. Ambient temperature is 300°K. Main Index

CHAPTER

2

• Solar flux magnitude varies sinusoidally with an amplitude of 750.0 W ⁄ m , and a period of one day.

• CHBDYG 10 absorbs heat for the first day. • CHBDYG 20 absorbs heat for the second day. • CHBDYG 30 radiates heat both days. Example 9b only:

• Grid 50 is the control node on the QVECT entry. It is forced to vary with time as absorptivity (a) varies with the “attack” angle of the sun, i.e.,

α(θ )

U CNTRLND

θ

t

• So the value of U CNTRLND equals α ( θ ) at any given time (or any given angle: o

o

180 → 12 hr = 43,200 sec, 1 → 240 sec ).

• Absorptivity is set to 1.0 on the RADM card so that U CNTRLND will act as absorptivity: {

P in = α [ e ( t ) ⋅ n ] F ( t – τ ) Q 0 U CNTRLND 1.0

α(θ )

P in = α [ e ( t ) ⋅ n ] F ( t – τ ) Q 0 α ( θ )

• Ex9a. - α = constant • Ex9b. - α = f ( θ ) The MSC.Nastran input file is shown in Listing 5-51.

Main Index

201

202

.

Listing 5-51 Example 9a Input File

ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 9A ANALYSIS = HEAT THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL SPC = 10 IC = 20 TSTEPNL = 100 DLOAD = 200 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS YTITLE = PLATE TEMPERATURE KELVIN TCURVE = PLATE TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) BEGIN BULK PARAM,TABS,0.0 PARAM,SIGMA,5.67E-08 TSTEPNL,100,1728,100.0,1,,,,U $ GRID,1,,0.0,0.0,0.0 GRID,2,,1.0,0.0,0.0 GRID,3,,1.0,1.0,0.0 GRID,4,,0.0,1.0,0.0 GRID,99,,99.0,99.0,99.0 $ CQUAD4,1,5,1,2,3,4 PSHELL,5,15,0.005 MAT4,15,204.0,896.0,2707.0 $ CHBDYG,10,,AREA4,,,45,,,+CHG10 +CHG10,1,2,3,4 CHBDYG,20,,AREA4,,,45,,,+CHG20 +CHG20,1,2,3,4 CHBDYG,30,,AREA4,,,45,,,+CHG30 +CHG30,4,3,2,1 $ DLOAD,200,1.0,1.0,300,1.0,400 TLOAD2,300,1000,,,0.0,43200.0,1.157E-5,-90.0,+TLD300 +TLD300,0.0,0.0 TLOAD2,400,2000,,,86400.0,129600.0,1.157E-5,-90.0,+TLD400 +TLD400,0.0,0.0 QVECT,1000,750.0,,,0.0,0.0,-1.0,,+QVCT1 +QVCT1,10

Main Index

CHAPTER

Listing 5-51 Example 9a Input File (continued) QVECT,2000,750.0,,,0.0,0.0,-1.0,,+QVCT2 +QVCT2,20 RADM,45,0.6,0.6 RADBC,99,1.0,,30 $ SPC,10,99,,300.0 TEMPD,20,300.0 $ ENDDATA

Results An MSC.Nastran X-Y plot of plate temperature versus time is shown in Figure 5-46.

Figure 5-46 Plate Temperature versus Time

Main Index

203

204

5.26

Example 9b - Diurnal Thermal Cycles Demonstrated Principles • Diurnal Heat Loads • Multiple Loads / Multiple CHBDYi’s • Control Node for Directionally Dependent Radiation Surface Properties

Discussion The loading pattern is substantially unchanged from the previous example; however, the effect of variation of surface absorptivity with angle of incident solar radiation is taken into account implicitly via the control node. As in the previous example, we provide independent CHBDY surface elements for each load and boundary condition specification resulting in a total of three surface elements attached to the conduction element. This can sometimes be convenient for postprocessing if we wish to isolate applied load segments of the same type. The MSC.Nastran input file is shown in Listing 5-52.

Main Index

CHAPTER

Listing 5-52 Example 9b Input File ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 9B ANALYSIS = HEAT THERMAL = ALL SPC = 10 IC = 20 TSTEPNL = 100 DLOAD = 200 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS YTITLE = PLATE TEMPERATURE KELVIN TCURVE = PLATE TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) XTITLE = TIME, SECONDS--THETA, DEGREES -- (1.0 DEGREE = 240.0 SECONDS) YTITLE = ABSORPTIVITY TCURVE = ABSORPTIVITY VS. TIME--THETA XYPLOT TEMP/50(T1) XTITLE = TIME, SECONDS--THETA, DEGREES -- (1.0 DEGREE = 240.0 SECONDS) YTITLE = ABSORPTIVITY TCURVE = ABSORPTIVITY VS. TIME--THETA XMIN = 21600.0 XMAX = 43200.0 XYPLOT TEMP/50(T1) BEGIN BULK PARAM,TABS,0.0 PARAM,SIGMA,5.67E-08 TSTEPNL,100,1728,100.0,1,,,,U $ GRID,1,,0.0,0.0,0.0 GRID,2,,1.0,0.0,0.0 GRID,3,,1.0,1.0,0.0 GRID,4,,0.0,1.0,0.0 GRID,50,,50.0,50.0,50.0 GRID,99,,99.0,99.0,99.0 $ CQUAD4,1,5,1,2,3,4 PSHELL,5,15,0.005 MAT4,15,204.0,896.0,2707.0 RADM,45,1.0,0.6 RADM,46,0.6,0.6 $

Main Index

205

206

Listing 5-52 Example 9b Input File (continued) CHBDYG,10,,AREA4,,,45,,,+CHG10 +CHG10,1,2,3,4 CHBDYG,20,,AREA4,,,45,,,+CHG20 +CHG20,1,2,3,4 CHBDYG,30,,AREA4,,,46,,,+CHG30 +CHG30,4,3,2,1 DLOAD,200,1.0,1.0,300,1.0,400,1.0,500 TLOAD2,300,1000,,,0.0,43200.0,1.157E-5,-90.0,+TLD300 +TLD300,0.0,0.0 TLOAD2,400,2000,,,86400.0,129600.0,1.157E-5,-90.0,+TLD400 +TLD400,0.0,0.0 QVECT,1000,750.0,,,0.0,0.0,-1.0,50,+QVCT1 +QVCT1,10 QVECT,2000,750.0,,,0.0,0.0,-1.0,50,+QVCT2 +QVCT2,20 RADBC,99,1.0,,30 $ TLOAD1,500,600,,,700 TABLED1,700,,,,,,,,+TBD1 +TBD1,0.0,0.15,2400.0,0.50,3600.0,0.60,4800.0,0.55,+TBD2 +TBD2,7200.0,0.375,9600.0,0.275,12000.0,0.225,14400.0,0.20,+TBD3 +TBD3,16800.0,0.16,19200.0,0.15,21600.0,0.15,24000.0,0.15,+TBD4 +TBD4,26400.0,0.16,28800.0,0.20,31200.0,0.225,33600.0,0.275,+TBD5 +TBD5,36000.0,0.375,38400.0,0.55,39600.0,0.60,40800.0,0.50,+TBD6 +TBD6,43200.0,0.15,86400.0,0.15,88800.0,0.50,90000.0,0.60,+TBD7 +TBD7,91200.0,0.55,93600.0,0.375,96000.0,0.275,98400.0,0.225,+TBD8 +TBD8,100800.0,0.20,103200.0,0.16,105600.0,0.15,108000.0,0.15,+TBD9 +TBD9,110400.0,0.15,112800.0,0.16,115200.0,0.20,117600.0,0.225,+TBD10 +TBD10,120000.0,0.275,122400.0,0.375,124800.0,0.55,126000.0,0.60,+TBD11 +TBD11,127200.0,0.50,129600.0,0.15,172800.0,0.15,ENDT TEMPBC,600,TRAN,1.0,50 $ SPC,10,99,,300.0 TEMP,20,50,0.15 TEMPD,20,300.0 $ ENDDATA

Results MSC.Nastran X-Y plots showing absorptivity versus time are shown in Figure 5-47 and Figure 5-48. Plate temperature versus time is shown in Figure 5-49.

Main Index

CHAPTER

QVECT

nˆ θ

Figure 5-47 α ( θ ) versus θ

Main Index

207

208

α ( θ ) = 0.15 = constant

Sunrise

Noon

Sunset

Sunrise

α ( θ ) = 0.15 = constant

Noon

Figure 5-48 α ( θ ) versus θ

Main Index

Sunset

CHAPTER

Figure 5-49 Plate Temperature versus Time

Main Index

209

210

5.27

Example 10 - Thermostat Control Demonstrated Principles • NOLINs and MPCs • Thermostat Control

Discussion A thermostat is modeled using the nonlinear transient forcing function (NOLIN3) as a heating element and the multi-point constraint (MPC) relationship to provide the thermostat connections. One end of the rod element structure has the thermocouple attached to it and is subject to convective losses to the ambient environment at 0.0 °C . When this local temperature drops below 100.0 °C , heating occurs at the opposite end of the structure at a constant rate. Conversely, when the thermocouple temperature exceeds 100.0 °C , the heat load is removed. There is an inherent delay in this system associated with the distance between the thermocouple and the point of application of the heat load as well as the delay generated as a result of the thermal diffusivity of the material. P IN ( t ) (NOLIN3)

T ∞ = 0.0 1

2

3

4

5

6

h = 200. MPC

T 0 = 110

o

(Initial Condition)    50,000. , T 50 > 0  P IN ( t ) =   0.0 , T 50 ≤ 0    

– T 50 + 100. ⋅ T 51 – T 6 = 0 Let T 51 = 1.0 T 50 = – 1.0 ( – 100. + T 6 )

Dummy Grid Points: 50, 51, 99 Figure 5-50 Example 10 The MSC.Nastran input file is shown in Listing 5-53.

Main Index

CHAPTER

Listing 5-53 Example 10 Input File ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 10 ANALYSIS = HEAT THERMAL = ALL SPC = 10 IC = 20 MPC = 30 TSTEPNL = 100 NONLINEAR = 300 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS YTITLE = GRID 1 TEMPERATURE DEGREES CELSIUS TCURVE = GRID 1 TEMPERATURE VS. TIME XYPLOT TEMP/1(T1) XTITLE = TIME, SECONDS YTITLE = GRID 6 TEMPERATURE DEGREES CELSIUS TCURVE = GRID 6 TEMPERATURE VS. TIME XYPLOT TEMP/6(T1) BEGIN BULK TSTEPNL,100,30000,1.0,1 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.1,0.0,0.0 GRID,3,,0.2,0.0,0.0 GRID,4,,0.3,0.0,0.0 GRID,5,,0.4,0.0,0.0 GRID,6,,0.5,0.0,0.0 GRID,50,,50.0,50.0,50.0 GRID,51,,51.0,51.0,51.0 GRID,99,,99.0,99.0,99.0 $ CROD,1,5,1,2 CROD,2,5,2,3 CROD,3,5,3,4 CROD,4,5,4,5 CROD,5,5,5,6 PROD,5,15,1.0 MAT4,15,204.0,896.0,2707.0,200.0 $ CHBDYE,60,5,3 $ CONV,60,35,,,99 PCONV,35,15,0,0.0 $ NOLIN3,300,1,,50000.0,50,1,0.0

Main Index

211

212

Listing 5-53 Example 10 Input File (continued) SPC,10,51,,1.0 SPC,10,99,,0.0 TEMP,20,51,1.0 $ MPC,30,6,,-1.0,50,,-1.0,,+MPC +MPC,,51,,100.0 $ TEMP,20,99,0.0 TEMP,20,50,-10.0 TEMPD,20,110.0 $ ENDDATA

Results An MSC.Nastran X-Y plot of grid 1 temperature versus time is shown in Figure 5-52. An MSC.Nastran X-Y plot of grid 6 temperature versus time is shown in Figure 5-53.

Main Index

CHAPTER

Figure 5-51 Grid 1 Temperature versus Time

Figure 5-52 Grid 6 Temperature versus Time

Main Index

213

214

5.28

Example 11 - Transient Forced Convection Demonstrated Principle • Evolving Fluid Transients

Discussion It may be desirable to consider fluid flow problems from a transient view point. In particular, fluid loops when used in conjunction with the thermostat control described in “Example 10 Thermostat Control” on page 210 are most useful in transient analysis. Accurate temporal response requires some user control be exerted over the Courant Number as discussed in “Thermal Capabilities” on page 5. In some cases, where steady state convergence is difficult or impossible to achieve, it may prove beneficial to let the transient system evolve toward its long time solution, thereby achieving the steady state equivalent. The transient analysis has inherent damping associated with the heat capacitance and can also utilize numerical damping through the NDAMP parameter. Additionally, loading patterns can be applied gradually with respect to time in an ad hoc load incrementing scheme which may prove more flexible than the load incrementing which is available in the steady state solution sequence.

Fluid Problems - Consistent Units H20 Example: o

C p ∼ 4200. J ⁄ kg C ( 1J = 1W ⁄ sec ) ρ ∼ 1000. kg ⁄ m 3 kg µ ∼ 10 – 3 ------------------m ⋅ sec · m ∼ kg ⁄ sec l∼m ν ∼ m ⁄ sec o

h ∼ W ⁄ m2 C o

o

k ∼ W ⁄ m C ( .65 W ⁄ m C ) Dνρ m ⋅ m ⁄ sec ⋅ kg ⁄ m 3 Re = ----------- ⇒ -------------------------------------------------------- ⇒ NONDIMENSIONAL µ kg ⁄ m sec Main Index

CHAPTER

· m = ρνA ⇒ kg ⁄ m 3 ⋅ m ⁄ sec ⋅ m 2 ⇒ kg ⁄ s o Cp µ J ⁄ kg C ⋅ kg ⁄ m sec Pr = ---------- ⇒ ----------------------------------------------------------- ⇒ NONDIMENSIONAL o k W⁄m C 2 o

hx W⁄m C⋅m u = ------ ⇒ ---------------------------------------- ⇒ NONDIMENSIONAL o k W⁄m C o

T wall = 0 C o

T exit

T in = 100 C 1

L = 1.0 m,

2

3

4

5

6

7

9

10 11

· m = 0.1 kg ⁄ sec

D = 0.01 m,

K H = 0.023 ---- Re 0.8 Pr n D

8

n = 0.4 (heating of fluid) n = 0.3 (cooling of fluid) valid for 0.7 ≤ Pr ≤ 160. Re ≤ 10,000. L ---- ≥ 10. D

Use water properties at T = 82.22 °C (Heat Transfer, J. P. Holman). Figure 5-53 Example 11 The MSC.Nastran input file is shown in Listing 5-54.

Main Index

215

216

Listing 5-54 Example 11 Input File ID MSC-NASTRAN V68 SOL 159 TIME 10 CEND TITLE = EXAMPLE 11 ANALYSIS = HEAT THERMAL = ALL SPC = 10 IC =20 TSTEPNL = 100 OUTPUT(XYPLOT) XTITLE = TIME, SECONDS YTITLE = EXIT TEMPERATURE DEGREES CELSIUS TCURVE = EXIT TEMPERATURE VS. TIME XYPLOT TEMP/11(T1) BEGIN BULK TSTEPNL,100,400,0.005,1,,,,U,+TSTP +TSTP,0.05 $ GRID,1,,0.0,0.0,0.0 GRID,2,,0.1,0.0,0.0 GRID,3,,0.2,0.0,0.0 GRID,4,,0.3,0.0,0.0 GRID,5,,0.4,0.0,0.0 GRID,6,,0.5,0.0,0.0 GRID,7,,0.6,0.0,0.0 GRID,8,,0.7,0.0,0.0 GRID,9,,0.8,0.0,0.0 GRID,10,,0.9,0.0,0.0 GRID,11,,1.0,0.0,0.0 GRID,50,,50.0,50.0,50.0 GRID,99,,99.0,99.0,99.0 $ CHBDYP,10,25,FTUBE,,,1,2 CHBDYP,20,25,FTUBE,,,2,3 CHBDYP,30,25,FTUBE,,,3,4 CHBDYP,40,25,FTUBE,,,4,5 CHBDYP,50,25,FTUBE,,,5,6 CHBDYP,60,25,FTUBE,,,6,7 CHBDYP,70,25,FTUBE,,,7,8 CHBDYP,80,25,FTUBE,,,8,9 CHBDYP,90,25,FTUBE,,,9,10 CHBDYP,100,25,FTUBE,,,10,11 PHBDY,25,,0.01,0.01 $ CONVM,10,35,,50,99 CONVM,20,35,,50,99 CONVM,30,35,,50,99

Main Index

CHAPTER

Listing 5-54 Example 11 Input File (continued) CONVM,40,35,,50,99 CONVM,50,35,,50,99 CONVM,60,35,,50,99 CONVM,70,35,,50,99 CONVM,80,35,,50,99 CONVM,90,35,,50,99 CONVM,100,35,,50,99 PCONVM,35,15,1,1,0.023,0.8,0.4,0.3 MAT4,15,0.673,4195.0,970.2,,8.6E-4 $ SPC,10,1,,100.0 SPC,10,50,,0.1 SPC,10,99,,0.0 TEMP,20,1,100.0 TEMP,20,50,0.1 TEMP,20,99,0.0 TEMPD,20,100.0 $ ENDDATA

Results Temperature versus distance is shown in Figure 5-54. Exit temperature versus time is shown in Figure 5-55. Exit temperature versus mass flow rate is shown in Figure 5-56.

Main Index

217

218

100

(0.0, 100.) (0.1, 95.3) (0.2, 90.8)

90

(0.3, 86.6) (0.4, 82.5) 80

(0.5, 78.6)

T

(0.6, 75.0)

o

( C)

(0.7, 71.4)

70

(0.8, 68.1) (0.9, 64.9) (1.0, 61.8)

60

50 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Distance (meters) Figure 5-54 Temperature versus Distance

Main Index

0.8

0.9

1.0

CHAPTER

Figure 5-55 Exit Temperature versus Time

Main Index

219

220

80

(1.1, 74.1)

75 (0.9, 73.2) (0.7, 72.0) (0.5, 70.4)

(1.2, 74.4) (1.0, 73.7)

(0.6, 71.3)

70 (0.4, 69.3)

(0.3, 67.9)

T exit

(0.8, 72.6)

(1.3, 74.8)

o

( C) (0.2, 65.7)

65

(0.1, 61.8)

60

(0.075, 60.2) (0.05, 58.2)

55 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7 0.8

0.9

1.0

1.1

1.2

1.3

1.4

· m ( kg ⁄ sec ) Figure 5-56 Exit Temperature versus Mass Flow Rate at Equilibrium (Constant Properties)

Main Index

CHAPTER

5.29

Example 12 - Thermostat Control with Deadband Applied to a Heat Source Demonstated Principles • Thermal Control Mechanisms

Discussion Thermal loads (QVOL, QVECT, QBDY3) can be thermostatically controlled by including a CONTRLT Bulk Data entry in the model. A schematic of the process is given in Figure 5-57.

Switch Status = Off

PL PH

T Sensor

Switch Status = On

Figure 5-57 This capability provides thermal control for heating elements with these features: 1. Sensor temperature can be measured from any GRID or scalar point in the model. 2. Numerous switch formats are available with user-defined deadbands. 3. The sensor (thermacouple) can be continuously monitored or it can be evaluated at a user-defined sampling rate starting from TIME = 0.0 When the sensor is sampled, the control logic is evaluated and any necessary control action is enforced. 4. The control device can account for physical actuator time delay and rise and decay time constants. Main Index

221

222

5. Automatic time stepping is handled internaly giving priority to any controller action which is in effect. Outside of the control action regions, the time steps size reverts back to the time step size, DT, specified by the user on the TSTEPNL statement. The standard nonlinear time-step adjustment algorithm is not implemented for control logic analysis.

Example - Lumped Heat Capacitance with Thermostat Control of a Volumetric Heat Source QVOL

h, T ∞ Figure 5-58 ρ ⋅ Vol ⋅ C p = 6000. J ⁄ °C QVOL = 12000. W T(o)

= 0.0 °C

h⋅A

= 100.0 W ⁄ °C

T∞

= 0.0 °C

PL

= 80.0 °C

PH

= 100.0 °C h⋅A 1 1 = ------------------------------- = ------ ----------ρ ⋅ Vol ⋅ C p 60 sec

B

Input

Main Index

T(t)

= 120. ⋅ ( 1 – e

T ( 107.5 )

= 100.0 °C

– Bt

)

CHAPTER

5.30

Example 13 - Cryogenic Heat Shielding Demonstrated Principles • Axisymmetric View Factors • Multiple Cavities • Radiation Matrix Control

Discussion A study is performed to examine the effects of multiple radiation shields for maintaining a cryogenic environment. The number of cylindrical layers of material as well as the surface emissivities are varied and the total heat flow for each variation is recovered. The radiation exchange can be modeled in several ways. If each radiation gap is treated as an individual cavity, then the minimum number of view factor calculations will be performed. In this case, the surface exchange elements should be designated as can shade for the element on the inner radius and can be shaded for the element on the outer radius. These designations are made on the shade field on the VIEW Bulk Data entry. For axisymmetric view factor calculations, it will often be difficult to set the shadowing flags correctly. The user may find it easier to make shade = both in these instances and pay a penalty in CPUs. If a multiple cavity approach is used, then there will be a RADLST and RADMTX for each cavity. Using a single cavity approach, all the radiation surface elements are entered on a single RADLST, and the VIEW3D routine automatically sorts out those that can see each other and determines the magnitude of the axisymmetric view factors between each active pair. The accuracy of the axisymmetric view factors can be controlled in several ways. The process used in MSC.Nastran relies on internally creating a semi-circle of computational elements and applying symmetry arguments in forming the view factor between REV type surface elements. This is described in greater detail in Appendix . Since the core or component view factors are computed using the generalized 3D methods (Gaussian/contour integrations with error corrections), similar modeling principles apply. A good model will select NCOMP (field 9 on RADCAV) to generate elements that are approximately square. The model represents az-slice of a container configuration, however, nothing special has been included in the model to prevent the exchange surfaces from communicating with the external environment. This can be controlled by setting the MTXTYP = 4 on the RADLST Bulk Data entry. The flow of heat is then purely radial with no exchange with space.

Main Index

223

224

Model Geometry - Axisymmetric Analysis with Radiation Exchange Z 1.50 1.0

.25 .25

T o, h o

k nˆ nˆ

nˆ nˆ

nˆ

Ti

n = 2

n = 1

.

.

.50

.

Dimensions in Centimeters R

Ti

= 77°k

T o = 293°k 2

ho

= 10.0 w ⁄ m °k

k

= .01 w ⁄ m k

∈

= .1, .5, .9

n

= 1, 2, 3, 4

2

Listing 5-55 shield_scale Get from Dan Chu

Results View Factor Calculation:

Main Index

CHAPTER

Main Index

225

226

Main Index

MSC.Nastran Thermal Analysis User’s Guide

APPENDIX

A

Nomenclature for Thermal Analysis

■ Commonly Used Terms

Main Index

228

A.1

Commonly Used Terms This appendix provides nomenclature for terms commonly used in thermal analysis.

Main Index

k

Thermal conductivity

ρ

Density

Cp

Specific heat

h, H

Free convection heat transfer coefficient

H

Enthalpy

V

Velocity

µ

Dynamic viscosity

υ

Kinematic viscosity

Nu

Nusselt’s number

Re

Reynolds’ number

Pr

Prandtl’s number

Gr

Grashof’s number

β

Volume coefficient of expansion

q

Heat flux

Q

Heat flow

T, u

Temperature

g

Acceleration due to gravity

Tw

Wall temperature

T∞

Ambient temperature

σ

Stefan-Boltzmann constant

υ

Planck’s Second constant

F ij

View factor

t

Time

ε

Emissivity

α · m

Absorptivity Mass flow rate

MSC.Nastran Thermal Analysis User’s Guide

APPENDIX

B

Executive Control Section

■ Frequently Used Executive Control Statements

Main Index

230

2.1

Frequently Used Executive Control Statements This appendix lists the Executive Control statements that are often used for thermal analysis. The Executive Control statements are listed alphabetically. The description of each statement is similar to that found in the MSC.Nastran Quick Reference Guide. The MSC.Nastran Quick Reference Guide describes all of the Executive Control statements.

Main Index

CHAPTER B Executive Control Section

CEND

End of Executive Control Delimiter

Designates the end of the Executive Control Section. Format: CEND Remark: 1. CEND is required unless an ENDJOB statement appears in the File Management Section.

Main Index

231

232

Request Diagnostic Output

DIAG

Requests diagnostic output or special options. Format: DIAG [=] k1[k2, ..., kn] Describer

Meaning

ki

A list separated by commas and/or spaces of desired diagnostics.

Remarks: 1. The DIAG statement is optional. 2. Multiple DIAG statements are allowed. 3. The following table lists the possible values for ki and their corresponding actions:

Main Index

k=1

Dumps memory when a nonpreface fatal message is generated.

k=2

Prints database directory information before and after each DMAP statement. Prints bufferpooling information.

k=3

Prints “DATABASE USAGE STATISTICS” after execution of each functional module. This message is the same as the output that appears after the run terminates. See the “Output Description” on page 373 of the MSC.Nastran Reference Guide.

k=4

Prints cross-reference tables for compiled sequences. Equivalent to the COMPILER REF statement.

k=5

Prints the BEGIN time on the operator’s console for each functional module. See the “Output Description” on page 373 of the MSC.Nastran Reference Guide.

k=6

Prints the END time for each functional module in the log file or day file and on the operator’s console. Modules that consume less time than the threshold set by SYSTEM(20) do not create a message. See the “Output Description” on page 373 of the MSC.Nastran Reference Guide.

k=7

Prints eigenvalue extraction diagnostics for the Complex Determinate method.

k=8

Prints matrix trailers as the matrices are generated in the Execution Summary Table. See the “Output Description” on page 373 of the MSC.Nastran Reference Guide.

k=9

Not used.

k=10

Uses alternate nonlinear loading in linear transient analysis. Replaces N n + 1 with ( N n + 1 + N n + N n – 1 ) ⁄ 3

k=11

DBLOAD, DBUNLOAD, and DBLOCATE diagnostics.

CHAPTER B Executive Control Section

Main Index

k=12

Prints eigenvalue extraction diagnostics for complex Inverse Power and complex Lanczos methods.

k=13

Prints the open core length (the value of REAL on VAX computers). See the “Output Description” on page 373 of the MSC.Nastran Reference Guide.

k=14

Prints solution sequence. Equivalent to the COMPILER LIST statement.

k=15

Prints table trailers.

k=16

Traces real inverse power eigenvalue extraction operations

k=17

Punches solution sequences. Equivalent to the COMPILER DECK statement.

k=18

In aeroelastic analysis, prints internal grid points specified on SET2 Bulk Data entries.

k=19

Prints data for MPYAD and FBS method selection in the Execution Summary Table.

k=20

Similar to DIAG 2 except the output appears in the Execution Summary Table and has a briefer and more user-friendly format. However, the .f04 file will be quite large if DIAG 20 is specified with an MSC.Nastran solution sequence. A DMAP Alter with DIAGON(20) and DIAGOFF(20) is recommended. DIAG 20 also prints DBMGR, DBFETCH, and DBSTORE subDMAP diagnostics. See the MSC.Nastran 2005 DMAP Programmer’s Guide.

k=21

Prints diagnostics of DBDIR and DBENTRY table.

k=22

EQUIV and EQUIVX module diagnostics.

k=23

Not used.

k=24

Prints files that are left open at the end of a module execution. Also prints DBVIEW diagnostics.

k=25

Outputs internal plot diagnostics.

k=26

Dynamic file allocation diagnostics on IBM/MVS computers.

k=27

Prints Input File Processor (IFP) table. See the MSC.Nastran Programmer’s Manual, Section 4.5.9.

k=28

Punches the link specification table. (XBSBD). The Bulk Data and Case Control Sections are ignored, and no analysis is performed.

k=29

Process link specification table update. The Bulk Data and Case Control Sections are ignored, and no analysis is performed. See the MSC.Nastran Programmer’s Manual, Section 6.10.3.1.

233

234

Main Index

k=30

In link 1, punches the XSEMii data (i.e., set ii via DIAG 1 through 15). The Bulk Data and Case Control Sections are ignored, and no analysis is performed. After link 1, this turns on BUG output. Used also by MATPRN module. See also Remark 5 on the “TSTEP” on page 2137 Bulk Data entry.

k=31

Prints link specification table and module properties list (MPL) data. The Bulk Data and Case Control Sections are ignored, and no analysis is performed.

k=32

Prints diagnostics for XSTORE and PVA expansion.

k=33

Not used.

k=34

Turns off plot line optimization.

k=35

Prints diagnostics for 3-D slideline contact analysis in SOLs 106 and 129.

k=36

Prints extensive tables generated by the GP0 module in p-version analysis.

k=37

Disables the superelement congruence test option and ignores User Fatal Messages 4277 and 4278. A better alternative is available with PARAMeter CONFAC. See “Parameters” on page 601.

k=38

Prints material angles for CQUAD4, CQUAD8, CTRIA3, and CTRIA6 elements. The angle is printed only for elements that specify MCID in field 8 of the connection entry.

k=39

Traces module FA1 operations and aerodynamic splining in SOLs 145 and 146.

k=40

Print constraint override/average information for edges and faces in p-adaptive analysis

k=41

Traces GINO OPEN/CLOSE operations.

k=42

Not used.

k=43

Not used.

k=44

Prints a mini-dump for fatal errors and suppresses user message exit.

k=45

Prints the same database directory information as DIAG 2 except that it prints only after each DMAP statement.

k=46

Used by MSC development for GINO printout.

k=47

Prints DBMGR, DBFETCH, and DBSTORE subDMAP diagnostics.

k=48

Used by MSC development for GINO printout.

k=49

DIAG 49 is obsolete and should not be used. The utility f04rprt should be used to summarize the f04 Execution Summary instead..

CHAPTER B Executive Control Section

k=50

Traces the nonlinear solution in SOLs 106, 129, 153, and 159. Prints subcase status; echoes NLPARM, NLPCI, and TSTEPNL entry fields; and prints initial arc-length. Prints iteration summary only in SOLs 129, and 159. In static aeroelastic analysis (SOL 144), prints transformation information associated with the generation of the DJX matrix in the ADG module and intermediate solutions information in the ASG module.

k=51

Prints intermediate displacement, load error vectors, and additional iteration information helpful to debugging in SOLs 106, 129, 153, and 159.

k=52

Disables the printing of errors at each time step in SOLs 129 and 159.

k=53

MESSAGE module output will also be printed in the execution summary table. See the “Output Description” on page 373 of the MSC.Nastran Reference Guide.

k=54

Linker debug print.

k=55

Performance timing.

k=56

Extended print of Execution Summary table (prints all DMAP statements and RESTART deletions). See the “Output Description” on page 373 of the MSC.Nastran Reference Guide.

k=57

Executive table (XDIRLD) performance timing and last-time-used (LTU) diagnostics.

k=58

Data block deletion debug and timing constants echo.

k=59

Buffpool debug printout.

k=60

Prints diagnostics for data block cleanup at the end of each module execution in subroutines DBCLN, DBEADD, and DBERPL.

k=61

GINO block allocator diagnostics.

k=62

GINO block manager diagnostics.

k=63

Prints each item checked by the RESTART module and its NDDL description.

k=64

Requests upward compatibility DMAP conversion from Version 65 only. Ignored in Version 70.5 and later systems.

Examples: DIAG 8,53 or DIAG 8 DIAG 53 Main Index

235

236

ECHO

Control Printed Echo

Controls the echo (printout) of the Executive Control Section. Formats: ECHOOFF ECHOON Remarks: 1. The ECHO statement is optional. 2. ECHOOFF suppresses the echo of subsequent Executive Control statements. ECHOON reactivates the echo after an ECHOOFF statement.

Main Index

CHAPTER B Executive Control Section

Comment

ID

Specifies a comment. Format: ID [=] i1, i2 Describer

Meaning

i1, i2

Character strings (1 to 8 characters in length and the first character must be alphabetic).

Remark: 1. The ID statement is optional and not used by the program.

Main Index

237

238

.

Execute a Solution Sequence

SOL

Specifies the solution sequence or main subDMAP to be executed. Format:   n SOL   [ SOLIN = obj-DBset  subDMAP-name 

NOEXE ]

Describer

Meaning

n

Solution number. See Remark 6. for the list of valid numbers. (Integer>0)

subDMAP-name

The name of a main subDMAP. See the MSC.Nastran 2005 DMAP Programmer’s Guide. (Character; 1 to 8 alphanumeric characters in length and the first character must be alphabetic.)

obj-DBset

The character name of a DBset where the OSCAR is stored. See Remarks 1. and 2. (Character; 1 to 8 alphanumeric characters in length and the first character must be alphabetic.)

NOEXE

Suppresses execution after compilation and/or linkage of the solution is complete. Also, the Bulk Data and Case Control Sections are not read or processed.

Remarks: 1. If SOLIN keyword is not given and if there are no LINK statements within the input data, the program will perform an automatic link. The program will first collect the objects created in the current run by the COMPILE statement and the remaining objects stored in the MSCOBJ DBset. The program will then perform an automatic link of the collected objects. 2. If the SOLIN keyword is not given but a LINK statement is provided, the SOLIN default will be obtained from the SOLOUT keyword on the LINK statement. 3. The OSCAR (Operation Sequence Control ARray) defines the problem solution sequence. The OSCAR consists of a sequence of entries with each entry containing all of the information needed to execute one step of the problem solution. The OSCAR is generated from information supplied by the user’s entries in the Executive Control Section. 4. The SOLIN keyword will skip the automatic link and execute the OSCAR on the specified DBset. 5. The DOMAINSOLVER may be used in conjunction with Solution Sequences 101, 103, 108, and 111 to select domain decomposition solution methods. 6. The following Solution Sequences are currently available in MSC.Nastran:

Main Index

CHAPTER B Executive Control Section

Table 2-1 Structured Solution Sequences SOL Number

Main Index

SOL Name

Description

101

SESTATIC

Statics with Options: Linear Steady State Heat Transfer Alternate Reduction Inertia Relief Design Sensitivity - Statics

103

SEMODES

Normal Modes with Option: Design Sensitivity - Modes

105

SEBUCKL

Buckling with options: Static Analysis Alternate Reduction Inertia Relief Design Sensitivity - Buckling

106

NLSTATIC

Nonlinear or Linear Statics

107

SEDCEIG

Direct Complex Eigenvalues

108

SEDFREQ

Direct Frequency Response

109

SEDTRAN

Direct Transient Response

110

SEMCEIG

Modal Complex Eigenvalues

111

SEMFREQ

Modal Frequency Response

112

SEMTRAN

Modal Transient Response

114

CYCSTATX

Cyclic Statics with Option: Alternate Reduction

115

CYCMODE

Cyclic Normal Modes

116

CYCBUCKL

Cyclic Buckling

118

CYCFREQ

Cyclic Direct Frequency Response

129

NLTRAN

Nonlinear or Linear Transient Response

144

AESTAT

Static Aeroelastic Response

145

SEFLUTTR

Aerodynamic Flutter

146

SEAERO

Aeroelastic Response

153

NLSCSH

Static Structural and/or Steady State Heat Transfer Analysis with Options: Linear or Nonlinear Analysis

159

NLTCSH

Transient Structural and/or Transient Heat Transfer Analysis with Options: Linear or Nonlinear Analysis

239

240

Table 2-1 Structured Solution Sequences (continued) SOL Number

SOL Name

Description

190

DBTRANS

Database Transfer, “Output Description” on page 373 of the MSC.Nastran Reference Guide.

200

DESOPT

Design Optimization

Table 2-2 Unstructured Solution Sequences SOL Number

SOL Name

Description

1

STATICS1

Statics and Linear Heat Transfer

3

MODES

Normal Modes

4

GNOLIN

Geometric Nonlinear

5

BUCKLING

Buckling

7

DCEIG

Direct Complex Eigenvalues

8

DFREQ

Direct Frequency Response

9

DTRAN

Direct Transient Response

10

MCEIG

Modal Complex Eigenvalues

11

MFREQ

Modal Frequency Response

12

MTRAN

Modal Transient Response

14

CYCSTAT

Cyclic Statics

15

CYCMODES

Cyclic Modes

16

CYCBUCK

Cyclic Buckling

Examples: 1. In the following example, SOL 103 is executed from MSCOBJ. SOL 103 2. In the following example, the PHASE0 subDMAP is altered, SOL 103 is relinked onto the OBJSCR DBset (which is the default for SOLOUT), and SOL 103 is executed. SOL 103 COMPILE PHASE1 ALTER ’DTIIN’ TABPT SETREE,,,,// $ . . . ENDALTER $ Main Index

CHAPTER B Executive Control Section

3. In the following example, the solution sequence called DYNAMICS is executed from the USROBJ DBset. SOL DYNAMICS SOLIN = USROBJ

Main Index

241

242

TIME Sets the maximum CPU and I/O time. Format: TIME[=]t1[,t2] Describer

Meaning

t1

Maximum allowable execution time in CPU minutes. (Real or Integer>0; Default=1.89E9 seconds)

t2

Maximum allowable I/O limit in minutes. (Real or Integer>0; Default is infinity, which is machine dependent.)

Remarks: 1. The TIME statement is optional. 2. If t2 is specified then t1 must be specified. Examples: 1. The following example designates a runtime of 8 hours: TIME 480 2. The following example designates 90 seconds: TIME 1.5

Main Index

MSC.Nastran Thermal Analysis User’s Guide

APPENDIX

C

Case Control Commands

■ Thermal Analysis Case Control Commands

Main Index

244

3.1

Thermal Analysis Case Control Commands This appendix lists the Case Control commands that are often used for thermal analysis. The Case Control commands are listed alphabetically. The description of each command is similar to that found in the MSC.Nastran Quick Reference Guide. The MSC.Nastran Quick Reference Guide describes all of the Case Control commands.

Main Index

CHAPTER C Case Control Commands

Comment

$

Used to insert comments into the input file. Comment statements may appear anywhere within the input file. Format: $ followed by any characters out to column 80. Example: $ TEST FIXTURE-THIRD MODE

Remarks: 1. Comments are ignored by the program. 2. Comments will appear only in the unsorted echo of the Bulk Data.

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Analysis Discipline Subcase Assignment

ANALYSIS

Specifies the type of analysis being performed for the current subcase. Format: ANALYSIS=type Examples: ANALYSIS=STATICS ANALYSIS=MODES Describer

Meaning

type

Analysis type. Allowable values and applicable solution sequences (Character): Statics Normal Modes also in SOL 110, 111, 112 Buckling BUCK Direct Frequency DFREQ Modal Frequency MFREQ Modal Transient MTRAN Direct Complex DCEIG Eigenvalue Analysis Modal Complex MCEIG Eigenvalue Analysis Static Aeroelasticity SAERO Static Aeroelastic DIVERGE Divergence Flutter FLUTTER Heat Transfer Analysis HEAT STRUCTURE Structural Analysis STATICS MODES

(SOL 200 only)

(SOLs 153 and 159 only)

Remarks: 1. ANALYSIS=STRUC is the default in SOLs 153 and 159. 2. In SOL 200, all subcases, including superelement subcases, must be assigned by an ANALYSIS command either in the subcase or above all subcases. Also, all subcases assigned by ANALYSIS=MODES must contain a DESSUB. 3. ANALYSIS=DIVERG is only available for analysis in SOL 200. Sensitivity and optimization are not supported for this analysis type. 4. In order to obtain normal modes data recovery in SOLs 110, 111, and 112, ANALYSIS = MODES must be specified under one or more separate subcases(s) which contain requests for data recovery intended for normal modes only. For example, in SOL 111: Main Index

CHAPTER C Case Control Commands

METH=40 SPC=1 SUBCASE 1 $ Normal Modes ANALYSIS=MODES DISP=ALL SUBCASE 2 $ Frequency response STRESS=ALL DLOAD=12 FREQ=4

All commands which control the boundary conditions (SPC, MPC, and SUPORT) and METHOD selection should be copied inside the ANALYSIS=MODES subcase or specified above the subcase level.

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DLOAD

Dynamic Load Set Selection

Selects a dynamic load or an acoustic source to be applied in a transient or frequency response problem. Format: DLOAD=n Example: DLOAD=73 Describer

Meaning

n

Set identification of a DLOAD, RLOAD1, RLOAD2, TLOAD1, TLOAD2, or ACSRCE Bulk Data entry. (Integer>0)

Remarks: 1. RLOAD1 and RLOAD2 may only be selected in a frequency response problem. 2. TLOAD1 and TLOAD2 may be selected in a transient or frequency response problem. 3. Either a RLOADi or TLOADi entry (but not both) must be selected in an aeroelastic response problem. If RLOADi is selected, a frequency response is calculated. If TLOADi is selected, then transient response is computed by Fourier transform. When there are only gust loads (GUST entry), the DLOAD selects a TLOADi or RLOADi entry with zero load along with field 3 of the GUST command. 4. The DLOAD command will be ignored if specified for upstream superelements in dynamic analysis. To apply loads to upstream superelements, please see the LOADSET command.

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CHAPTER C Case Control Commands

ENTHALPY

Heat Transfer Enthalpy Output Request

Requests form of enthalpy vector output in transient heat transfer analysis (SOL 159). Format:  ENTHALPY  SORT1 ,  SORT2

PRINT, PUNCH   PLOT 

 ALL    =   n    NONE 

Example: ENTHALPY=5 Describer

Meaning

SORT1

Output will be presented as a tabular listing of grid points for each time.

SORT2

Output will be presented as a tabular listing of time for each grid point.

PRINT

The printer will be the output medium.

PUNCH

The punch file will be the output medium.

PLOT

Generates but does not print enthalpies.

ALL

Enthalpy for all points will be output.

NONE

Enthalpy for no points will be output.

n

Set identification of previously appearing SET command. Only enthalpies of points with identification numbers that appear on this SET command will be output. (Integer>0)

Remark: 1. ENTHALPY=NONE is used to override a previous ENTHALPY=n or ENTHALPY=ALL command.

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FLUX

Heat Transfer Gradient and Flux Output Request

Requests the form and type of gradient and flux output in heat transfer analysis. Format:  ALL    FLUX [ ( PRINT, PLOT, PUNCH ) ] =   n    NONE  Examples: FLUX=ALL FLUX(PUNCH,PRINT)=17 FLUX=25 Describer

Meaning

PRINT

The printer will be the output medium.

PUNCH

The punch file will be the output medium.

PLOT

The output will be sent to the plot file.

ALL

Flux for all elements will be output.

NONE

Flux for no elements will be output.

n

Set identification of a previously appearing SET command. Only fluxes of elements with identification numbers that appear on this SET command will be output. (Integer>0)

Remarks: 1. FLUX=ALL in SOL 159 may produce excessive output. 2. FLUX=NONE overrides an overall request.

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CHAPTER C Case Control Commands

HDOT

Heat Transfer Rate of Change of Enthalpy Output Request

Requests form of rate of change of enthalpy vector output in transient heat transfer analysis (SOL 159). Format:  HDOT  SORT1 ,  SORT2

PRINT, PUNCH   PLOT 

 ALL    =   n   NONE  

Example: HDOT=5 Describer

Meaning

SORT1

Output will be presented as a tabular listing of grid points for each time.

SORT2

Output will be presented as a tabular listing of time for each grid point.

PRINT

The printer will be the output medium.

PUNCH

The punch file will be the output medium.

PLOT

Generates but does not print rate of change of enthalpy.

ALL

Rate of change of enthalpy for all points will be output.

NONE

Rate of change of enthalpy for no points will be output.

n

Set identification of previously appearing SET command. Only rates of change of enthalpy for points with identification numbers that appear on this SET command will be output. (Integer>0)

Remark: 1. HDOT=NONE is used to override a previous HDOT=n or HDOT=ALL command.

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Transient Analysis Initial Condition Set Selection

IC

Selects the initial conditions for transient analysis (SOLs 109, 112, 129 and 159). Format: PHYSICAL IC

MODAL STATSUB[,DIFFK]

= n

Examples: IC = 10 IC(PHYSICAL) = 100 IC(MODAL) = 200 IC(STATSUB) = 1000 IC(STATSUB,DIFFK) = 2000 Describer

Meaning

PHYSICAL

The TIC Bulk Data entries selected by set n define initial conditions for coordinates involving grid, scalar and extra points. (Default).

MODAL

The TIC Bulk Data entries selected by set n define initial conditions for modal coordinates and extra points. See Remark 3.

STATSUB

Use the solution of the static analysis subcase n as the initial condition. See Remark 4.

DIFFK

Include the effects of differential stiffness in the solution. See Remarks 4. and 5.

n

For the PHYSICAL (the default) and MODAL options, n is the set identification number of TIC Bulk Data entries for structural analysis (SOL 109, 112 and 129) or TEMP and TEMPD entries for heat transfer analysis (SOL 159). For the STATSUB option, n is the ID of a static analysis subcase. (Integer > 0)

Remarks: 1. For structural analysis, TIC entries will not be used (therefore, no initial conditions) unless selected in the Case Control Section. 2. Only the PHYSICAL option (the default) may be specified in heat transfer analysis (SOL 159). 3. IC(MODAL) may be specified only in modal transient analysis (SOL 112). 4. IC(STATSUB) and IC(STATSUB,DIFFK) may not both be specified in the same execution. 5. The DIFFK keyword is meaningful only when used in conjunction with the STATSUB keyword. Main Index

CHAPTER C Case Control Commands

6. The following examples illustrate the usage of the various options of the IC Case Control command. $ SPECIFY INITIAL CONDITIONS FOR PHYSICAL COORDINATES $ IN SOL 109 OR SOL 112 IC(PHYSICAL) = 100 or IC = 100 $ SPECIFY INITIAL CONDITIONS FOR MODAL COORDINATES $ IN SOL 112 IC(MODAL) = 200 $ SPECIFY STATIC SOLUTION AS INITIAL CONDITION $ IN SOL 109 OR SOL 112 $ (DIFFERENTIAL STIFFNESS EFFECT NOT INCLUDED) SUBCASE 10 $ STATIC ANALYSIS LOAD = 100 SUBCASE 20 $ TRANSIENT ANALYSIS IC(STATSUB) = 10 $ POINTS TO STATIC ANALYSIS SUBCASE ID $ SPECIFY STATIC SOLUTION AS INITIAL CONDITION $ IN SOL 109 OR SOL 112 $ (DIFFERENTIAL STIFFNESS EFFECT INCLUDED SUBCASE 100 $ STATIC ANALYSIS LOAD = 1000 SUBCASE 200 $ TRANSIENT ANALYSIS IC(STATSUB,DIFFK) = 100 $ POINTS TO STATIC ANALYSIS SUBCASE ID

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INCLUDE

Insert External File

Inserts an external file into the input file. The INCLUDE statement may appear anywhere within the input data file. Format: INCLUDE ’filename’ Describer

Meaning

filename

Physical filename of the external file to be inserted. The user must supply the name according to installation or machine requirements. It is recommended that the filename be enclosed by single right-hand quotation marks (’).

Example: The following INCLUDE statement is used to obtain the Bulk Data from another file called MYBULK.DATA: SOL 101 CEND TITLE = STATIC ANALYSIS LOAD = 100 INCLUDE ’MYCASE.DATA’ BEGIN BULK ENDDATA Remarks: 1. INCLUDE statements may be nested; that is, INCLUDE statements may appear inside the external file. The nested depth level must not be greater than 10. 2. The total length of any line in an INCLUDE statement must not exceed 72 characters. Long file names may be split across multiple lines. For example the file: /dir123/dir456/dir789/filename.dat may be included with the following input: INCLUDE ‘/dir123 /dir456 /dir789/filename.dat’ 3. See the MSC.Nastran 2005 Installation and Operations Guide for more examples.

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CHAPTER C Case Control Commands

LOAD

External Static Load Set Selection

Selects an external static load set. Format: LOAD=n Example: LOAD=15 Describer

Meaning

n

Set identification of at least one external load Bulk Data entry. The set identification must appear on at least one FORCE, FORCE1, FORCE2, FORCEAX, GRAV, MOMAX, MOMENT, MOMENT1, MOMENT2, LOAD, PLOAD, PLOAD1, PLOAD2, PLOAD4, PLOADX, QVOL, QVECT, QHBDY, QBDY1, QBDY2, QBDY3, PRESAX, RFORCE, SPCD, or SLOAD entry. (Integer>0)

Remarks: 1. A GRAV entry cannot have the same set identification number as any of the other loading entry types. If it is desired to apply a gravity load along with other static loads, a LOAD Bulk Data entry must be used. 2. LOAD is only applicable in linear and nonlinear statics, inertia relief, differential stiffness, buckling, and heat transfer problems. 3. The total load applied will be the sum of external (LOAD), thermal (TEMP(LOAD)), element deformation (DEFORM), and constrained displacement (SPC) loads. 4. Static, thermal, and element deformation loads should have unique set identification numbers.

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MPC

Multipoint Constraint Set Selection

Selects a multipoint constraint set. Format: MPC=n Example: MPC=17 Describer

Meaning

n

Set identification number of a multipoint constraint set. This set identification number must appear on at least one MPC or MPCADD Bulk Data entry. (Integer>0)

Remarks: 1. In cyclic symmetry analysis, this command must appear above the first SUBCASE command. 2. Multiple boundary (MPC sets) conditions are not allowed in superelement analysis. If more than one MPC set is specified per superelement (including the residual), then the second and subsequent sets will be ignored.

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CHAPTER C Case Control Commands

NLPARM

Nonlinear Static Analysis Parameter Selection

Selects the parameters used for nonlinear static analysis. Format: NLPARM=n Example: NLPARM=10 Describer

Meaning

n

Set identification of NLPARM and NLPCI Bulk Data entries. (Integer>0)

Remarks: 1. NLPARM and NLPCI entries in the Bulk Data will not be used unless selected. 2. NLPARM may appear above or within a subcase.

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NONLINEAR

Nonlinear Dynamic Load Set Selection

Selects nonlinear dynamic load set for transient problems. Format: NONLINEAR=n Example: NONLINEAR=75 Describer

Meaning

n

Set identification of NOLINi or NLRGAP Bulk Data entry. (Integer>0)

Remark: 1. NOLINi Bulk Data entry will be ignored unless selected in the Case Control Section.

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CHAPTER C Case Control Commands

Applied Load Output Request

OLOAD

Requests the form and type of applied load vector output. Format:  OLOAD  SORT1 , PRINT, PUNCH , REAL or IMAG , PSDF, ATOC, CRMS ,  SORT2 PLOT PHASE or RALL  ALL     , RPUNCH , [ CID ] =  n   NORPRINT    NONE  RPRINT

Examples: OLOAD=ALL‘ OLOAD(SORT1, PHASE)=5‘ OLOAD(SORT2, PRINT, PSDF, CRMS, RPUNCH=20 OLOAD(PRINT, RALL, NORPRINT)=ALL

Main Index

Describer

Meaning

SORT1

Output will be presented as a tabular listing of grid points for each load, frequency, eigenvalue, or time, depending on the solution sequence.

SORT2

Output will be presented as a tabular listing of frequency or time for each grid point.

PRINT

The printer will be the output medium.

PUNCH

The punch file will be the output medium.

REAL or IMAG

Requests rectangular format (real and imaginary) of complex output. Use of either REAL or IMAG yields the same output.

PHASE

Requests polar format (magnitude and phase) of complex output. Phase output is in degrees.

PSDF

Requests the power spectral density function be calculated and stored in the database for random analysis post-processing. Request must be made above the subcase level and RANDOM must be selected in the Case Control.

ATOC

Requests the autocorrelation function be calculated and stored in the database for random analysis post-processing. Request must be made above the subcase level and RANDOM must be selected in the Case Control.

CRMS

Requests all of PSDF, ATOC and CRMS be calculated for random analysis post-processing. Request must be made above the subcase level and RANDOM must be selected in the Case Control.

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Describer

Meaning

RALL

Requests all of PSDF, ATOC and CRMS be calculated for random analysis post-processing. Request must be made above the subcase level and RANDOM must be selected in the Case Control.

RPRINT

Writes random analysis results in the print file (Default).

NORPRINT

Disables the writing of random analysis results in the print file.

RPUNCH

Writes random analysis results in the punch file.

CID

Request to print output coordinate system ID in printed output file, F06 file.

ALL

Applied loads for all points will be output. See Remarks 2. and 8.

NONE

Applied load for no points will be output.

n

Set identification of a previously appearing SET command. Only loads on points with identification numbers that appear on this SET command will be output. (Integer > 0)

Remarks: 1. Both PRINT and PUNCH may be requested. 2. See Remark 2 under “DISPLACEMENT” on page 239 for a discussion of SORT1 and SORT2. In the SORT1 format, only nonzero values will be output. 3. In a statics problem, a request for SORT2 causes loads at all requested points (zero and nonzero) to be output. 4. OLOAD=NONE overrides an overall output request. 5. In the statics superelement solution sequences, and in the dynamics SOLs 107 through 112, 118, 145, 146, and 200. OLOADs are available for superelements and the residual structure only externally applied loads are printed, and not loads transmitted from upstream superelements. Transmitted loads can be obtained with GPFORCE requests.

• In the nonlinear transient analysis solution sequences SOLs 129 and 159, OLOADs are available only for residual structure points and include loads transmitted by upstream superelements. 6. In nonlinear analysis, OLOAD output will not reflect changes due to follower forces. 7. Loads generated via the SPCD Bulk Data entry do not appear in OLOAD output. 8. In SORT1 format, OLOADs recovered at consecutively numbered scalar points are printed in groups of six (sextets) per line of output. But if a scalar point is not consecutively numbered, then it will begin a new sextet on a new line of output. If a sextet can be formed and it is zero, then the line will not be printed. If a sextet cannot be formed, then zero values may be output.

Main Index

9. OLOAD results are output in the global coordinate system (see field CD on the GRID Bulk Data entry).

CHAPTER C Case Control Commands

10. In inertia relief analysis the OLOAD output is interpreted differently for SOLs 1, 101, and 200:

• In SOL 1, the output shows only the applied loads. • In SOLs 101 and 200, the output includes both the inertia loads and applied loads. 11. The option of PSDF, ATOC, CRMS and RALL, or any combination of them, can be selected for random analysis. The results can be either printed in the .f06 file or punched n the punch file, or output in both files. 12. Note that the CID keyword affects only grid point related output, such as DISPlacement, VELOcity, ACCEleration, OLOAD, SPCForce and MPCForce. In addition, CID keyword needs to appear only once in a grid related output request anywhere in the Case Control Section to turn on the printing algorithm.

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Case Control Delimiter

OUTPUT

Delimits the various types of commands for the structure plotter, curve plotter, grid point stress, and MSGSTRESS. Format:     PLOT    POST    OUTPUT   XYOUT      XYPLOT    CARDS    Examples: OUTPUT OUTPUT(PLOT) OUTPUT(XYOUT) Describer

Meaning

PLOT

Beginning of the structure plotter request. This command must precede all structure plotter control commands. Plotter commands are described in “OUTPUT(PLOT) Commands” on page 483.

POST

Beginning of grid point stress SURFACE and VOLUME commands. This command must precede all SURFACE and VOLUME commands.

XYOUT or XYPLOT

Beginning of curve plotter request. This command must precede all curve plotter control commands. XYPLOT and XYOUT are entirely equivalent. Curve plotter commands are described in “X-Y PLOT Commands” on page 525.

CARDS

The OUTPUT(CARDS) packet is used by the MSGSTRESS program. See the MSGMESH Analyst’s Guide for details. These commands have no format rules. This package must terminate with the command ENDCARDS (starting in column 1).

Remarks: 1. The structure plotter request OUTPUT(PLOT), the curve plotter request OUTPUT(XYOUT or XYPLOT), and the grid point stress requests (OUTPUT(POST)) must follow the standard Case Control commands. 2. If OUTPUT is specified without a describer, then the subsequent commands are standard Case Control commands. 3. Case Control commands specified after OUTPUT(POST) are SURFACE and VOLUME.

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CHAPTER C Case Control Commands

Parameter Specification

PARAM

Specifies values for parameters. Parameters are described in “Parameters” on page 601. Format: PARAM,n,V1,V2 Examples: PARAM,GRDPNT,0 PARAM,K6ROT,1.0 Describer

Meaning

n

Parameter name (one to eight alphanumeric characters, the first of which is alphabetic).

V1, V2

Parameter value based on parameter type, as follows: Type

V1

V2

Integer

Integer

Blank

Real, single precision

Real

Blank

Character

Character

Blank

Real, double precision

Real, Double Precision

Blank

Complex, single precision

Real or Blank

Real or Blank

Complex, double precision

Real, Double Precision

Real, Double Precision

Remarks: 1. The PARAM command is normally used in the Bulk Data Section and is described in the “Bulk Data Entries” on page 849. 2. The parameter values that may be defined in the Case Control Section are described in “Parameters” on page 601. Case Control PARAM commands in user-written DMAPs requires the use of the PVT module, described in the MSC.Nastran 2005 DMAP Programmer’s Guide.

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Set Definition, General Form

SET

Sets are used to define the following lists: 1. Identification numbers (point, element, or superelement) for processing and output requests. 2. Frequencies for which output will be printed in frequency response problems or times for transient response, using the OFREQ and OTIME commands, respectively. 3. Surface or volume identification numbers to be used in GPSTRESS or STRFIELD commands. Formats: SET n = { i 1 [ ,i 2, i 3, THRU i 4, EXCEPT i 5, i 6, i 7, i 8, THRU i 9 ] } SET n = { r 1 , [ r 2, r 3, r 4 ] } SET n=ALL Examples: SET 77=5 SET 88=5, 6, 7, 8, 9, 10 THRU 55 EXCEPT 15, 16, 77, 78, 79, 100 THRU 300 SET 99=1 THRU 100000 SET101=1.0, 2.0, 3.0 SET105=1.009, 10.2, 13.4, 14.0, 15.0 Describer

Meaning

n

Set identification number. Any set may be redefined by reassigning its identification number. SETs specified under a SUBCASE command are recognized for that SUBCASE only. (Integer>0)

i 1, i 2, etc.

Identification numbers. If no such identification number exists, the request is ignored. (Integer>0)

i 3 THRUi 4

Identification numbers ( i 4 > i 3 ) . (Integer>0)

EXCEPT

Main Index

Set identification numbers following EXCEPT will be deleted from output list as long as they are in the range of the set defined by the immediately preceding THRU. An EXCEPT list may not include a THRU list or ALL.

CHAPTER C Case Control Commands

Describer

Meaning

r 1, r 2, etc.

Frequencies or times for output. The nearest solution frequency or time will be output. EXCEPT and THRU cannot be used. If an OFREQ or OTIME command references the set then the values must be listed in ascending sequences, r 1 < r 2 < r 3 < r 4 ...etc., otherwise some output may be missing. If an OFREQ or OTIME command is not present, all frequencies or times will be output. (Real>0.0)

ALL

All members of the set will be processed.

Remarks: 1. A SET command may be more than one physical command. A comma at the end of a physical command signifies a continuation command. Commas may not end a set. THRU may not be used for continuation. Place a number after the THRU. 2. Set identification numbers following EXCEPT within the range of the THRU must be in ascending order. 3. In SET 88 above, the numbers 77, 78, etc., are included in the set because they are outside the prior THRU range.

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Single-Point Constraint Set Selection

SPC

Selects a single-point constraint set to be applied. Format: SPC=n Example: SPC=10 Describer

Meaning

n

Set identification number of a single-point constraint that appears on a SPC, SPC1, or SPCADD Bulk Data entry. (Integer>0)

Remarks: 1. In cyclic symmetry analysis, this command must appear above the first SUBCASE command. 2. Multiple boundary conditions are only supported in SOLs 101, 103, 105, 145 and 200. Multiple boundary conditions are not allowed for upstream superelements. the BC command must be specified to define multiple boundary conditions for the residual structure in SOLs 103, 105, 145 and 200.

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CHAPTER C Case Control Commands

SUBCASE

Subcase Delimiter

Delimits and identifies a subcase. Format: SUBCASE=n Example: SUBCASE=101 Describer

Meaning

n

Subcase identification number. (Integer>0)

Remarks: 1. The subcase identification number, n, must be greater than all previous subcase identification numbers. 2. Plot requests and RANDPS requests refer to n. 3. See the MODES command for use of this command in normal modes analysis. 4. If a comment follows n, then the first few characters of the comment will appear in the subcase label in the upper right-hand corner of the output.

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TEMPERATURE

Temperature Set Selection

Selects the temperature set to be used in either material property calculations or thermal loading in heat transfer and structural analysis. Format:  INITIAL    TEMPERATURE  MATERIAL    LOAD     BOTH

= n

Examples: TEMPERATURE(LOAD)=15 TEMPERATURE(MATERIAL)=7 TEMPERATURE=7 Describer

Meaning

MATERIAL

The selected temperature set will be used to determine temperaturedependent material properties indicated on the MATTi Bulk Data entries. See Remarks 6., 7. and 8.

LOAD

The selected temperature set will be used to determine an equivalent static load and to update material properties in a nonlinear analysis. See Remarks 2., 5., 6. and 7.

BOTH

Both MATERIAL and LOAD will use the same temperature set.

n

Set identification number of TEMP, TEMPD, TEMPP1, TEMPRB, TEMPF, or TEMPAX Bulk Data entries. (Integer > 0)

INITIAL

The selected temperature table will be used to determine initial temperature distribution in nonlinear static analysis. See Remarks 4., 6., 7., 8. and 9.

Remarks: 1. In linear analysis, only one temperature-dependent material request should be made in any problem and should be specified above the subcase level. If multiple requests are made, then only the last request will be processed. See also Remarks 6. and 7. 2. The total load applied will be the sum of external (LOAD command), thermal (TEMP(LOAD) command), element deformation (DEFORM command) and constrained displacement (SPC command) loads. 3. Static, thermal, and element deformation loads should have unique set identification numbers. 4. INITIAL is used in steady state heat transfer analysis for conduction material properties and provides starting values for iteration. Main Index

CHAPTER C Case Control Commands

5. In superelement data recovery restarts, TEMPERATURE(LOAD) requests must be respecified in the Case Control Section. 6. In linear static analysis, temperature strains are calculated with: εT = A ( To ) ⋅ ( T – To ) where A ( T o ) is the thermal expansion coefficient defined on the MATi Bulk Data entries, T is the load temperature defined with TEMPERATURE(LOAD) and T o is the initial temperature defined with TEMPERATURE(INITIAL). The following rules apply for TEMPERATURE(INITIAL), TEMPERATURE(MATERIAL), and TREF on the MATi entries:

• If TEMPERATURE(INITIAL) and TREF are specified, then the TEMPERATURE(INITIAL) set will be used as the initial temperature to calculate both the loads and the material properties.

• If TEMPERATURE(MATERIAL) and TREF are specified, then TREF will be used as the initial temperature in calculating the load and the TEMPERATURE(MATERIAL) set will be used for the calculation of material properties.

• If no TEMPERATURE(INITIAL) or TEMPERATURE(MATERIAL) is present, TREF will be used to calculate both the load and the material properties. 7. In nonlinear static analysis, temperature strains are calculated with ε T = A ( T ) ⋅ ( T – TREF ) – A ( T o ) ⋅ ( T o – TREF ) where A ( T ) is the thermal expansion coefficient defined on the MATi Bulk Data entries. T is the load temperature defined with TEMPERATURE(LOAD) and T o is the initial temperature defined with TEMPERATURE(INITIAL). The following rules apply

• The specification of TEMPERATURE(INITIAL) is required above the subcase level. The specification of TEMPERATURE(MATERIAL) or TEMPERATURE(BOTH) will cause a fatal error.

• If a subcase does not contain a TEMPERATURE(LOAD) request, then the thermal load set will default to the TEMPERATURE(INITIAL) set.

• TEMPERATURE(LOAD) will also cause the update of temperaturedependent material properties due to the temperatures selected in the thermal load set. Temperature-dependent material properties are specified with MATi, MATTi, MATS1, and/or TABLEST Bulk Data entries.

• If TREF and TEMPERATURE(INITIAL) are specified, then the TEMPERATURE(INITIAL) set will be used as the initial temperature to calculate both the loads and the material properties. Both are used in the definition of thermal strain. Main Index

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8. TEMPERATURE(MATERIAL) and TEMPERATURE(INITIAL) cannot be specified simultaneously in the same run. 9. TEMP(INIT) is not used with TEMPAX. 10. Temperature loads cause incorrect stresses in dynamic analysis.

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CHAPTER C Case Control Commands

Transfer Function Set Selection

TFL

Selects the transfer function set(s) to be added to the direct input matrices. Format: TFL=n Example: TFL=77 TFL = 1, 25, 77 Describer

Meaning

n

Set identification of a TF Bulk Data entry. (Integer>0)

Remarks: 1. Transfer functions will not be used unless selected in the Case Control Section. 2. Transfer functions are supported in dynamics problems only. 3. Transfer functions are described in the MSC.Nastran Advanced Dynamic Analysis User’s Guide. 4. It is recommended that PARAM,AUTOSPC,NO be specified when using transfer functions. See “Constraint and Mechanism Problem Identification in SubDMAP SEKR” on page 409 of the MSC.Nastran Reference Guide. 5. The transfer functions are additive if multiple TF values are referenced on the TFL command.

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THERMAL

Temperature Output Request

Requests the form and type of temperature output. Format:  THERMAL  SORT1 ,  SORT2

PRINT, PUNCH   PLOT 

 ALL    =   n    NONE 

Examples: THERMAL=5 THER(PRINT,PUNCH)=ALL Describer

Meaning

SORT1

Output is presented as a tabular listing of point temperatures for each load or time step.

SORT2

Output is presented as a tabular listing of loads or time steps for each.

PRINT

The printer will be the output medium.

PUNCH

The punch file will be the output medium.

PLOT

Compute temperatures but do not print.

ALL

Temperatures for all points will be output.

NONE

Temperatures for no points will be output.

n

Set identification of a previously appearing SET command. Only temperatures of points with identification numbers that appear on this SET command will be output. (Integer>0)

Remarks: 1. The THERMAL output request is designed for use with the heat transfer option. The printed output will have temperature headings. The PUNCH option produces TEMP Bulk Data entries, and the SID on the entries will be the subcase number (=1 if no SUBCASES are specified). 2. SORT1 is the default in steady state heat transfer analysis. SORT2 is the default in transient heat transfer analysis. 3. In a transient heat transfer analysis, the SID on the punched TEMP Bulk Data entries, equal the time step number.

Main Index

CHAPTER C Case Control Commands

TSTEP

Transient Time Step Set Selection

Selects integration and output time steps for linear or nonlinear transient analysis. Format: TSTEP=n Example: TSTEP=731 Describer

Meaning

n

Set identification number of a TSTEP or TSTEPNL Bulk Data entry. (Integer>0)

Remarks: 1. A TSTEP entry must be selected to execute a linear transient analysis (SOLs 9, 12, 109, or 112) and TSTEPNL for a nonlinear transient analysis (SOLs 129 and 159). 2. A TSTEPNL entry must be selected in each subcase to execute a nonlinear transient problem. 3. For the application of time-dependent loads in modal frequency response analysis (SOLs 111 and 146), or TSTEP entry must be selected by the TSTEP command. The time-dependent loads will be recomputed in frequency domain by a Fourier Transform.

Main Index

273

274

TSTEPNL

Transient Time Step Set Selection for Nonlinear Analysis

See the description of the “TSTEP” on page 461.

Main Index

MSC.Nastran Thermal Analysis User’s Guide

APPENDIX

D

Bulk Data Entries

■ Commonly Used Bulk Data Entries

Main Index

276

4.1

Commonly Used Bulk Data Entries This appendix lists the Bulk Data entries that are often used for thermal analysis. Bulk Data entries are listed alphabetically. The description of each entry is similar to that found in the MSC.Nastran Quick Reference Guide. The MSC.Nastran Quick Reference Guide describes all of the Bulk Data entries. Figure 4-1 illustrates the interaction between the various Case Control commands and Bulk Data entries involved in the specification of thermal loads. Figure 4-2 illustrates the Bulk Data entry interaction for the application of heat transfer boundary conditions involving radiation and convection.

Main Index

CHAPTER D Bulk Data Entries

Case Control

Bulk Data

NLPARM TSTEPNL TFL MPC TEMP(INIT) IC SPC NONLINEAR DLOAD LOAD

NLPARM TSTEPNL TF MPC

TEMP TEMPD TEMPP1 TEMPP2 TEMPRB

SPC SPC1 SPCD TEMPBC GRID

GRID SPOINT

DLOAD

QVOL

QVECT CHBDYE CHBDYG CHBDYP

TABLED1 TABLED2 TABLED3 TABLED4 NOLIN2 NOLIN3 NOLIN4

SLOAD

CBAR CBEAM CBEND CHEXA CHEX1 CHEX2 CONROD CPENTA CQUAD4 CQUAD8 CROD CTETRA CTRIA3 CTRIA6 CTRIAX6 CTUBE

NOLIN1

PBAR PBEAM PBEND PSOLID PROD PSHELL PTUBE MAT4 MAT5 MATT4 MATT5

TABLED1 TABLED2 TABLED3 TABLED4

TLOAD1 TLOAD2 TEMPBC DELAY TABLED1 TABLED2 TABLED3 TABLED4 QVECT

TABLEM1 TABLEM2 TABLEM3 TABLEM4 RADM RADBND

PHBDY RADMT BDYOR TABLEM1 TABLEM2 TABLEM3 TABLEM4

QHBDY QBDY2 GRID QBDY1

BDYOR

CHBDYE CHBDYG CHBDYP

PHBDY

QBDY3 CHBDYE CHBDYG CHBDYP

Main Index

Figure 4-1 Thermal Loads – Bulk Data and Case Control Interaction

277

278

Free and Forced Convection CONV

Radiation Exchange

CHBDYE CHBDYG CHBDYP

CONVM CHBDYP PCONVM

GRID

BDYOR

RADBND

RADSET RADLST

PHBDY MAT4 MAT5 MATT4 MATT5

PCONV

SPC

Radiation

TABLEM1 TABLEM2 TABLEM3 TABLEM4

CHBDYE CHBDYG CHBDYP

RADMTX

RADM

RADMT

PHBDY BDYOR

TABLEM1 TABLEM2 TABLEM3 TABLEM4

View Factor Calculation VIEW CHBDYE CHBDYG CHBDYP RADCAV

PHBDY BDYOR

Radiation Boundary Condition RADBC CHBDYE CHBDYG CHBDYP

RADBND PHBDY RADM

RADMT

BDYOR TABLEM1 TABLEM2 TABLEM3 TABLEM4

Figure 4-2 Thermal Boundary Conditions – Bulk Data Interaction

Main Index

CHAPTER D Bulk Data Entries

Comment

$

Used to insert comments into the input file. Comment statements may appear anywhere within the input file. Format: $ followed by any characters out to column 80. Example: $ TEST FIXTURE-THIRD MODE Remarks: 1. Comments are ignored by the program. 2. Comments will appear only in the unsorted echo of the Bulk Data.

Main Index

279

280

CHBDYi Entry Default Values

BDYOR

Defines default values for the CHBDYP, CHBDYG, and CHBDYE entries. Format: 1 BDYOR

2

3

4

5

6

TYPE

IVIEWF

IVIEWB

RADMINF

CE

E1

E2

E3

AREA4

2

2

3

7

8

9

RADMIDB

PID

GO

3

10

10

Example: BDYOR

Field

Contents

TYPE

Default surface type. See Remark 2. (Character)

IVIEWF

Default identification number of front VIEW entry. (Integer > 0 or blank)

IVIEWB

Default identification number of back VIEW entry. (Integer > 0 or blank)

RADMIDF

Default identification number of a RADM entry for front face. (Integer > 0 or blank)

RADMIDB

Default identification number of a RADM entry for back face. (Integer > 0 or blank)

PID

Default PHBDY property entry identification number. (Integer > 0 or blank)

GO

Default orientation grid point. (Integer > 0; Default = 0)

CE

Default coordinate system for defining the orientation vector. (Integer > 0 or blank)

E1, E2, E3

Default components of the orientation vector in coordinate system CE. The origin of this vector is grid point G1 on a CHBDYP entry. (Real or blank)

Remarks: 1. Only one BDYOR entry may be specified in the Bulk Data Section. 2. TYPE specifies the type of CHBDYi element surface; allowable values are: POINT, LINE, REV, AREA3, AREA4, ELCYL, FTUBE, AREA6, AREA8, and TUBE. 3. IVIEWF and IVIEWB are specified for view factor calculations only (see VIEW entry). 4. GO is only used from BDYOR if neither GO nor the orientation vector is defined on the CHBDYP entry and GO is > 0. 5. E1, E2, E3 is not used if GO is defined on either the BDYOR entry or the CHBDYP entry.

Main Index

CHAPTER D Bulk Data Entries

Scalar Damper Connection

CDAMP1

Defines a scalar damper element. Format: 1

2

3

4

5

6

7

CDAMP1

EID

PID

G1

C1

G2

C2

19

6

0

23

2

8

9

10

Example: CDAMP1

Field

Contents

EID

Unique element identification number. (0 < Integer < 100,000,000)

PID

Property identification number of a PDAMP property entry. (Integer > 0; Default = EID)

G1, G2

Geometric grid point identification number. (Integer > 0)

C1, C2

Component number. (0 < Integer < 6; 0 or up to six unique integers, 1 through 6 may be specified in the field with no embedded blanks. 0 applies to scalar points and 1 through 6 applies to grid points.)

Remarks: 1. Scalar points may be used for G1 and/or G2, in which case the corresponding C1 and/or C2 must be zero or blank. Zero or blank may be used to indicate a grounded terminal G1 or G2 with a corresponding blank or zero C1 or C2. A grounded terminal is a point with a displacement that is constrained to zero. 2. Element identification numbers should be unique with respect to all other element identification numbers. 3. The two connection points (G1, C1) and (G2, C2), must be distinct. 4. For a discussion of the scalar elements, see “Scalar Elements (CELASi, CMASSi, CDAMPi)” on page 193 of the MSC.Nastran Reference Guide. 5. When CDAMP1 is used in heat transfer analysis, it generates a lumped heat capacity. 6. A scalar point specified on this entry need not be defined on an SPOINT entry. 7. If Gi refers to a grid point then Ci refers to degrees-of-freedom(s) in the displacement coordinate system specified by CD on the GRID entry.

Main Index

281

282

Scalar Damper Property and Connection

CDAMP2

Defines a scalar damper element without reference to a material or property entry. Format: 1

2

3

4

5

6

7

CDAMP2

EID

B

G1

C1

G2

C2

16

2.98

32

1

8

9

10

Example: CDAMP2

Field

Contents

EID

Unique element identification number. (0 < Integer < 100,000,000)

B

Value of the scalar damper. (Real)

G1, G2

Geometric grid point identification number. (Integer > 0)

C1, C2

Component number. (0 < Integer < 6; 0 or up to six unique integers, 1 through 6 may be specified in the field with no embedded blanks. 0 applies to scalar points and 1 through 6 applies to grid points.)

Remarks: 1. Scalar points may be used for G1 and/or G2, in which case the corresponding C1 and/or C2 must be zero or blank. Zero or blank may be used to indicate a grounded terminal G1 or G2 with a corresponding blank or zero C1 or C2. A grounded terminal is a point with a displacement that is constrained to zero. 2. Element identification numbers should be unique with respect to all other element identification numbers. 3. The two connection points (G1, C1) and (G2, C2), must be distinct. 4. For a discussion of the scalar elements, see “Scalar Elements (CELASi, CMASSi, CDAMPi)” on page 193 of the MSC.Nastran Reference Guide. 5. When CDAMP2 is used in heat transfer analysis, it generates a lumped heat capacity. 6. A scalar point specified on this entry need not be defined on an SPOINT entry. 7. If Gi refers to a grid point then Ci refers to degrees-of-freedom(s) in the displacement coordinate system specified by CD on the GRID entry.

Main Index

CHAPTER D Bulk Data Entries

Scalar Damper Connection to Scalar Points Only

CDAMP3

Defines a scalar damper element that is connected only to scalar points. Format: 1

2

3

4

5

CDAMP3

EID

PID

S1

S2

16

978

24

36

6

7

8

9

10

Example: CDAMP3

Field

Contents

EID

Unique element identification number. (0 < Integer < 100,000,000)

PID

Property identification number of a PDAMP entry. (Integer > 0; Default = EID)

S1, S2

Scalar point identification numbers. (Integer > 0; S1 ≠ S2 )

Remarks: 1. S1 or S2 may be blank or zero, indicating a constrained coordinate. 2. Element identification numbers should be unique with respect to all other element identification numbers. 3. Only one scalar damper element may be defined on a single entry. 4. For a discussion of the scalar elements, see “Scalar Elements (CELASi, CMASSi, CDAMPi)” on page 193 of the MSC.Nastran Reference Guide. 5. When CDAMP3 is used in heat transfer analysis, it generates a lumped heat capacity. 6. A scalar point specified on this entry need not be defined on an SPOINT entry.

Main Index

283

284

Scalar Damper Property and Connection to Scalar Points Only

CDAMP4

Defines a scalar damper element that connected only to scalar points and without reference to a material or property entry. Format: 1

2

3

4

5

CDAMP4

EID

B

S1

S2

16

-2.6

4

9

6

7

8

9

10

Example: CDAMP 4

Field

Contents

EID

Unique element identification number. (0 < Integer < 100,000,000)

B

Scalar damper value. (Real)

S1, S2

Scalar point identification numbers. (Integer > 0; S1 ≠ S2 )

Remarks: 1. S1 or S2 may be blank or zero, indicating a constrained coordinate. 2. Element identification numbers should be unique with respect to all other element identification numbers. 3. Only one scalar damper element may be defined on a single entry. 4. For a discussion of the scalar elements, see “Scalar Elements (CELASi, CMASSi, CDAMPi)” on page 193 of the MSC.Nastran Reference Guide. 5. If this entry is used in heat transfer analysis, it generates a lumped heat capacity. 6. A scalar point specified on this entry need not be defined on an SPOINT entry.

Main Index

CHAPTER D Bulk Data Entries

Scalar Damper with Material Property

CDAMP5

Defines a damping element that refers to a material property entry and connection to grid or scalar points. This element is intended for heat transfer analysis only. Format: 1

2

3

4

5

CDAMP5

EID

PID

G1

G2

1

4

10

20

6

7

8

9

10

Example: CDAMP5

Field

Contents

EID

Unique element identification number. (0 < Integer < 100,000,000)

PID

Identification number of a PDAMP5 property entry. (Integer > 0; Default = EID)

G1, G2

Grid or scalar point identification numbers. (Integer > 0 and G1 ≠ G2 )

Remarks: 1. G1 or G2 may be blank or zero indicating a constraint. 2. Element identification numbers should be unique with respect to all other element identification numbers. 3. CDAMP5 generates a lumped heat capacity in heat transfer analysis. 4. A scalar point specified on CDAMP5 need not be defined on an SPOINT entry.

Main Index

285

286

Scalar Spring Connection

CELAS1

Defines a scalar spring element. Format: 1

2

3

4

5

6

7

CELAS1

EID

PID

G1

C1

G2

C2

2

6

8

1

8

9

10

Example: CELAS1

Field

Contents

EID

Unique element identification number. (0 < Integer < 100,000,000)

PID

Property identification number of a PELAS entry. (Integer > 0; Default = EID)

G1, G2

Geometric grid point identification number. (Integer > 0)

C1, C2

Component number. (0 < Integer < 6; blank or zero if scalar point.)

Remarks: 1. Scalar points may be used for G1 and/or G2, in which case the corresponding C1 and/or C2 must be zero or blank. Zero or blank may be used to indicate a grounded terminal G1 or G2 with a corresponding blank or zero C1 or C2. A grounded terminal is a point with a displacement that is constrained to zero. If only scalar points and/or ground are involved, it is more efficient to use the CELAS3 entry. 2. Element identification numbers should be unique with respect to all other element identification numbers. 3. The two connection points (G1, C1) and (G2, C2) must be distinct. 4. For a discussion of the scalar elements, see “Scalar Elements (CELASi, CMASSi, CDAMPi)” on page 193 of the MSC.Nastran Reference Guide. 5. A scalar point specified on this entry need not be defined on an SPOINT entry. 6. If Gi refers to a grid point then Ci refers to degrees-of-freedom(s) in the displacement coordinate system specified by CD on the GRID entry.

Main Index

CHAPTER D Bulk Data Entries

Scalar Spring Property and Connection

CELAS2

Defines a scalar spring element without reference to a property entry. Format: 1

2

3

4

5

6

7

8

9

CELAS2

EID

K

G1

C1

G2

C2

GE

S

28

6.2+3

32

19

4

10

Example: CELAS2

Field

Contents

EID

Unique element identification number. (0 < Integer < 100,000,000)

K

Stiffness of the scalar spring. (Real)

G1, G2

Geometric grid point or scalar identification number. (Integer > 0)

C1, C2

Component number. (0 < Integer < 6; 0 blank or zero if scalar point.)

GE

Damping coefficient. See Remarks 6. and 8. (Real)

S

Stress coefficient. (Real)

Remarks: 1. Scalar points may be used for G1 and/or G2, in which case the corresponding C1 and/or C2 must be zero or blank. Zero or blank may be used to indicate a grounded terminal G1 or G2 with a corresponding blank or zero C1 or C2. A grounded terminal is a point with a displacement that is constrained to zero. If only scalar points and/or ground are involved, it is more efficient to use the CELAS4 entry. 2. Element identification numbers should be unique with respect to all other element identification numbers. 3. The two connection points (G1, C1) and (G2, C2) must be distinct. 4. For a discussion of the scalar elements, see “Scalar Elements (CELASi, CMASSi, CDAMPi)” on page 193 of the MSC.Nastran Reference Guide. 5. A scalar point specified on this entry need not be defined on an SPOINT entry. 6. If PARAM,W4 is not specified, GE is ignored in transient analysis. See “Parameters” on page 601. 7. If Gi refers to a grid point then Ci refers to degrees-of-freedom in the displacement coordinate system specified by CD on the GRID entry. 8. To obtain the damping coefficient GE, multiply the critical damping ratio C ⁄ C 0 by 2.0.

Main Index

287

288

Scalar Spring Connection to Scalar Points Only

CELAS3

Defines a scalar spring element that connects only to scalar points. Format: 1

2

3

4

5

CELAS3

EID

PID

S1

S2

19

2

14

15

6

7

8

9

10

Example: CELAS3

Field

Contents

EID

Unique element identification number. (0 < Integer < 100,000,000)

PID

Property identification number of a PELAS entry. (Integer > 0; Default = EID)

S1, S2

Scalar point identification numbers. (Integer > 0; S1 ≠ S2 )

Remarks: 1. S1 or S2 may be blank or zero, indicating a constrained coordinate. 2. Element identification numbers should be unique with respect to all other element identification numbers. 3. Only one scalar spring element may be defined on a single entry. 4. For a discussion of the scalar elements, see “Scalar Elements (CELASi, CMASSi, CDAMPi)” on page 193 of the MSC.Nastran Reference Guide. 5. A scalar point specified on this entry need not be defined on an SPOINT entry.

Main Index

CHAPTER D Bulk Data Entries

Scalar Spring Property and Connection to Scalar Points Only

CELAS4

Defines a scalar spring element that is connected only to scalar points, without reference to a property entry. Format: 1

2

3

4

5

CELAS4

EID

K

S1

S2

42

6.2-3

2

6

7

8

9

10

Example: CELAS4

Field

Contents

EID

Unique element identification number. (0 < Integer < 100,000,000)

K

Stiffness of the scalar spring. (Real)

S1, S2

Scalar point identification numbers. (Integer > 0; S1 ≠ S2 )

Remarks: 1. S1 or S2, but not both, may be blank or zero indicating a constrained coordinate. 2. Element identification numbers should be unique with respect to all other element identification numbers. 3. A structural damping coefficient is not available with CELAS4. The value of g is assumed to be 0.0. 4. No stress coefficient is available with CELAS4. 5. Only one scalar spring element may be defined on a single entry. 6. For a discussion of the scalar elements, see “Scalar Elements (CELASi, CMASSi, CDAMPi)” on page 193 of the MSC.Nastran Reference Guide. 7. A scalar point specified on this entry need not be defined on an SPOINT entry.

Main Index

289

290

Geometric Surface Element Definition (Element Form)

CHBDYE

Defines a boundary condition surface element with reference to a heat conduction element. Format: 1

2

3

4

5

6

7

8

CHBDYE

EID

EID2

SIDE

IVIEWF

IVIEWB

RADMIDF

RADMIDB

2

10

1

3

3

2

2

9

10

Example: CHBDYE

Field

Contents

EID

Surface element identification number for a specific side of a particular element. See Remarks 1. and 9. (Unique (0 < Integer < 100,000,000) among all elements.)

EID2

A heat conduction element identification number. (Integer > 0)

SIDE

A consistent element side identification number. See Remark 6. (1 < Integer < 6)

IVIEWF

A VIEW entry identification number for the front face of surface element. (Integer > 0, see Remark 2. for default.)

IVIEWB

A VIEW entry identification number for the back face of surface element. (Integer > 0, see Remark 2. for default.)

RADMIDF

RADM identification number for front face of surface element. (Integer > 0, see Remark 2. for default.)

RADMIDB

RADM identification number for back face of surface element. (Integer > 0, see Remark 2. for default.)

Remarks: 1. EID is a unique elemental ID associated with a particular surface element. EID2 identifies the general heat conduction element being considered for this surface element. 2. The defaults for IVIEWF, IVIEWB, RADMIDF, and RADMIDB may be specified on the BDYOR entry. If a particular field is blank both on the CHBDYE entry and the BDYOR entry, then the default is zero. 3. For the front face of shell elements, the right-hand rule is used as one progresses around the element surface from G1 to G2 to ... Gn. For the edges of shell elements or the ends of line elements, an outward normal is used to define the front surface. 4. If the surface element is to be used in the calculation of view factors, it must have an associated VIEW entry. 5. All conduction elements to which any boundary condition is to be applied must be individually identified with the application of one of the surface element entries: CHBDYE, CHBDYG, or CHBDYP. Main Index

CHAPTER D Bulk Data Entries

6. Side conventions for solid elements. The sides of the solid elements are numbered consecutively according to the order of the grid point numbers on the solid element entry. The sides of solid elements are either quadrilaterals or triangles. For each element type, tabulate the grid points (gp) at the corners of each side. 8-node or 20-node CHEXA side

gp

gp

gp

gp

1

4

3

2

1

2

1

2

6

5

3

2

3

7

6

4

3

4

8

7

5

4

1

5

8

6

5

6

7

8

gp

CPENTA side

gp

gp

gp

1

3

2

1

2

1

2

5

4

3

2

3

6

5

4

3

1

4

6

5

4

5

6

CTETRA side

gp

gp

gp

1

3

2

1

2

1

2

4

3

2

3

4

4

3

1

4

7. Side conventions for shell elements. Side 1 of shell elements (top) are of an AREA type, and additional sides (2 through a maximum of 5 for a QUAD) are of LINE type. (See “CHBDYG” on page 293 for surface type definition.) Area Type Sides –The first side is that given by the right-hand rule on the shell elements grid points. Main Index

291

292

Line Type Sides –The second side (first line) proceeds from grid point 1 to grid point 2 of the shell element, and the remaining lines are numbered consecutively. The thickness of the line is that of the shell element, and the normal to the line is outward from the shell element in the plane of the shell. Note that any midside nodes are ignored in this specification. 8. Side conventions for line elements. LINE elements have one linear side (side 1) with geometry that is the same as that of the element and two POINT-type sides corresponding to the two points bounding the linear element (first grid point-side 2; second grid point-side 3). The TUBE-type element has two linear sides of type TUBE. The first side represents the outside with diameters equal to that of the outside of the tube. The second side represents the inside with diameters equal to that of the inside of the tube. Point Sides – Point sides may be used with any linear element. The direction of the outward normals of these points is in line with the element axis, but pointing away from the element. The area assigned to these POINT-type sides is consistent with the element geometry. Rev Sides –The CTRIAX6 element has associated with it three REV sides. The first side is associated with Grid Points G1, G2, and G3. The positive face identification normals point away from the element. 9. Application of boundary conditions to CHBDYE is referenced through the EID. Boundary conditions can reference either the front or back face of the CHBDYE by specifying +EID or -EID respectively. Correspondingly, the back face is minus the normal vector of the front face. Similarly, IVIEWF and RADMIDF are associated with +EID and IVIEWB and RADMIDB with -EID. For radiation problems, if the RADMIDF or RADMIDB is zero, default radiant properties assume perfect black body behavior.

Main Index

CHAPTER D Bulk Data Entries

Geometric Surface Element Definition (Grid Form)

CHBDYG

Defines a boundary condition surface element without reference to a property entry. Format: 1

2

CHBDYG

EID G1

3

G2

4

5

6

7

8

TYPE

IVIEWF

IVIEWB

RADMIDF

RADMIDB

G3

G4

G5

G6

G7

AREA4

3

3

2

2

102

101

9

10

G8

Example: CHBDYG

2 100

103

Field

Contents

EID

Surface element identification number. (Unique (0 < Integer < 100,000,000) among all elemental entries.)

TYPE

Surface type. See Remark 3. (Character)

IVIEWF

A VIEW entry identification number for the front face. (Integer > 0; see Remark 2. for default.)

IVIEWB

A VIEW entry identification number for the back face. (Integer > 0; see Remark 2. for default.)

RADMIDF

RADM identification number for front face of surface element. (Integer > 0; see Remark 2. for default.)

RADMIDB

RADM identification number for back face of surface element. (Integer > 0; see Remark 2. for default.)

Gi

Grid point IDs of grids bounding the surface. (Integer > 0)

Remarks: 1. EID is a unique ID associated with a particular surface element as defined by the grid points. 2. The defaults for TYPE, IVIEWF, IVIEWB, RADMIDF, and RADMIDB may be specified on the BDYOR entry. If a particular field is blank on both the CHBDYG entry and the BDYOR entry, then the default is zero. 3. TYPE specifies the kind of element surface; allowed types are: REV, AREA3, AREA4, AREA6, and AREA8. See Figure 4-3, Figure 4-4, and Figure 4-5.

• TYPE = REV

Main Index

293

294

The “REV” type has two primary grid points that must lie in the x-z plane of the basic coordinate system with x>0. A midside grid point G3 is optional and supports convection or heat flux from the edge of the six-noded CTRIAX6 element. The defined area is a conical section with z as the axis of symmetry. A property entry is required for convection, radiation, or thermal vector flux. Automatic view factor calculations with VIEW data are not supported for the REV option. z G2 G3

n T G1 x

y

Figure 4-3 Normal Vector for CHBDYG Element of Type “REV” .

The unit normal lies in the x-z plane, and is given by n = ( ey × T ) ⁄ ey × T e y is the unit vector in the y direction.

• TYPE = AREA3, AREA4, AREA6, or AREA8 These types have three and four primary grid points, respectively, that define a triangular or quadrilateral surface and must be ordered to go around the boundary. A property entry is required for convection, radiation, or thermal vector flux. G3

G1

G2

G4

G3

G1

G2

AREA3

AREA4

G3

G6

G1

G4

G5

G4

G2

AREA6 (Grid points G4 through G6 optional) Main Index

G7

G3

G6

G8

G1

G5

G2

AREA8 (Grid points G5 through G8 optional)

CHAPTER D Bulk Data Entries

Figure 4-4 TYPE Examples G3 or G4

n T 1x G2 G1

T 12

Figure 4-5 Normal Vector for CHBDYG Element of Types “AREAi” The unit normal vector is given by ( T 12 × T 1x ) n = -----------------------------T 12 × T 1x (G3 is used for triangles, and G4 is used for quadrilaterals.) 4. For defining the front face, the right-hand rule is used on the sequence G1 to G2 to ... Gn of grid points. 5. If the surface element is to be used in the calculation of view factors, it must have an associated VIEW entry. 6. All conduction elements to which any boundary condition is to be applied must be individually identified with one of the surface element entries: CHBDYE, CHBDYG, or CHBDYP. See Remark 9. of CHBDYE for application of boundary conditions using CHBDYG entries and a discussion of front and back faces.

Main Index

295

296

Geometric Surface Element Definition (Property Form)

CHBDYP

Defines a boundary condition surface element with reference to a PHBDY entry. Format: 1

2

3

4

5

6

7

8

9

CHBDYP

EID

PID

TYPE

IVIEWF

IVIEWB

G1

G2

G0

RADMIDF

RADMIDB

GMID

CE

E1

E2

E3

2

5

POINT

2

2

101

3

3

0.0

0.0

10

Example: CHBDYP

500 1.0

Field

Contents

EID

Surface element identification number. (Unique (0 < Integer < 100,000,000) among all element identification numbers.)

PID

PHBDY property entry identification numbers. (Integer > 0)

TYPE

Surface type. See Remark 3. (Character)

IVIEWF

VIEW entry identification number for the front face. (Integer > 0 or blank)

IVIEWB

VIEW entry identification number for the back face. (Integer > 0 or blank)

G1, G2

Grid point identification numbers of grids bounding the surface. (Integer > 0)

GO

Orientation grid point. (Integer > 0; Default = 0)

RADMIDF

RADM entry identification number for front face. (Integer > 0 or blank)

RADMIDB

RADM entry identification number for back face. (Integer > 0 or blank)

GMID

Grid point identification number of a midside node if it is used with the line type surface element.

CE

Coordinate system for defining orientation vector. (Integer > 0; Default = 0)

Ei

Components of the orientation vector in coordinate system CE. The origin of the orientation vector is grid point G1. (Real or blank)

Remarks: 1. EID is a unique ID associated with a particular surface element as defined by the grid point(s). 2. The defaults for PID, TYPE, IVIEWF, IVIEWB, GO, RADMIDF, RADMIDB, CE, and Ei may be specified on the BDYOR entry. If a particular field is blank on both the CHBDYP entry and the BDYOR entry, then the default is zero.

Main Index

CHAPTER D Bulk Data Entries

3. TYPE specifies the kind of element surface; the allowed types are: “POINT,” “LINE,” “ELCYL,” “FTUBE,” and “TUBE.” For TYPE = “FTUBE” and TYPE = “TUBE,” the geometric orientation is completely determined by G1 and G2; the GO, CE, E1, E2, and E3 fields are ignored.

• TYPE = “POINT” TYPE = “POINT” has one primary grid point, requires a property entry, and the normal vector Vi must be specified if thermal flux is to be used. V n G1

Figure 4-6 Normal Vector for CHBDYP Element of Type “POINT” (See Remarks 4. and 5) The unit normal vector is given by n = V ⁄ V where V is specified in the Ei field and given in the basic system at the referenced grid point. See Remarks 4 and 5 for the determination of V .

• TYPE = “LINE,” “FTUBE,” or “TUBE” The TYPE = “LINE” type has two primary grid points, requires a property entry, and the vector is required. TYPE = “FTUBE” and TYPE = “TUBE” are similar to TYPE = “LINE” except they can have linear taper with no automatic view factor calculations. GMID is an option for the TYPE = “LINE” surface element only and is ignored for TYPE = “FTUBE” and “TUBE”. G2 GMID

n

V

T

G1

Figure 4-7 Normal Vector for CHBDYP Element with TYPE=“LINE”, TYPE=“FTUBE”, or TYPE=“TUBE” (See Remarks 4 and 5) The unit normal lies in the plane V and T , is perpendicular to T , and is given by: T × (V × T) n = ----------------------------------T × (V × T)

• TYPE = “ELCYL”

Main Index

297

298

TYPE = “ELCYL” (elliptic cylinder) has two connected primary grid points and requires a property entry. The vector must be nonzero. Automatic view factor calculations are not available.

n V T

R1 R2

Figure 4-8 Normal Vector for CHBDYP Element of TYPE=“ELCYL” (See Remarks 4 and 5) The same logic is used to determine n as for TYPE = LINE. The “radius” R1 is in the n direction, and R2 is the perpendicular to n and T (see fields 7 and 8 of PHBDY entry). 4. For TYPE = “POINT,” TYPE = “LINE,” and TYPE = “ELCYL,” geometric orientation is required. The required information is sought in the following order:

• If GO > 0 is found on the CHBDYP entry, it is used. • Otherwise, if a nonblank CE is found on the CHBDYP continuation entry, this CE and the corresponding vectors E1, E2, and E3 are used.

• If neither of the above, the same information is sought in the same way from the BDYOR entry.

• If none of the above apply, a warning message is issued. 5. The geometric orientation can be defined by either GO or the vector E1, E2, E3.

• If GO > zero: For a TYPE = “POINT” surface, the normal to the front face is the vector from G1 to GO. For the TYPE = “LINE” surface, the plane passes through G1, G2, GO and the right-hand rule is used on this sequence to get the normal to the front face. For TYPE = “ELCYL” surface the first axis of the ellipse lies on the G1, G2, GO plane, and the second axis is normal to this plane. For TYPE = “FTUBE” or “TUBE” surface, no orientation is required, and GO is superfluous.

• If GO is zero: For a TYPE = “POINT” surface, the normal to the front face is the orientation vector. For the TYPE = “LINE” surface, the plane passes through G1, G2, and the orientation vector; the front face is based on the right-hand rule for the vectors G2-G1 and the orientation vector. For TYPE = “ELCYL” surface, the first axis of the ellipse lies on the G1, G2, orientation vector plane, and the second axis is normal to this plane. Main Index

CHAPTER D Bulk Data Entries

6. The continuation entry is optional. 7. If the surface element is to be used in the calculation of view factors, it must have an associated VIEW entry. 8. All conduction elements to which any boundary condition is to be applied must be individually identified with the application of one of the surface element entries: CHBDYE, CHBDYG, or CHBDYP entries.

Main Index

299

300

Thermal Control ELement for Heat Transfer Analysis

CONTRLT

Defines the control mechanism for QVECT, QVOL, QBCY3, in heat transfer analysis (SOL 159). Format: 1 CONTRLT

2

3

4

5

6

7

8

9

ID

Sensor

SFORM

CTYPE

Pl

Ph

PTYPE

PZERO

DT

Delay

TAUc

TA8

100

20

3

68.

73.

1

0.

10

Example: CONTRLT

Field

Contents

ID

Control node ID as well as CONTROLT ID (Integer > 0, no default). See Remark 1.

Sensor

Grid or scalar point ID of the sensor (Integer > 0, no default). See Remark 2.

SFORM

Sensor output form (Character, T, default = T). See Remark 3.

CTYPE

Control type (Character, TSTAT for thermostat, default = TSTAT). See Remark 4.

Pl, Ph

Lower and upper limit value for desired temperature in the thermostat (real, no default). See Remark 5.

PTYPE

Process type (Integer value 1 thru 6). No default, see Remark 5.

PZERO

Initial controller value (0. < Real < 1., Default = 0.) See Remark 4.

DT

Monitoring time interval, or sampling period (Real > 0., Default = 0) See Remark 6.

Delay

Time delay after the switch is triggered or time for delayed control action in PID control. (Real < 0., Default = 0.) See Remark 7.

TAUc

Decay time constant for actuator response (Real > 0., default = 0.) See Remark 7.

Remarks: 1. The CONTRLT ID is referenced by CNTRLND entry identified on any of the QVECT, QVOL, QBDY3, Bulk Data entries. If any grid or scalar point ID is the same as the CONTRLT ID, then the combined logic associated with the controller and the control node will be in force for the LBC referenced. Any number of CONTROLT statements may exist in a single model. 2. Sensor point, where a feedback temperature or rate of change of temperature is measured. May be a dependent DOF in a MPC relationship. 3. Sensor output may only be temperature (T) 4. Control type can only be TSTAT. The PZERO field cannot have any other value but 0.0 or 1.0. 5. The upper and lower limit values (Pl and Ph) define a dead band for a thermostat. The available thermostat controller (TSTAT) formats are (PTYPE = 1 thru 6). Main Index

CHAPTER D Bulk Data Entries

Heat Boundary Element Free Convection Entry

CONV

Specifies a free convection boundary condition for heat transfer analysis through connection to a surface element (CHBDYi entry). Format: 1 CONV

2

3

4

5

6

7

8

9

EID

PCONID

FLMND

CNTRLND

TA1

TA2

TA3

TA4

TA5

TA6

TA7

TA8

2

101

3

201

10

Example: CONV

301

Field

Contents

EID

CHBDYG, CHBDYE, or CHBDYP surface element identification number. (Integer > 0)

PCONID

Convection property identification number of a PCONV entry. (Integer > 0)

FLMND

Point for film convection fluid property temperature. (Integer > 0; Default = 0)

CNTRLND Control point for free convection boundary condition. (Integer > 0; Default = 0) TAi

Ambient points used for convection. (Integer > 0 for TA1 and Integer > 0 for TA2 through TA8; Default for TA2 through TA8 is TA1.)

Remarks: 1. The basic exchange relationship can be expressed in one of the following forms:

• q = H ⋅ ( T – TAMB )

EXPF

( T – TAMB ) , CNTRLND = 0

• q = ( H ⋅ u CNTRLND ) ( T – TAMB ) • q = H(T

EXPF

– TAMB

• q = ( H ⋅ u CNTRLND ) ( T

EXPF

EXPF

EXPF

( T – TAMB ) , CNTRLND ≠ 0

) , CNTRLND = 0

– TAMB

EXPF

) , CNTRLND ≠ 0

EXPF is specified on the PCONV entry. (See “PCONV” on page 1843 entry for additional clarification of forms.) 2. The continuation entry is not required. 3. CONV is used with an CHBDYi (CHBDYG, CHBDYE, or CHBDYP) entry having the same EID.

Main Index

4. The temperature of the film convection point provides the look up temperature to determine the convection film coefficient. If FLMND=0, the reference temperature has several options. It can be the average of surface and ambient temperatures, the surface temperature, or the ambient temperature, as defined in the FORM field of the PCONV Bulk Data entry.

301

302

5. If only one ambient point is specified then all the ambient points are assumed to have the same temperature. If midside ambient points are missing, the temperature of these points is assumed to be the average of the connecting corner points. 6. See the Bulk Data entry, “PCONV” on page 1843, for an explanation of the mathematical relationships involved in free convection and the reference temperature for convection film coefficient.

Main Index

CHAPTER D Bulk Data Entries

Heat Boundary Element Forced Convection Entry

CONVM

Specifies a forced convection boundary condition for heat transfer analysis through connection to a surface element (CHBDYi entry). Format: 1

2

3

4

5

6

7

CONVM

EID

PCONID

FLMND

CNTMDOT

TA1

TA2

101

1

201

301

20

21

8

9

10

Example: CONVM

Field

Contents

EID

CHBDYP element identification number. (Integer > 0)

PCONID

Convection property identification number of a PCONVM entry. (Integer > 0)

FLMND

Point used for fluid film temperature. (Integer > 0; Default = 0)

CNTMDOT Control point used for controlling mass flow. (Integer > 0) TA1, TA2

Ambient points used for convection. (Integer > 0 for TA1 and Integer > 0 for TA2; Default for TA2 is TA1.)

Remarks: 1. CONVM is used with an CHBDYP entry of type FTUBE having the same EID. 2. The temperature of the fluid film point may be specified to determine the material properties for the fluid. If FLMND=0, the reference temperature has several options. It can be the average of surface and ambient temperatures, the surface temperatures, or the ambient temperature, as defined in the FORM field of the PCONVM Bulk Data entry. 3. CNTMDOT must be set to the desired mass flow rate (mdot) to effect the advection of energy downstream at an mdot ⋅ C p ⋅ T rate. In addition to the effect that mdot has on the transfer of thermal energy in the streamwise direction, this control point value is also used in computing the tube Reynolds number and subsequently the forced convection heat transfer coefficient if requested. This enables the fluid stream to exchange heat with its surroundings. 4. If only the first ambient point is specified then, the second ambient point is assumed to have the same temperature. 5. See the Bulk Data entry, “PCONVM” on page 1845, for an explanation of the mathematical relationships available for forced convection and the reference temperature for fluid material properties.

Main Index

303

304

Dynamic Load Time Delay

DELAY

Defines the time delay term τ in the equations of the dynamic loading function. Format: 1 DELAY

2

3

4

5

6

7

8

SID

P1

C1

T1

P2

C2

T2

5

21

6

4.25

7

6

8.1

9

10

Example: DELAY

Field

Contents

SID

Identification number of the DELAY entry. (Integer > 0)

Pi

Grid, extra, or scalar point identification number. (Integer > 0)

Ci

Component number. (Integer 1 through 6 for grid point, blank or 0 for extra point or scalar point.)

Ti

Time delay τ for designated point Pi and component Ci. (Real)

Remarks: 1. One or two dynamic load time delays may be defined on a single entry. 2. SID must also be specified on a RLOAD1, RLOAD2, TLOAD1, TLOAD2, or ACSRCE entry. See those entry descriptions for the formulas that define the manner in which the time delay τ is used. 3. A DAREA and/or LSEQ entry should be used to define a load at Pi and Ci. 4. In superelement analysis, DELAY entries may only be applied to loads on points in the residual structure.

Main Index

CHAPTER D Bulk Data Entries

Dynamic Load Combination or Superposition

DLOAD

Defines a dynamic loading condition for frequency response or transient response problems as a linear combination of load sets defined via RLOAD1 or RLOAD2 entries for frequency response or TLOAD1 or TLOAD2 entries for transient response. Format: 1 DLOAD

2

3

4

5

6

7

8

9

SID

S

S1

L1

S2

L2

S3

L3

S4

L4

-etc.-

*

17

1.0

2.0

6

-2.0

7

2.0

8

-2.0

9

10

Examples: DLOAD

Field

Contents

SID

Load set identification number. (Integer > 0)

S

Scale factor. (Real)

Si

Scale factors. (Real)

Li

Load set identification numbers of RLOAD1, RLOAD2, TLOAD1, TLOAD2, and ACSRC entries. (Integer > 0)

Remarks: 1. Dynamic load sets must be selected in the Case Control Section with DLOAD = SID. 2. The load vector being defined by this entry is given by { P } = S ∑ Si { P i } i

3. Each Li must be unique from any other Li on the same entry. 4. SID must be unique from all TLOADi and RLOADi entries. 5. Nonlinear transient load sets (NOLINi entries) may not be specified on DLOAD entries. NOLINi entries are selected separately in the Case Control Section by the NONLINEAR command. 6. A DLOAD entry may not reference a set identification number defined by another DLOAD entry. 7. TLOAD1 and TLOAD2 loads may be combined only through the use of the DLOAD entry. 8. RLOAD1 and RLOAD2 loads may be combined only through the use of the DLOAD entry. Main Index

305

306

Direct Matrix Input

DMI

Defines matrix data blocks. Generates a matrix of the following form: X 11 X 12 … X 1n X 21 X 22 … X 2n · · · ·

[ NAME ] =

X m1 … … X mn where the elements X ij may be real ( X ij = A ij ) or complex ( X ij = A ij + iB ij ) . The matrix is defined by a single header entry and one or more column entries. Only one header entry is required. A column entry is required for each column with nonzero elements. Header Entry Format: 1 DMI

2

3

4

5

6

NAME

“0”

FORM

TIN

7

8

9

TOUT

M

N

A(I1+1,J)

-etc.-

I2

B(I1+1,J)

-etc.-

4

2

4

2

0.0

3

Column Entry Format for Real Matrices: DMI

NAME

J

A(I2,J)

I1

A(I1,J)

-etc.-

Column Entry Format for Complex Matrices: DMI

NAME

J

I1

A(I1,J)

I2

A(I2,J)

B(I2,J)

-etc.-

B(I1,J)

A(I1+1,J)

Example of a Real Matrix: DMI

BBB

0

2

1

1

DMI

BBB

1

1

1.

3.

5.

DMI

BBB

2

2

6.

4

8.

1.0 3.0 5.0 0.0

BBB =

0.0 6.0 0.0 8.0

Example of a Complex Matrix:

Main Index

DMI

QQQ

0

2

3

3

DMI

QQQ

1

1

1.0

2.0

3.0

10

CHAPTER D Bulk Data Entries

DMI

5.0

6.0

QQQ

2

2

[ QQQ ] =

6.0

1.0 3.0 5.0 0.0

+ + + +

7.0

2.0i 0.0i 6.0i 0.0i

, , , ,

0.0 6.0 0.0 8.0

4

+ + + +

8.0

0.0i 7.0i 0.0i 9.0i

Field

Contents

NAME

Name of the matrix. See Remark 1. Name is used to reference the data block in the DMAP sequence. (One to eight alphanumeric characters, the first of which must be alphabetic.)

FORM

Form of matrix, as follows: (Integer) 1 = Square matrix (not symmetric) 2 = General rectangular matrix 3 = Diagonal matrix (M=number of rows, N = 1) 4 = Lower triangular factor 5 = Upper triangular factor 6 = Symmetric matrix 8 = Identity matrix (M=number of rows, N = M)

TIN

Type of matrix being input, as follows: (Integer) 1 = Real, single precision (one field used/element) 2 = Real, double precision (one field used/element) 3 = Complex, single precision (two fields used/element) 4 = Complex, double precision (two fields used/element)

Main Index

9.0

307

308

Field

Contents

TOUT

Type of matrix being output, as follows: (Integer) 0 = Set by precision cell 1 = Real, single precision 2 = Real, double precision 3 = Complex, single precision 4 = Complex, double precision

M

Number of rows in NAME. (Integer > 0)

N

Number of columns in NAME. Except for FORM 3 and 8. (Integer > 0)

"0"

Indicates the header entry.

J

Column number of NAME. (Integer > 0)

I1, I2, etc.

Row number of NAME, which indicates the beginning of a group of nonzero elements in the column. See Remark 13. (Integer > 0)

A(Ix,J)

Real part of element (see TIN). (Real)

B(Ix,J)

Imaginary part of element (see TIN). (Real)

Remarks: 1. In order to use the DMI feature, the user must write a DMAP, or make alterations to a solution sequence that includes the DMIIN module. See the MSC.Nastran 2005 DMAP Programmer’s Guide. All of the rules governing the use of data blocks in DMAP sequences apply. 2. The total number of DMIs and DTIs may not exceed 1000. 3. Field 3 of the header entry must contain an integer of zero (0). 4. For symmetric matrices, the entire matrix must be input. 5. Only nonzero terms need be entered. 6. Leading and trailing zeros in a column do not have to be entered. However, a blank field between nonzero fields on this entry is not equivalent to a zero. If a zero input is required, the appropriate type zero must be entered (i.e., 0.0 or 0.0D0). 7. Complex input must have both the real and imaginary parts entered if either part is nonzero; i.e., the zero component must be input explicitly. 8. If A(Ix,J) is followed by "THRU" in the next field and an integer row number "IX" after the THRU, then A(lx,J) will be repeated in each row through IX. The "THRU" must follow an element value. For example, the entries for a real matrix RRR would appear as follows: 1

Main Index

2

3

4

5

DMI

NAME

J

I1

A(I1,J)

DMI

RRR

1

2

1.0

6

THRU

7

10

8

9

I1

A(I2,J)

12

2.0

10

CHAPTER D Bulk Data Entries

These entries will cause the first column of the matrix RRR to have a zero in row 1, the values 1.0 in rows 2 through 10, a zero in row 11, and 2.0 in row 12. 9. Each column must be a single logical entry. The terms in each column must be specified in increasing row number order. 10. The "FORM" options 4, 5, and 8 are nonstandard forms and may be used only in conjunction with the modules indicated in Table 4-1. Table 4-1 DMI FORM Options FORM

Matrix Description

4

Modules ADD

FBS

MATPRN

Lower Triangular Factor

X

X

5

Upper Triangular Factor

X

X

8

Identity

X

X

X

MPYAD

X

11. Form 3 matrices are converted to Form 6 matrices, which may be used by any module. 12. Form 7 matrices may not be defined on this entry. 13. I1 must be specified. I2, etc. are not required if their matrix elements follow the preceding element in the next row of the matrix. For example, in the column entry for column 1 of QQQ, neither I2 nor I3 is specified. 14. The DMIG entry is more convenient for matrices with rows and columns that are referenced by grid or scalar point degrees-of-freedom.

Main Index

309

310

Direct Matrix Input at Points

DMIG

Defines direct input matrices related to grid, extra, and/or scalar points. The matrix is defined by a single header entry and one or more column entries. A column entry is required for each column with nonzero elements. Header Entry Format: 1 DMIG

2

3

4

5

6

7

8

9

NAME

“0"

IFO

TIN

TOUT

POLAR

G1

C1

A1

B1

3

3.+5

3.+3

1.0

0.

10

NCOL

Column Entry Format: DMIG

NAME

GJ

CJ

G2

C2

A2

B2

-etc.-

DMIG

STIF

0

1

3

4

DMIG

STIF

27

1

2

4

2.5+10

Example:

2 0.

50

Field

Contents

NAME

Name of the matrix. See Remark 1. (One to eight alphanumeric characters, the first of which is alphabetic.)

IFO

Form of matrix input. IFO = 6 must be specified for matrices selected by the K2GG, M2GG, and B2GG Case Control commands. (Integer) 1 = Square 9 or 2 = Rectangular 6 = Symmetric

TIN

Type of matrix being input: (Integer) 1 = Real, single precision (One field is used per element.) 2 = Real, double precision (One field is used per element.) 3 = Complex, single precision (Two fields are used per element.) 4 = Complex, double precision (Two fields are used per element.)

TOUT

Type of matrix that will be created: (Integer) 0 = Set by precision system cell (Default) 1 = Real, single precision 2 = Real, double precision 3 = Complex, single precision 4 = Complex, double precision

POLAR Main Index

Input format of Ai, Bi. (Integer=blank or 0 indicates real, imaginary format; Integer > 0 indicates amplitude, phase format.)

CHAPTER D Bulk Data Entries

Field

Contents

NCOL

Number of columns in a rectangular matrix. Used only for IFO = 9. See Remarks 5. and 6. (Integer > 0)

GJ

Grid, scalar or extra point identification number for column index. (Integer > 0)

CJ

Component number for grid point GJ. (0 < Integer < 6; blank or zero if GJ is a scalar or extra point.)

Gi

Grid, scalar, or extra point identification number for row index. (Integer > 0)

Ci

Component number for Gi for a grid point. ( 0 < CJ ≤ 6 ; blank or zero if Gi is a scalar or extra point.)

Ai, Bi

Real and imaginary (or amplitude and phase) parts of a matrix element. If the matrix is real (TIN = 1 or 2), then Bi must be blank. (Real)

Remarks: 1. Matrices defined on this entry may be used in dynamics by selection in the Case Control with K2PP = NAME, B2PP = NAME, M2PP = NAME for [Kpp], [Bpp], or [Mpp], respectively. Matrices may also be selected for all solution sequences by K2GG = NAME, B2GG = NAME, and M2GG = NAME. The g-set matrices are added to the structural matrices before constraints are applied, while p-set matrices are added in dynamics after constraints are applied. Load matrices may be selected by P2G = NAME for dynamic and superelement analyses. 2. The header entry containing IFO, TIN and TOUT is required. Each nonnull column is started with a GJ, CJ pair. The entries for each row of that column follows. Only nonzero terms need be entered. The terms may be input in arbitrary order. A GJ, CJ pair may be entered more than once, but input of an element of the matrix more than once will produce a fatal message. 3. Field 3 of the header entry must contain an integer 0. 4. For symmetric matrices (IFO = 6), a given off-diagonal element may be input either below or above the diagonal. While upper and lower triangle terms may be mixed, a fatal message will be issued if an element is input both below and above the diagonal. 5. The recommended format for rectangular matrices requires the use of NCOL and IFO = 9. The number of columns in the matrix is NCOL. (The number of rows in all DMIG matrices is always either p-set or g-set size, depending on the context.) The GJ term is used for the column index. The CJ term is ignored. 6. If NCOL is not used for rectangular matrices, two different conventions are available:

• If IFO = 9, GJ and CJ will determine the sorted sequence, but will otherwise be ignored; a rectangular matrix will be generated with the columns submitted being in the 1 to N positions, where N is the number of logical entries submitted (not counting the header entry).

• If IFO = 2, the number of columns of the rectangular matrix will be equal to the index of the highest numbered non-null column (in internal sort). Trailing null columns of the g- or p-size matrix will be truncated. Main Index

311

312

7. The matrix names must be unique among all DMIGs. 8. TIN should be set consistent with the number of decimal digits required to read the input data adequately. For a single-precision specification on a short-word machine, the input will be truncated after about eight decimal digits, even when more digits are present in a double-field format. If more digits are needed, a double precision specification should be used instead. However, note that a double precision specification requires a “D” type exponent even for terms that do not need an exponent. For example, unity may be input as 1.0 in single precision, but the longer form 1.0D0 is required for double precision. 9. On long-word machines, almost all matrix calculations are performed in single precision and on short-word machines, in double precision. It is recommended that DMIG matrices also follow these conventions for a balance of efficiency and reliability. The recommended value for TOUT is 0, which instructs the program to inspect the system cell that measures the machine precision at run time and sets the precision of the matrix to the same value. TOUT = 0 allows the same DMIG input to be used on any machine. If TOUT is contrary to the machine type specified (for example, a TOUT of 1 on a short-word machine), unreliable results may occur. 10. If any DMIG entry is changed or added on restart then a complete re-analysis is performed. Therefore, DMIG entry changes or additions are not recommended on restart.

Main Index

CHAPTER D Bulk Data Entries

Dynamic Load Phase Lead

DPHASE

Defines the phase lead term θ in the equation of the dynamic loading function. Format: 1 DPHASE

2

3

4

5

6

7

8

SID

P1

C1

TH1

P2

C2

TH2

4

21

6

2.1

8

6

7.2

9

10

Example: DPHASE

Field

Contents

SID

Identification number of DPHASE entry. (Integer > 0)

Pi

Grid, extra, or scalar point identification number. (Integer > 0)

Ci

Component number. (Integers 1 through 6 for grid points; zero or blank for extra or scalar points)

THi

Phase lead θ in degrees. (Real)

Remarks: 1. One or two dynamic load phase lead terms may be defined on a single entry. 2. SID must be referenced on a RLOADi entry. Refer to the RLOAD1 or RLOAD2 entry for the formulas that define how the phase lead θ is used. 3. A DAREA and/or LSEQ entry should be used to define a load at Pi and Ci. 4. In superelement analysis, DPHASE entries may only be applied to loads on points in the residual structure.

Main Index

313

314

INCLUDE

Insert External File

Inserts an external file into the input file. The INCLUDE statement may appear anywhere within the input data file. Format: INCLUDE’filename’ Describer: filename

Physical filename of the external file to be inserted. The user must supply the name according to installation or machine requirements. It is recommended that the filename be enclosed by single right-hand quotation marks.

Example: The following INCLUDE statement is used to obtain the Bulk Data from another file called MYBULK.DATA: SOL 101 CEND TITLE = STATIC ANALYSIS LOAD = 100 BEGIN BULK INCLUDE ’MYBULK.DATA’ ENDDATA Remarks: 1. INCLUDE statements may be nested; that is, INCLUDE statements may appear inside the external file. The nested depth level must not be greater than 10. 2. The total length of any line in an INCLUDE statement must not exceed 72 characters. Long file names may be split across multiple lines. For example the file: /dir123/dir456/dir789/filename.dat may be included with the following input: INCLUDE ‘/dir123 /dir456 /dir789/filename.dat’ 3. See the MSC.Nastran 2005 Installation and Operations Guide for more examples.

Main Index

CHAPTER D Bulk Data Entries

Static Load Combination (Superposition)

LOAD

Defines a static load as a linear combination of load sets defined via FORCE, MOMENT, FORCE1, MOMENT1, FORCE2, MOMENT2, PLOAD, PLOAD1, PLOAD2, PLOAD4, PLOADX1, SLOAD, RFORCE, and GRAV entries. Format: 1 LOAD

2

3

4

5

6

7

8

9

SID

S

S1

L1

S2

L2

S3

L3

S4

L4

-etc.-

101

-0.5

1.0

3

6.2

4

10

Example: LOAD

Field

Contents

SID

Load set identification number. (Integer > 0)

S

Overall scale factor. (Real)

Si

Scale factor on Li. (Real)

Li

Load set identification numbers defined on entry types listed above. (Integer > 0)

Remarks: 1. The load vector { P } is defined by { P } = S ∑ Si { P Li } i

2. Load set IDs (Li) must be unique. 3. This entry must be used if acceleration loads (GRAV entry) are to be used with any of the other types. 4. In the static solution sequences, the load set ID must be selected by the Case Control command LOAD=SID. In the dynamic solution sequences, SID must be referenced in the LID field of an LSEQ entry, which in turn must be selected by the Case Control command LOADSET. 5. A LOAD entry may not reference a set identification number defined by another LOAD entry.

Main Index

315

316

Heat Transfer Material Properties, Isotropic

MAT4

Defines the constant or temperature-dependent thermal material properties for conductivity, heat capacity, density, dynamic viscosity, heat generation, reference enthalpy, and latent heat associated with a single-phase change. Format: 1 MAT4

2

3

4

5

6

7

8

9

MID

K

CP

r

H

m

HGEN

REFENTH

TCH

TDELTA

QLAT

1

204.

.900

10

Example: MAT4

2700.

Field

Contents

MID

Material identification number. (Integer > 0)

K

Thermal conductivity. (Blank or Real > 0.0)

CP

Heat capacity per unit mass at constant pressure (specific heat). (Blank or Real > 0.0)

ρ

Density. (Real > 0.0; Default = 1.0)

H

Free convection heat transfer coefficient. (Real or blank)

m

Dynamic viscosity. See Remark 2. (Real > 0.0 or blank)

HGEN

Heat generation capability used with QVOL entries. (Real > 0.0; Default = 1.0)

REFENTH

Reference enthalpy. (Real or blank)

TCH

Lower temperature limit at which phase change region is to occur. (Real or blank)

TDELTA

Total temperature change range within which a phase change is to occur. (Real > 0.0 or blank)

QLAT

Latent heat of fusion per unit mass associated with the phase change. (Real > 0.0 or blank)

Remarks: 1. The MID must be unique with respect to all other MAT4 and MAT5 entries. MAT4 may specify material properties for any conduction elements as well as properties for a forced convection fluid (see CONVM). MAT4 also provides the heat transfer coefficient for free convection (see CONV). 2. For a forced convection fluid, µ must be specified.

Main Index

CHAPTER D Bulk Data Entries

3. REFENTH is the enthalpy corresponding to zero temperature if the heat capacity CP is a constant. If CP is obtained through a TABLEM lookup, REFENTH is the enthalpy at the first temperature in the table. 4. Properties specified on the MAT4 entry may be defined as temperature dependent by use of the MATT4 entry.

Main Index

317

318

Thermal Material Property Definition

MAT5

Defines the thermal material properties for anisotropic materials. Format: 1 MAT5

2

3

4

5

6

7

8

9

MID

KXX

KXY

KXZ

KYY

KYZ

KZZ

CP

RHO

HGEN

24

.092

0.20

0.2

10

Example: MAT5

.083

2.00

Field

Contents

MID

Material identification number. (Integer > 0)

Kij

Thermal conductivity. (Real)

CP

Heat capacity per unit mass. (Real > 0.0 or blank)

RHO

Density. (Real>0.0; Default=1.0)

HGEN

Heat generation capability used with QVOL entries. (Real > 0.0; Default = 1.0)

Remarks: 1. The thermal conductivity matrix has the following form:

K =

KXX KXY KXZ KXY KYY KYZ KXZ KYZ KZZ

2. The material identification number may be the same as a MAT1, MAT2, or MAT3 entry but must be unique with respect to other MAT4 or MAT5 entries. 3. MAT5 materials may be made temperature-dependent by use of the MATT5 entry. 4. When used for axisymmetric analysis (CTRIAX6), material properties are represented where: KXX = radial conductivity component KYY = axial conductivity component

Main Index

CHAPTER D Bulk Data Entries

Thermal Material Temperature Dependence

MATT4

Specifies table references for temperature-dependent MAT4 material properties. Format: 1 MATT4

2

3

4

MID

T(K)

T(CP)

10

11

5

6

7

8

T(H)

T(µ)

T(HGEN)

9

10

Example(s): MATT4

2

Field

Contents

MID

Identification number of a MAT4 entry that is temperature dependent. (Integer > 0)

T(K)

Identification number of a TABLEMj entry that gives the temperature dependence of the thermal conductivity. (Integer > 0 or blank)

T(CP)

Identification number of a TABLEMj entry that gives the temperature dependence of the thermal heat capacity. (Integer > 0 or blank)

T(H)

Identification number of a TABLEMj entry that gives the temperature dependence of the free convection heat transfer coefficient. (Integer > 0 or blank)

T(µ)

Identification number of a TABLEMj entry that gives the temperature dependence of the dynamic viscosity. (Integer > 0 or blank)

T(HGEN)

Identification number of a TABLEMj entry that gives the temperature dependence of the internal heat generation property for QVOL. (Integer > 0 or blank)

Remarks: 1. The basic quantities on the MAT4 entry are always multiplied by the corresponding tabular function referenced by the MATT4 entry. 2. If the fields are blank or zero, then there is no temperature dependence of the referenced quantity on the MAT4 entry.

Main Index

319

320

Thermal Anisotropic Material Temperature Dependence

MATT5

Specifies temperature-dependent material properties on MAT5 entry fields via TABLEMi entries. Format: 1 MATT5

2

3

4

5

6

7

8

9

MID

T(KXX)

T(KXY)

T(KXZ)

T(KYY)

T(KYZ)

T(KZZ)

T(CP)

10

T(HGEN)

Example: MATT5

24

73

Field

Contents

MID

Identification number of a MAT5 entry that is to be temperature dependent. (Integer > 0)

T(Kij)

Identification number of a TABLEMi entry. The TABLEMi entry specifies temperature dependence of the matrix term. (Integer > 0 or blank)

T(CP)

Identification number of a TABLEMi entry that specifies the temperature dependence of the thermal heat capacity. (Integer > 0 or blank)

T(HGEN)

Identification number of a TABLEMi entry that gives the temperature dependence of the internal heat generation property for the QVOL entry. (Integer > 0 or blank)

Remarks: 1. The basic quantities on the MAT5 entry are always multiplied by the tabular function referenced by the MATT5 entry. 2. If the fields are blank or zero, then there is no temperature dependence of the referenced quantity on the basic MAT5 entry.

Main Index

CHAPTER D Bulk Data Entries

Multipoint Constraint

MPC

Defines a multipoint constraint equation of the form

∑ Aj u j

= 0

j

where u j represents degree-of-freedom Cj at grid or scalar point Gj. Format: 1 MPC

2

3

4

5

6

7

8

SID

G1

C1

A1

G2

C2

A2

G3

C3

A3

-etc.-

28

3

6.2

2

1

4

-2.91

9

10

Example: MPC

3

4.29

Field

Contents

SID

Set identification number. (Integer > 0)

Gj

Identification number of grid or scalar point. (Integer > 0)

Cj

Component number. (Any one of the Integers 1 through 6 for grid points; blank or zero for scalar points.)

Aj

Coefficient. (Real; Default = 0.0 except A1 must be nonzero.)

Remarks: 1. Multipoint constraint sets must be selected with the Case Control command MPC = SID. 2. The first degree-of-freedom (G1, C1) in the sequence is defined to be the dependent degree-of-freedom. A dependent degree-of-freedom assigned by one MPC entry cannot be assigned dependent by another MPC entry or by a rigid element. 3. Forces of multipoint constraint may be recovered in all solution sequences, except SOL 129, with the MPCFORCE Case Control command. 4. The m-set degrees-of-freedom specified on this entry may not be specified on other entries that define mutually exclusive sets. See the “Degree-of-Freedom Sets” on page 1557 for a list of these entries. 5. By default, the grid point connectivity created by the MPC, MPCADD, and MPCAX entries is not considered during resequencing, (see the PARAM,OLDSEQ description in “Parameters” on page 1409). In order to consider the connectivity during resequencing, SID must be specified on the PARAM,MPCX entry. Using the example above, specify PARAM,MPCX,3. Main Index

321

322

Multipoint Constraint Set Combination

MPCADD

Defines a multipoint constraint set as a union of multipoint constraint sets defined via MPC entries. Format: 1

2

3

4

5

6

7

8

9

MPCADD

SID

S1

S2

S3

S4

S5

S6

S7

S8

S9

-etc.-

101

2

3

1

6

4

10

Example: MPCADD

Field

Contents

SID

Set identification number. (Integer > 0)

Sj

Set identification numbers of multipoint constraint sets defined via MPC entries. (Integer > 0)

Remarks: 1. Multipoint constraint sets must be selected with the Case Control command MPC = SID. 2. The Sj must be unique and may not be the identification number of a multipoint constraint set defined by another MPCADD entry. 3. MPCADD entries take precedence over MPC entries. If both have the same SID, only the MPCADD entry will be used. 4. By default, the grid point connectivity created by the MPC, MPCADD, and MPCAX entries is not considered during resequencing, (see the PARAM,OLDSEQ description in “Parameters” on page 1409). In order to consider the connectivity during resequencing, SID must be specified on the PARAM,MPCX entry. Using the example above, specify PARAM,MPCX,101.

Main Index

CHAPTER D Bulk Data Entries

Parameters for Nonlinear Static Analysis Control

NLPARM

Defines a set of parameters for nonlinear static analysis iteration strategy. Format: 1

2

3

4

5

6

7

8

9

NLPARM

ID

NINC

DT

KMETHOD

KSTEP

MAXITER

CONV

INTOUT

EPSU

EPSP

EPSW

MAXDIV

MAXQN

MAXLS

FSTRESS

LSTOL

MAXR

MAXBIS

10

RTOLB

Example: NLPARM

15

5

ITER

Field

Contents

ID

Identification number. (Integer > 0)

NINC

Number of increments. See Remark 16. (0 < Integer < 1000; Default=10)

DT

Incremental time interval for creep analysis. See Remark 3. (Real > 0.0; Default = 0.0 for no creep.)

KMETHOD Method for controlling stiffness updates. See Remark 4. (Character = “AUTO”, “ITER”, or “SEMI”; Default = “AUTO”.)

Main Index

KSTEP

Number of iterations before the stiffness update for ITER method. See Remark 5. (Integer > 1; Default = 5)

MAXITER

Limit on number of iterations for each load increment. See Remark 6. (Integer > 0; Default = 25)

CONV

Flags to select convergence criteria. See Remark 7. (Character = “U”, “P”, “W”, or any combination; Default = “PW”.)

INTOUT

Intermediate output flag. See Remark 8. (Character = “YES”, “NO”, or “ALL”; Default = NO)

EPSU

Error tolerance for displacement (U) criterion. See Remark 16. (Real > 0.0; Default = 1.0E-2;)

EPSP

Error tolerance for load (P) criterion. See Remark 16. (Real > 0.0; Usual default = 1.0E-2)

EPSW

Error tolerance for work (W) criterion. See Remark 16. (Real > 0.0; Usual default = 1.0E-2)

MAXDIV

Limit on probable divergence conditions per iteration before the solution is assumed to diverge. See Remark 9. (Integer ≠ 0; Default = 3)

MAXQN

Maximum number of quasi-Newton correction vectors to be saved on the database. See Remark 10. (Integer > 0; Default = MAXITER)

323

324

Field

Contents

MAXLS

Maximum number of line searches allowed for each iteration. See Remark 11. (Integer > 0; Default = 4)

FSTRESS

Fraction of effective stress ( σ ) used to limit the subincrement size in the material routines. See Remark 12. (0.0 < Real < 1.0; Default = 0.2)

LSTOL

Line search tolerance. See Remark 11. (0.01 < Real < 0.9; Default = 0.5)

MAXBIS

Maximum number of bisections allowed for each load increment. See Remark 13. (-10 < MAXBIS < 10; Default = 5)

MAXR

Maximum ratio for the adjusted arc-length increment relative to the initial value. See Remark 14. (1.0 < MAXR < 40.0; Default = 20.0)

RTOLB

Maximum value of incremental rotation (in degrees) allowed per iteration to activate bisection. See Remark 15. (Real > 2.0; Default = 20.0)

Remarks: 1. The NLPARM entry is selected by the Case Control command NLPARM = ID. Each solution subcase requires an NLPARM command. 2. In cases of static analysis (DT = 0.0) using Newton methods, NINC is the number of equal subdivisions of the load change defined for the subcase. Applied loads, gravity loads, temperature sets, enforced displacements, etc., define the new loading conditions. The differences from the previous case are divided by NINC to define the incremental values. In cases of static analysis (DT = 0.0) using arc-length methods, NINC is used to determine the initial arc-length for the subcase, and the number of load subdivisions will not be equal to NINC. In cases of creep analysis (DT > 0.0), NINC is the number of time step increments. 3. The unit of DT must be consistent with the unit used on the CREEP entry that defines the creep characteristics. Total creep time for the subcase is DT multiplied by the value in the field NINC; i.e., DT*NINC. 4. The stiffness update strategy is selected in the KMETHOD field.

• If the AUTO option is selected, the program automatically selects the most efficient strategy based on convergence rates. At each step the number of iterations required to converge is estimated. Stiffness is updated, if (i) estimated number of iterations to converge exceeds MAXITER, (ii) estimated time required for convergence with current stiffness exceeds the estimated time required for convergence with updated stiffness, and (iii) solution diverges. See Remarks 9. and 13. for diverging solutions.

• If the SEMI option is selected, the program for each load increment (i) performs a single iteration based upon the new load, (ii) updates the stiffness matrix, and (iii) resumes the normal AUTO option.

Main Index

CHAPTER D Bulk Data Entries

• If the ITER option is selected, the program updates the stiffness matrix at every KSTEP iterations and on convergence if KSTEP < MAXITER. However, if KSTEP > MAXITER, stiffness matrix is never updated. Note that the Newton-Raphson iteration strategy is obtained by selecting the ITER option and KSTEP = 1, while the Modified Newton-Raphson iteration strategy is obtained by selecting the ITER option and KSTEP = MAXITER. 5. For AUTO and SEMI options, the stiffness matrix is updated on convergence if KSTEP is less than the number of iterations that were required for convergence with the current stiffness. 6. The number of iterations for a load increment is limited to MAXITER. If the solution does not converge in MAXITER iterations, the load increment is bisected and the analysis is repeated. If the load increment cannot be bisected (i.e., MAXBIS is attained or MAXBIS = 0) and MAXDIV is positive, the best attainable solution is computed and the analysis is continued to the next load increment. If MAXDIV is negative, the analysis is terminated. 7. The test flags (U = displacement error, P = load equilibrium error, and W = work error) and the tolerances (EPSU, EPSP, and EPSW) define the convergence criteria. All the requested criteria (combination of U, P, and/or W) are satisfied upon convergence. See the MSC.Nastran Handbook for Nonlinear Analysis for more details on convergence criteria. 8. INTOUT controls the output requests for displacements, element forces and stresses, etc. YES or ALL must be specified in order to be able to perform a subsequent restart from the middle of a subcase. INTOUT

Output Processed

YES

For every computed load increment.

NO

For the last load of the subcase.

ALL

For every computed and user-specified load increment.

• For the Newton family of iteration methods (i.e., when no NLPCI command is specified), the option ALL is equivalent to option YES since the computed load increment is always equal to the user-specified load increment.

• For arc-length methods (i.e., when the NLPCI command is specified) the computed load increment in general is not going to be equal to the user-specified load increment, and is not known in advance. The option ALL allows the user to obtain solutions at the desired intermediate load increments. 9. The ratio of energy errors before and after the iteration is defined as divergence rate i ( E ) , i.e.,

E

Main Index

i

i T

i

{ ∆u } { R } = ---------------------------------------i T i–1 { ∆u } { R }

325

326

Depending on the divergence rate, the number of diverging iteration (NDIV) is incremented as follows: i

i

If E ≥ 1 or E < – 10 If – 10

12

12

, then NDIV = NDIV + 2

i

< E < – 1 , then NDIV = NDIV + 1

The solution is assumed to diverge when NDIV > |MAXDIV|. If the solution diverges and the load increment cannot be further bisected (i.e., MAXBIS is attained or MAXBIS is zero), the stiffness is updated based on the previous iteration and the analysis is continued. If the solution diverges again in the same load increment while MAXDIV is positive, the best solution is computed and the analysis is continued to the next load increment. If MAXDIV is negative, the analysis is terminated on the second divergence. 10. The BFGS update is performed if MAXQN > 0. As many as MAXQN quasi-Newton vectors can be accumulated. The BFGS update with these QN vectors provides a secant modulus in the search direction. If MAXQN is reached, no additional ON vectors will be accumulated. Accumulated QN vectors are purged when the stiffness is updated and the accumulation is resumed. 11. The line search is performed as required, if MAXLS > 0. In the line search, the displacement increment is scaled to minimize the energy error. The line search is not performed if the absolute value of the relative energy error is less than the value specified in LSTOL. 12. The number of subincrements in the material routines (elastoplastic and creep) is determined so that the subincrement size is approximately FSTRESS ⋅ σ (equivalent stress). FSTRESS is also used to establish a tolerance for error correction in the elastoplastic material; i.e., error in yield function < FSTRESS ⋅ σ If the limit is exceeded at the converging state, the program will exit with a fatal message. Otherwise, the stress state is adjusted to the current yield surface. 13. The number of bisections for a load increment/arc-length is limited to the absolute value of MAXBIS. Different actions are taken when the solution diverges depending on the sign of MAXBIS. If MAXBIS is positive, the stiffness is updated on the first divergence, and the load is bisected on the second divergence. If MAXBIS is negative, the load is bisected every time the solution diverges until the limit on bisection is reached. If the solution does not converge after |MAXBIS| bisections, the analysis is continued or terminated depending on the sign of MAXDIV. See Remark 9. 14. MAXR is used in the adaptive load increment/arc-length method to define the overall upper and lower bounds on the load increment/arc-length in the subcase; i.e., ∆l n 1 ------------------ ≤ -------- ≤ MAXR MAXR ∆l o Main Index

CHAPTER D Bulk Data Entries

where ∆l n is the arc-length at step n and ∆l o is the original arc-length. The arc-length method for load increments is selected by an NLPCI Bulk Data entry. This entry must have the same ID as the NLPARM Bulk Data entry. 15. The bisection is activated if the incremental rotation for any degree-of-freedom ( ∆θ x, ∆θ y, or ∆θ z ) exceeds the value specified by RTOLB. This bisection strategy is based on the incremental rotation and controlled by MAXBIS. 16. Default tolerance sets are determined based on model type and desired accuracy. Accuracy is under user control and can be specified on the PARAM, NLTOL entry. NLTOL’s value is used only if the CONV, EPSU, EPSP and EPSW fields are blank, and if NINC is set to a value of 10 or larger. Otherwise, the NLTOL selection will be overridden. The tables below list tolerances according to NLTOL selections:

Main Index

327

328

Table 4-2 Default Tolerances for Static Nonlinear SOL 106 Models Without Gaps, Contact or Heat Transfer NLTOL

Designation

CONV

EPSU

EPSP

EPSW

0

Very high

PW

_______

1.0E-3

1.0E-7

1

High

PW

_______

1.0E-2

1.0E-3

2

Engineering

PW

_______

1.0E-2

1.0E-2

3

Prelim Design

PW

_______

1.0E-1

1.0E-1

Engineering

PW

_______

1.0E-2

1.0E-2

None

Table 4-3 Default Tolerances for Static Nonlinear SOL 106 Models With Gaps or Contact (Enter NLTOL Values of 0 or 2 Only or Omit the Parameter) NLTOL

Designation

CONV

EPSU

EPSP

EPSW

0

Very high

PW

_______

1.0E-3

1.0E-7

2

Engineering

PW

_______

1.0E-3

1.0E-5

None

Engineering

PW

_______

1.0E-3

1.0E-5

Table 4-4 Default Tolerances for Static Nonlinear SOL 106 or 153 Models With Heat Transfer (Enter NLTOL Value of 0 Only or Omit the Parameter) NLTOL

Main Index

Designation

CONV

EPSU

EPSP

EPSW

0

Very high

PW

_______

1.0E-3

1.0E-7

None

Very high

PW

_______

1.0E-3

1.0E-7

CHAPTER D Bulk Data Entries

Nonlinear Transient Load as a Tabular Function

NOLIN1

Defines nonlinear transient forcing functions of the form Function of displacement: P i ( t ) = S ⋅ T ( u j ( t ) )

Eq. 4-1

· Function of velocity: P i ( t ) = S ⋅ T ( u j ( t ) )

Eq. 4-2

· where u j ( t ) and u j ( t ) are the displacement and velocity at point GJ in the direction of CJ. Format: 1

2

3

4

5

6

7

8

NOLIN1

SID

GI

CI

S

GJ

CJ

TID

21

3

4

2.1

3

10

6

9

10

Example: NOLIN1

Field

Contents

SID

Nonlinear load set identification number. (Integer > 0)

GI

Grid, scalar, or extra point identification number at which nonlinear load is to be applied. (Integer > 0)

CI

Component number for GI. (0 < Integer < 6; blank or zero if GI is a scalar or extra point.)

S

Scale factor. (Real)

GJ

Grid, scalar, or extra point identification number. (Integer > 0)

CJ

Component number for GJ according to the following table:

TID

Type of Point

Displacement

Velocity

Grid

1 < Integer < 6

11 < Integer < 16

Scalar

Blank or zero

Integer = 10

Extra

Blank or zero

Integer = 10

Identification number of a TABLEDi entry. (Integer > 0)

Remarks: 1. Nonlinear loads must be selected with the Case Control command NONLINEAR = SID. 2. Nonlinear loads may not be referenced on DLOAD entry. Main Index

329

330

3. All degrees-of-freedom referenced on NOLIN1 entries must be members of the solution set. This means the e-set (EPOINT entry) for modal formulation and the d-set for direct formulation. 4. Nonlinear loads as a function of velocity (Equation 2) are denoted by components ten greater than the actual component number; i.e., a component of 11 is component 1 (velocity). The velocity is determined by u j, t – u j, t – 1 · u j, t = ---------------------------------∆t where ∆t is the time step interval and u j, t – 1 is the displacement of GJ-CJ for the previous time step.

Main Index

CHAPTER D Bulk Data Entries

Nonlinear Transient Load as the Product of Two Variables

NOLIN2

Defines nonlinear transient forcing functions of the form Pi ( t ) = S ⋅ Xj ( t ) ⋅ Xk ( t ) where X j ( t ) and X k ( t ) can be either displacement or velocity at points GJ and GK in the directions of CJ and CK. Format: 1

2

3

4

5

6

7

8

9

NOLIN2

SID

GI

CI

S

GJ

CJ

GK

CK

14

2

1

2.9

2

1

2

10

Example: NOLIN2

Field

Contents

SID

Nonlinear load set identification number. (Integer > 0)

GI

Grid, scalar, or extra point identification number at which nonlinear load is to be applied. (Integer > 0)

CI

Component number for GI. (0 < Integer < 6; blank or zero if GI is a scalar or extra point.)

S

Scale factor. (Real)

GJ, GK

Grid, scalar, or extra point identification number. (Integer > 0)

CJ, CK

Component number for GJ, GK according to the following table: Type of Point

Displacement

Velocity

Grid

1 < Integer < 6

11 < Integer < 16

Scalar

Blank or zero

Integer = 10

Extra

Blank or zero

Integer = 10

Remarks: 1. Nonlinear loads must be selected with the Case Control command NONLINEAR=SID. 2. Nonlinear loads may not be referenced on a DLOAD entry. 3. All degrees-of-freedom referenced on NOLIN2 entries must be members of the solution set. This means the e-set for modal formulation and the d-set for direct formulation. 4. GI-CI, GJ-CJ, and G K-CK may be the same point. Main Index

331

332

· 5. Nonlinear loads may be a function of displacement ( X = u ) or velocity ( X = u ) . Velocities are denoted by a component number ten greater than the actual component number; i.e., a component of 10 is component 0 (velocity). The velocity is determined by ut – ut – 1 · u t = ------------------------∆t where ∆t is the time step interval and u t – 1 is the displacement of GJ-CJ or GK-CK for the previous time step.

Main Index

CHAPTER D Bulk Data Entries

Nonlinear Transient Load as a Positive Variable Raised to a Power

NOLIN3

Defines nonlinear transient forcing functions of the form   S ⋅ [ X ( t ) ] A, X ( t ) > 0 j j Pi ( t ) =   0, X j ( t ) ≤ 0  where X j ( t ) may be a displacement or a velocity at point GJ in the direction of CJ. Format: 1

2

3

4

5

6

7

8

NOLIN3

SID

GI

CI

S

GJ

CJ

A

4

102

-6.1

2

15

-3.5

9

10

Example: NOLIN3

Field

Contents

SID

Nonlinear load set identification number. (Integer > 0)

GI

Grid, scalar, or extra point identification number at which the nonlinear load is to be applied. (Integer > 0)

CI

Component number for GI. (0 < Integer < 6; blank or zero if GI is a scalar or extra point.)

S

Scale factor. (Real)

GJ

Grid, scalar, extra point identification number. (Integer > 0)

CJ

Component number for GJ according to the following table:

A

Type of Point

Displacement

Velocity

Grid

1 < Integer < 6

11 < Integer < 16

Scalar

Blank or zero

Integer = 10

Extra

Blank or zero

Integer = 10

Exponent of the forcing function. (ReaI)

Remarks: 1. Nonlinear loads must be selected with the Case Control command NONLINEAR = SID. 2. Nonlinear loads may not be referenced on a DLOAD entry. Main Index

333

334

3. All degrees-of-freedom referenced on NOLIN3 entries must be members of the solution set. This means the e-set for modal formulation and the d-set for direct formulation. · 4. Nonlinear loads may be a function of displacement ( X j = u j ) or velocity ( X j = u j ) . Velocities are denoted by a component number ten greater than the actual component number; e.g., a component of 16 is component 6 (velocity). The velocity is determined by u j, t – u j, t – 1 · u j, t = ---------------------------------∆t where ∆t is the time step interval and u j, t – 1 is the displacement of GJ-CJ for the previous time step. 5. Use a NOLIN4 entry for the negative range of X j ( t ) .

Main Index

CHAPTER D Bulk Data Entries

Nonlinear Transient Load as a Negative Variable Raised to a Power

NOLIN4

Defines nonlinear transient forcing functions of the form   – S ⋅ [ – X ( t ) ] A, X ( t ) < 0 j j Pi ( t ) =   0, X j ( t ) ≥ 0  where X j ( t ) may be a displacement or a velocity at point GJ in the direction of CJ. Format: 1

2

3

4

5

6

7

8

NOLIN4

SID

GI

CI

S

GJ

CJ

A

2

4

6

2.0

101

9

10

Example: NOLIN4

16.3

Field

Contents

SID

Nonlinear load set identification number. (Integer > 0)

GI

Grid, scalar, or extra point identification number at which nonlinear load is to be applied. (Integer > 0)

CI

Component number for GI. (0 < Integer < 6; blank or zero if GI is a scalar or extra point.)

S

Scale factor. (Real)

GJ

Grid, scalar, or extra point identification number. (Integer > 0)

CJ

Component number for GJ according to the following table:

A

Type of Point

Displacement

Veloicty

Grid

1 < Integer < 6

11 < Integer < 16

Scalar

Blank or zero

Integer = 10

Extra

Blank or zero

Integer = 10

Exponent of forcing function. (Real)

Remarks: 1. Nonlinear loads must be selected with the Case Control command NONLINEAR = SID. 2. Nonlinear loads may not be referenced on a DLOAD entry. Main Index

335

336

3. All degrees-of-freedom referenced on NOLIN4 entries must be members of the solution set. This means the e-set for modal formulation and the d-set for direct formulation. · 4. Nonlinear loads may be a function of displacement ( X j = u j ) or velocity ( X j = u j ) . Velocities are denoted by a component number ten greater than the actual component number; i.e., a component of 10 is component 0 (velocity). The velocity is determined by u j, t – u j, t – 1 · u j, t = ---------------------------------∆t where ∆t is the time step interval and uj, t – 1 is the displacement of GJ-CJ for the previous time step. X (t) Use a NOLIN3 entry for the positive range of j .

Main Index

CHAPTER D Bulk Data Entries

Parameter

PARAM

Specifies values for parameters used in solution sequences or user-written DMAP programs. Format: 1

2

3

4

PARAM

N

V1

V2

IRES

1

5

6

7

8

9

10

Example: PARAM

Field

Contents

N

Parameter name (one to eight alphanumeric characters, the first of which is alphabetic).

V1, V2

Parameter value based on parameter type, as follows: Type

V1

V2

Integer

Integer

Blank

Real, single-precision

Real

Blank

Character

Character

Blank

Real, double-precision

Double-precision real

Blank

Complex, single-precision

Real or blank

Real or blank

Complex, double-precision

Double-precision real

Double-precision real

Remarks: 1. See “Parameters” on page 601 for a list of parameters used in solution sequences that may be set by the user on PARAM entries. 2. If the large field entry format is used, the second physical entry must be present, even though fields 6 through 9 are blank.

Main Index

337

338

Convection Property Definition

PCONV

Specifies the free convection boundary condition properties of a boundary condition surface element used for heat transfer analysis. Format: 1 PCONV

2

3

4

5

PCONID

MID

FORM

EXPF

3

2

0

.25

6

7

8

9

10

Example: PCONV

Field

Contents

PCONID

Convection property identification number. (Integer > 0)

MID

Material property identification number. (Integer > 0)

FORM

Type of formula used for free convection. (Integer 0, 1, 10, 11, 20, or 21; Default = 0)

EXPF

Free convection exponent as implemented within the context of the particular form that is chosen. See Remark 3. (Real > 0.0; Default = 0.0)

Remarks: 1. Every surface to which free convection is to be applied must reference a PCONV entry. PCONV is referenced on the CONV Bulk Data entry. 2. MID is used to supply the convection heat transfer coefficient (H). 3. EXPF is the free convection temperature exponent.

• If FORM = 0, 10, or 20, EXPF is an exponent of (T – TAMB), where the convective heat transfer is represented as q = H ⋅ u CNTRLND ⋅ ( T – TAMB )

EXPF

⋅ ( T – TAMB ) .

• If FORM = 1, 11, or 21, q = H ⋅ u CNTRLND ⋅ ( T

EXPF

– TAMB

EXPF

)

where T represents the elemental grid point temperatures and TAMB is the associated ambient temperature. 4. FORM specifies the formula type and the reference temperature location used in calculating the convection film coefficient if FLMND = 0.

• If FORM = 0 or 1, the reference temperature is the average of element grid point temperatures (average) and the ambient point temperatures (average). Main Index

CHAPTER D Bulk Data Entries

• If FORM = 10 or 11, the reference temperature is the surface temperature (average of element grid point temperatures).

• If FORM = 20 or 21, the reference temperature is the ambient temperature (average of ambient point temperatures).

Main Index

339

340

Forced Convection Property Definition

PCONVM

Specifies the forced convection boundary condition properties of a boundary condition surface element used for heat transfer analysis. Format: 1 PCONV M

2

3

4

5

6

7

8

9

PCONID

MID

FORM

FLAG

COEF

EXPR

EXPPI

EXPPO

3

2

1

1

.023

0.80

0.40

0.30

10

Example: PCONV M

Field

Contents

PCONID

Convection property identification number. (Integer > 0)

MID

Material property identification number. (Integer > 0)

FORM

Type of formula used for convection. (Integer = 0, 1, 10, 11, 20, or 21; Default = 0)

FLAG

Flag for mass flow convection. (Integer = 0 or 1; Default = 0)

COEF

Constant coefficient used for forced convection. (Real > 0.0)

EXPR

Reynolds number convection exponent. (Real > 0.0; Default = 0.0)

EXPPI

Prandtl number convection exponent for heat transfer into the working fluid. (Real > 0.0; Default = 0.0)

EXPPO

Prandtl number convection exponent for heat transfer out of the working fluid. (Real > 0.0; Default = 0.0)

Remarks: 1. Every surface to which forced convection is applied must reference a PCONVM entry. PCONVM is referenced on the CONVM entry. 2. MID specifies material properties of the working fluid at the temperature of the point FLMND. FLMND is specified on the CONVM entry. 3. The material properties are used in conjunction with the average diameter and mass flow rate (mdot). MID references the material properties and supplies the fluid conductivity (k), heat capacity (cp), and viscosity ( µ ) needed to compute the Reynolds (Re) and Prandtl (Pr) numbers as follows: Re = 4 ⋅ mdot ⁄ ( π ⋅ diameter ⋅ µ ) Pr = cp ⋅ µ ⁄ k 4. FORM controls the type of formula used in determination of the forced convection film coefficient h. There are two cases: Main Index

CHAPTER D Bulk Data Entries

• If FORM = 0, 10, or 20 than h = coef ⋅ Re

EXPR

⋅ Pr

EXPP

.

• If FORM = 1, 11, or 21 then the above h is multiplied by k and divided by the average hydraulic diameter.

• FORM also specifies the reference temperature used in calculating material properties for the fluid if FLMND = 0.

• If FORM = 0 or 1, the reference temperature is the average of element grid point temperatures (average) and the ambient point temperature (average).

• If FORM = 10 or 11, the reference temperature is the surface temperature (average of element grid point temperatures).

• If FORM = 20 or 21, the reference temperature is the ambient temperature (average of ambient point temperature). 5. In the above expression, EXPP is EXPPI or EXPPO, respectively, for heat flowing into or out of the working fluid. This determination is performed internally. 6. FLAG controls the convective heat transfer into the downstream point (the second point as identified on the CHBDYi statement is downstream if mdot is positive).

• FLAG = 0, no convective flow (stationary fluid). • FLAG = 1, convective energy flow that is consistent with the Streamwise Upwind Petrov Galerkin (SUPG) element formulation. 7. No phase change or internal heat generation capabilities exist for this element.

Main Index

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342

Scalar Damper Property

PDAMP

Specifies the damping value of a scalar damper element using defined CDAMP1 or CDAMP3 entries. Format: 1

2

3

4

5

6

7

8

9

PDAMP

PID1

B1

PID2

B2

PID3

B3

PID4

B4

14

2.3

2

6.1

10

Example: PDAMP

Field

Contents

PIDi

Property identification number. (Integer > 0)

Bi

Force per unit velocity. (Real)

Remarks: 1. Damping values are defined directly on the CDAMP2 and CDAMP4 entries, and therefore do not require a PDAMP entry. 2. A structural viscous damper, CVISC, may also be used for geometric grid points. 3. Up to four damping properties may be defined on a single entry. 4. For a discussion of scalar elements, see “Scalar Elements (CELASi, CMASSi, CDAMPi)” on page 193 of the MSC.Nastran Reference Guide.

Main Index

CHAPTER D Bulk Data Entries

Scalar Damper Property for CDAMP5

PDAMP5

Defines the damping multiplier and references the material properties for damping. CDAMP5 is intended for heat transfer analysis only. Format: 1

2

3

4

PDAMP5

PID

MID

B

2

3

4.0

5

6

7

8

9

Example: PDAMP5

Field

Contents

PID

Property identification number. (Integer > 0)

MID

Material identification number of a MAT4 or MAT5 entry. (Integer > 0)

B

Damping multiplier. (Real > 0.0)

Remark: 1. B is the mass that multiplies the heat capacity CP on the MAT4 or MAT5 entry.

Main Index

10

343

344

Scalar Elastic Property

PELAS

Specifies the stiffness, damping coefficient, and stress coefficient of a scalar elastic (spring) element (CELAS1 or CELAS3 entry). Format: 1 PELAS

2

3

4

5

6

7

8

9

PID1

K1

GE1

S1

PID2

K2

GE2

S2

7

4.29

0.06

7.92

27

2.17

0.0032

10

Example: PELAS

Field

Contents

PIDi

Property identification number. (Integer > 0)

Ki

Elastic property value. (Real)

GEi

Damping coefficient, g e . See Remarks 5. and 6. (Real) Stress coefficient. (Real)

Si Remarks:

1. Be careful using negative spring values. 2. Spring values are defined directly on the CELAS2 and CELAS4 entries, and therefore do not require a PELAS entry. 3. One or two elastic spring properties may be defined on a single entry. 4. For a discussion of scalar elements, see “Scalar Elements (CELASi, CMASSi, CDAMPi)” on page 193 of the MSC.Nastran Reference Guide. 5. If PARAM,W4 is not specified, GEi is ignored in transient analysis. See “Parameters” on page 601. 6. To obtain the damping coefficient GE, multiply the critical damping ratio C ⁄ C 0 by 2.0. 7. If PELAS is used in conjunction with PELAST, Ki > 0, and the initial slope of the nonlinear force-displacement relationship defined by the PELAST should agree with Ki.

Main Index

CHAPTER D Bulk Data Entries

CHBDYP Geometric Element Definition

PHBDY

A property entry referenced by CHBDYP entries to give auxiliary geometric information for boundary condition surface elements. Format: 1 PHBDY

2

3

4

5

PID

AF

D1

D2

2

.02

1.0

1.0

6

7

8

9

10

Example: PHBDY

Field

Contents

PID

Property identification number. (Unique Integer among all PHBDY entries). (Integer > 0)

AF

Area factor of the surface used only for CHBDYP element TYPE = “POINT”, TYPE = “LINE”, TYPE = “TUBE”, or TYPE = “ELCYL”. For TYPE = “TUBE”, AF is the constant thickness of the hollow tube. (Real>0.0 or blank)

D1, D2

Diameters associated with the surface. Used with CHBDYP element TYPE = “ELCYL”, “TUBE”, and “FTUBE”. (Real > 0.0 or blank; Default for D2 = D1)

Remarks: 1. The PHBDY entry is used with CHBDYP entries. 2. AF

• For TYPE = “POINT” surfaces, AF is the area. • For TYPE = “LINE” or TYPE = “ELCYL” surfaces, AF is the effective width: area = AF ⋅ ( length ) .

• For TYPE = “FTUBE” and outer TYPE = “TUBE” surfaces D1 + D2 area = π ⋅  ----------------------- ⋅ 2

2 D1 – D2 2 ( LGTH ) +  ---------------------- 2

3. D1 and D2 are used only with TYPE = “ELCYL”, TYPE = “TUBE”, and TYPE = “FTUBE” surfaces.

• For TYPE = “ELCYL” surfaces, D1 and D2 are the two diameters associated with the ellipse.

• For TYPE = “FTUBE” and outer TYPE = “TUBE” surfaces, D1 and D2 are the diameters associated with the first and second grid points, respectively.

Main Index

345

346

• For inner TYPE = “TUBE” surfaces, the diameters are reduced by twice the thickness ( 2 ⋅ AF ) .

Main Index

CHAPTER D Bulk Data Entries

Boundary Heat Flux Load for CHBDYj Elements, Form 1

QBDY1

Defines a uniform heat flux into CHBDYj elements. Format: 1 QBDY1

2

3

4

5

6

7

8

9

SID

Q0

EID1

EID2

EID3

EID4

EID5

EID6

109

1.-5

721

10

Example: QBDY1

Alternate Format and Example: QBDY1

SID

Q0

EID1

“THRU”

EID2

QBDY1

109

1.-5

725

THRU

735

Field

Contents

SID

Load set identification number. (Integer > 0)

Q0

Heat flux into element. (Real)

EIDi

CHBDYj element identification numbers. (Integer ≠ 0 or “THRU”. For “THRU” option EID2 > EID1.)

Remarks: 1. QBDY1 entries must be selected with the Case Control command LOAD = SID in order to be used in static analysis. The total power into an element is given by the equation: P in = ( Effective area ) ⋅ Q0 2. QBDY1 entries must be referenced on a TLOAD entry for use in transient analysis. The total power into an element is given by the equation: P in ( t ) = ( Effective area ) ⋅ Q0 ⋅ F ( t – τ ) where the function of time F ( t – τ ) is specified on a TLOAD1 or TLOAD2 entry. 3. The sign convention for Q0 is positive for heat input.

Main Index

347

348

Boundary Heat Flux Load for CHBDYj Elements, Form 2

QBDY2

Defines grid point heat flux into CHBDYj elements. Format: 1 QBDY2

2

3

4

5

6

7

8

9

SID

EID

Q01

Q02

Q03

Q04

Q05

Q06

Q07

Q08

109

721

1.-5

1.-5

2.-5

2.-5

10

Example: QBDY2

Field

Contents

SID

Load set identification number. (Integer >0)

EID

Identification number of an CHBDYj element. (Integer > 0)

Q0i

Heat flux at the i-th grid point on the referenced CHBDYj element. (Real or blank)

Remarks: 1. QBDY2 entries must be selected with the Case Control command LOAD=SID in order to be used in static analysis. The total power into each point i on an element is given by P i = AREA i ⋅ Q0i 2. QBDY2 entries must be referenced on a TLOAD entry for use in transient analysis. All connected grid points will have the same time function but may have individual delays. The total power into each point i on an element is given by P i ( t ) = AREA i ⋅ Q0i ⋅ F ( t – τ i ) where F ( t – τ i ) is a function of time specified on a TLOAD1 or TLOAD2 entry. 3. The sign convention for Q0i is positive for heat flux input to the element.

Main Index

CHAPTER D Bulk Data Entries

Boundary Heat Flux Load for a Surface

QBDY3

Defines a uniform heat flux load for a boundary surface. Format: 1 QBDY3

2

3

4

5

6

7

8

9

SID

Q0

CNTRLN D

EID1

EID2

EID3

EID4

EID5

EID6

etc.

2

20.0

10

1

THRU

50

BY

2

10

Example: QBDY3

Field

Contents

SID

Load set identification number. (Integer > 0)

Q0

Thermal heat flux load, or load multiplier. Q0 is positive for heat flow into a surface. (Real)

CNTRLND

Control point for thermal flux load. (Integer > 0; Default = 0)

EIDi

CHBDYj element identification numbers. (Integer ≠ 0 or “THRU” or “BY”)

Remarks: 1. QBDY3 entries must be selected in Case Control (LOAD = SID) to be used in steady state. The total power into a surface is given by the equation:

• if CNTRLND ≤ 0 then P in = ( Effective area ) ⋅ Q0 • if CNTRLND > 0 then P in = ( Effective area ) ⋅ Q0 ⋅ u CNTRLND where u CNTRLND is the temperature of the control point and is used as a load multiplier. 2. In transient analysis SID is referenced by a TLOADi Bulk Data entry through the DAREA entry. A function of time F ( t – τ ) defined on the TLOADi multiplies the general load, with τ specifying time delay. The load set identifier on the TLOADi entry must be selected in Case Control (DLOAD = SID) for use in transient analysis. If multiple types of transient loads exist, they must be combined by the DLOAD Bulk Data entry. 3. The CNTRLND multiplier cannot be used with any higher-order elements. 4. When using “THRU” or “BY”, all intermediate CHBDYE, CHBDYG, or CHBDYP elements must exist.

Main Index

349

350

Boundary Heat Flux Load

QHBDY

Defines a uniform heat flux into a set of grid points. Format: 1 QHBDY

2

3

4

5

6

7

8

9

SID

FLAG

Q0

AF

G1

G2

G3

G4

G5

G6

G7

G8

2

AREA4

20.0

101

102

104

103

10

Example: QHBDY

Field

Contents

SID

Load set identification number. (Integer > 0)

FLAG

Type of face involved (must be one of the following: “POINT”, “LINE”, “REV”, “AREA3", “AREA4", “AREA6", “AREA8")

Q0

Magnitude of thermal flux into face. Q0 is positive for heat into the surface. (Real)

AF

Area factor depends on type. (Real > 0.0 or blank)

Gi

Grid point identification of connected grid points. (Integer > 0 or blank)

Remarks: 1. The continuation entry is optional. 2. For use in steady state analysis, the load set is selected in the Case Control Section (LOAD = SID). 3. In transient analysis SID is referenced by a TLOADi Bulk Data entry through the DAREA entry. A function of time defined on the TLOADi entry multiplies the general load. specifies time delay. The load set identifier on the TLOADi entry must be selected in Case Control (DLOAD = SID) for use in transient analysis. If multiple types of transient loads exist, they must be combined by the DLOAD Bulk Data entry. 4. The heat flux applied to the area is transformed to loads on the points. These points need not correspond to an HBDY surface element. 5. The flux is applied to each point i by the equation P i = AREA i ⋅ Q0 6. The number of connected points for the types are 1 (POINT), 2 (LINE, REV), 3 (AREA3), 4 (AREA4), 4-6 (AREA6), 5-8 (AREA8). 7. The area factor AF is used to determine the effective area for the POINT and LINE types. It equals the area and effective width, respectively. It is not used for the other types, which have their area defined implicitly and must be left blank. Main Index

CHAPTER D Bulk Data Entries

8. The type of face (FLAG) defines a surface in the same manner as the CHBDYi data entry. For physical descriptions of the geometry involved, see the CHBDYG discussion.

Main Index

351

352

Thermal Vector Flux Load

QVECT

Defines thermal vector flux from a distant source into a face of one or more CHBDYi boundary condition surface elements. Format: 1 QVECT

2

3

4

5

6

7

8

9

SID

Q0

TSOUR

CE

E1 or TID1

E2 or TID2

E3 or TID3

CNTRLND

EID1

EID2

-etc.-

10

20.0

1000.0

1.0

1.0

1.0

101

20

21

22

10

Example: QVECT

23

Field

Contents

SID

Load set identification number. (Integer > 0)

Q0

Magnitude of thermal flux vector into face. (Real or blank)

TSOUR

Temperature of the radiant source. (Real or blank)

CE

Coordinate system identification number for thermal vector flux. (Integer > 0 or blank)

Ei

Vector components (direction cosines in coordinate system CE) of the thermal vector flux. (Real; Default = 0.0)

TIDi

TABLEDi entry identification numbers defining the components as a function of time. (Integer > 0)

CNTRLND

Control point. (Integer > 0; Default = 0)

EIDi

Element identification number of a CHBDYE, CHBDYG, or CHBDYP entry. (Integer ≠ 0 or “THRU”)

Remarks: 1. The continuation entry is required. 2. If the coordinate system CE is not rectangular, then the thermal vector flux is in different directions for different CHBDYi elements. The direction of the thermal vector flux over an element is aligned to be in the direction of the flux vector at the geometric center of the element. The geometric center is measured using the grid points and includes any DISLIN specification on the VIEW entry for TYPE=LINE CHBDYi elements. The flux is presumed to be uniform over the face of each element; i.e., the source is relatively distant. 3. For use in steady-state analysis, the load set is selected in the Case Control Section (LOAD = SID). The total power into an element is given by: Main Index

CHAPTER D Bulk Data Entries

• If CNTRLND = 0 then, P in = – αA ( e ⋅ n ) ⋅ Q0 . • If CNTRLND > 0 then, P in = – αA ( e ⋅ n ) ⋅ Q0 ⋅ u CNTRLND . where α = face absorptivity (supplied from a RADM statement). A = face area as determined from a CHBDYi surface element. e n

= vector of direction cosines E1, E2, E3. = face normal vector. See CHBDYi entries.

e ⋅ n = 0 if the vector product is positive, (i.e., the flux is coming from behind the face). u cntrlnd = temperature value of the control point used as a load multiplier. 4. If the absorptivity is constant, its value is supplied by the ABSORP field on the RADM entry. If the absorptivity is not a constant, the thermal flux is assumed to have a wavelength distribution of a black body at the temperature TSOUR.

• For a temperature-dependent absorptivity, the element temperature is used to determine α .

• For a wavelength-dependent absorptivity, the integration of the flux times α is computed for each wavelength band. The sum of the integrated thermal fluxes over all the wavelength bands is Q0. The wave bands are specified with the RADBND entry.

• The user has the responsibility of enforcing Kirchhoff’s laws. 5. In transient analysis, SID is referenced by a TLOADi Bulk Data entry through the DAREA specification. A function of time F ( t – τ ) defined on the TLOADi entry multiplies the general load. τ provides any required time delay. F ( t – τ ) is a function of time specified on the TLOADi entry. The value of is calculated for each loaded grid point. The load set identifier on the TLOADi entry must be selected in Case Control (DLOAD = SID) for use in transient analysis. If multiple types of transient loads exist, they must be combined by the DLOAD Bulk Data entry. The total power into an element is given by:

• If CNTRLND = 0 then, P in = – αA ( e ( t ) ⋅ n ) ⋅ Q0 ⋅ F ( t – τ ) . • If CNTRLND > 0 then, P in = – αA ( e ( t ) ⋅ n ) ⋅ F ( t – τ ) ⋅ Q0 ⋅ u CNTRLND . 6. If the referenced face is of TYPE = ELCYL, the power input is an exact integration over the area exposed to the thermal flux vector. 7. If the referenced face is of TYPE = REV, the thermal flux vector must be parallel to the axis of symmetry if an axisymmetric boundary condition is to be maintained.

Main Index

353

354

8. When applied to a surface element associated with a radiation enclosure cavity, any incident energy that is not absorbed ( α < 1.0 ) is lost from the system and is not accounted for in a reflective sense ( α + ρ = 1.0 ) .

Main Index

CHAPTER D Bulk Data Entries

Volume Heat Addition

QVOL

Defines a rate of volumetric heat addition in a conduction element. Format: 1 QVOL

2

3

4

5

6

7

8

9

SID

QVOL

CNTRLN D

EID1

EID2

EID3

EID4

EID5

EID6

etc.

5

10.0

101

10

12

11

9

10

Example: QVOL

Field

Contents

SID

Load set identification. (Integer > 0)

QVOL

Power input per unit volume produced by a heat conduction element. (Real)

CNTRLND

Control point used for controlling heat generation. (Integer > 0; Default = 0)

EIDi

A list of heat conduction elements. (Integer > 0 or “THRU” or “BY”)

Remarks: 1. EIDi has material properties (MAT4) that include HGEN, the element material property for heat generation, which may be temperature dependent. This association is made through the element EID. If HGEN is temperature dependent, it is based on the average element temperature. 2. QVOL provides either the constant volumetric heat generation rate or the load multiplier. QVOL is positive for heat generation. For steady-state analysis, the total power into an element is

• If CNTRLND = 0, then P in = volume ⋅ HGEN ⋅ QVOL . • If CNTRLND > 0, then P in = volume ⋅ HGEN ⋅ QVOL ⋅ u CNTRLND . where u CNTRLND is the temperature multiplier. 3. For use in steady-state analysis, the load set is selected in the Case Control Section (LOAD = SID). 4. In transient analysis SID is referenced by a TLOADi Bulk Data entry. A function of time F [ t – τ ] defined on the TLOADi entry multiplies the general load where τ specifies time delay. The load set identifier on the TLOADi entry must be selected in Case Control (DLOAD = SID) for use in transient analysis. If multiple types of transient loads exist, they must be combined by the DLOAD Bulk Data entry. 5. For “THRU” or “BY”, all intermediate referenced heat conduction elements must exist. 6. The CNTRLND multiplier cannot be used with any higher-order elements. Main Index

355

356

Space Radiation Specification

RADBC

Specifies an CHBDYi element face for application of radiation boundary conditions. Format: 1 RADBC

2

3

4

5

6

7

8

NODAMB

FAMB

CNTRLND

EID1

EID2

EID3

-etc.-

5

1.0

101

10

9

10

Example: RADBC

Field

Contents

NODAMB

Ambient point for radiation exchange. (Integer > 0)

FAMB

Radiation view factor between the face and the ambient point. (Real > 0.0)

CNTRLND Control point for radiation boundary condition. (Integer > 0; Default = 0) CHBDYi element identification number. ( Integer ≠ 0 or “THRU” or “BY”)

EIDi Remarks:

1. The basic exchange relationship is: 4

4

• if CNTRLND = 0, then q = σ ⋅ FAMB ⋅ ( ε e T e – α e T amb ) • if CNTRLND > 0, then 4

4

q = σ ⋅ FAMB ⋅ u CNTRLND ⋅ ( ε e T e – α e T amb ) 2. NODAMB is treated as a black body with its own ambient temperature for radiation exchange between the surface element and space. No surface element that is a member of a radiation enclosure cavity may also have a radiation boundary condition applied to it. 3. Two PARAM entries are required when stipulating radiation heat transfer:

• ABS defines the absolute temperature scale; this value is added internally to any specified temperature given in the problem. Upon solution completion, this value is subtracted internally from the solution vector.

• SIGMA ( σ ) is the Stefan-Boltzmann constant. 4. RADBC allows for surface radiation to space in the absence of any cavity behavior. The emissivity and absorptivity are supplied from a RADM entry. 5. When using “THRU” or “BY”, all intermediate referenced CHBDYi surface elements must exist.

Main Index

CHAPTER D Bulk Data Entries

Radiation Wavelength Band Definition

RADBND

Specifies Planck’s second radiation constant and the wavelength breakpoints used for radiation exchange problems. Format: 1

2

3

4

5

6

7

8

9

RADBND

NUMBER

PLANCK2

LAMBDA1

LAMBDA2

LAMBDA3

LAMBDA4

LAMBDA5

LAMBDA6

LAMBDA7

etc.

6

14388.0

1.0

2.0

4.0

8.0

12.0

10

Example: RADBND

Field

Contents

NUMBER

Number of radiation wave bands. See Remarks. (Integer > 1)

PLANCK2

Planck’s second radiation constant. See Remarks. (Real > 0.0)

LAMBDAi

Highest wavelength of the i-th wave band. See Remarks. (Real > 0.0)

Remarks: 1. Only one RADBND entry may be specified in the Bulk Data Section and must always be used in conjunction with the RADM entry. 2. PLANCK2 has the units of wavelength times temperature. The same units of length must be used for LAMBDAi as for PLANCK2. The units of temperature must be the same as those used for the radiating surfaces. For example: 25898.µm °R or 14388.µm °K . 3. The first wavelength band extends from 0 to LAMBDA1 and the last band extends from LAMBDAn to infinity, where n = NUMBER – 1 . 4. Discontinuous segments in the emissivity versus wavelength piecewise linear curve must be treated as a wavelength band of zero width. 5. LAMBDAi must be specified in ascending order, and all LAMBDAi fields where i is greater than or equal to NUMBER must be blank.

Main Index

357

358

Radiation Cavity Identification

RADCAV

Identifies the characteristics of each radiant enclosure. Format: 1

2

3

4

5

6

7

8

9

RADCAV

ICAVITY

ELEAMB

SHADOW

SCALE

PRTPCH

NFECI

RMAX

NREV

SET11

SET12

SET21

SET22

SET31

SET32

etc.

1

1

3

5

10

Example: RADCAV

.99 4

7

5

Field

Contents

ICAVITY

Unique cavity identification number associated with enclosure radiation. (Integer > 0)

ELEAMB

CHBDYi surface element identification number for radiation if the view factors add up to less than 1.0. (Unique Integer > 0 among all CHBDYi elements or blank.)

SHADOW

Flag to control third body shading calculation during view factor calculation for each identified cavity. (Character = “YES” or “NO”; Default = “YES”)

SCALE

View factor that the enclosure sum will be set to if a view factor is greater than 1.0. (0.0 < Real < 1.0; Default = 0.0)

PRTPCH

Facilitates the blocking of view factor printing and punching onto RADLST and RADMTX entries. (Integer = 0, 1, 2, or 3; Default = 0): PRTPCH

Main Index

5

Print/Punch

0 (default)

print and punch

1

no print

2

no punch

3

no print or punch

NFECI

Controls whether finite difference or contour integration methods are to be used in the calculation of view factors in the absence of a VIEW3D Bulk Data entry. (Character = “FD” or “CONT”; See Remark 4. for default.)

RMAX

Subelement area factor. See Remark 5. (Real > 0.0; Default = 0.1)

NREV

Number of computational elements used in determination of axisymmetric view factors. See Remark 8. (Integer > 0; Default = 31)

SETij

Set identification pairs for the calculation of global view factors. Up to 30 pairs may be specified (i = 1 to 2 and j = 1 to 30). (Integer > 0)

CHAPTER D Bulk Data Entries

Remarks: 1. For the surfaces of an incomplete enclosure (view factors add up to less than 1.0), a complete enclosure may be achieved (SUM = 1.0) by specifying an ambient element, ELEAMB. When multiple cavities are defined, each cavity must have a unique ambient element if ambient elements are desired. No elements can be shared between cavities. 2. Third-body shadowing is ignored in the cavity if SHADOW = “NO”. In particular, if it is known a priori that there is no third-body shadowing, SHADOW = NO overrides KSHD and KBSHD fields on the VIEW Bulk Data entry as well as reduces the calculation time immensely. 3. The view factors for a complete enclosure may add up to slightly more than 1.0 due to calculation inaccuracies. SCALE can be used to adjust all the view factors proportionately to acquire a summation equal to the value specified for SCALE. If SCALE is left blank or set to 0.0, no scaling is performed. 4. If the VIEW3D Bulk Data entry is not specified, the view factors are calculated using finite difference and contour integration methods. If NFECI = “FD”, then all view factors are calculated using the finite difference technique. NFECI = “CONT” invokes contour integration for all view factor calculations. If NFECI is blank, the program selects a method to use between any two particular elements based on RMAX. 2

5. The comparison value for RMAX is equal to A s ⁄ d rs where A s is the area of a subelement and d rs is the distance between two subelements r and s for which view factors are being computed. When NFECI is blank, the program selects the contour 2 integral method only if A s ⁄ d rs > RMAX . 6. When a number of elements are grouped together and considered as a conglomerate surface, view factors can be calculated between these groups. These are referred to as global view factors. The SET1 Bulk Data entry is used to define the conglomerate. When using this feature, negative EIDs are not allowed. 7. If a RADLST and RADMTX entry exists for this cavity ID, new view factors are not computed and the existing RADLST and RADMTX are used in the thermal analysis. 8. The VIEW3D Bulk Data entry must be specified for the calculation of axisymmetric view factors. The process relies on the internal construction of a semi-circle of computational elements. NREV specifies the number of such elements desired.

Main Index

359

360

Listing of Enclosure Radiation Faces

RADLST

Identifies the individual CHBDYi surface elements that comprise the entire radiation enclosure. Format: 1

2

3

4

5

6

7

8

9

RADLST

ICAVITY

MTXTYP

EID1

EID2

EID3

EID4

EID5

EID6

EID7

-etc.-

2

1

2

3

4

5

6

7

10

Example: RADLST

Field

Contents

ICAVITY

Unique cavity identification number that links a radiation exchange matrix with its listing of enclosure radiation faces. (Integer > 0)

MTXTYP

Type of radiation exchange matrix used for this cavity. (Integer < 4 and ≠ 0; Default = 1 for an enclosure without an ambient element. Default = 4 for an enclosure with an ambient element as specified on the RADCAV entry.)

EIDi

1:

Symmetric view factor matrix [F] and nonconservative radiation matrix [R].

2:

Symmetric exchange factor matrix [ ℑ ] and conservative radiation matrix [R].

3:

Unsymmetric exchange factor matrix [ ℑ ] and conservative radiation matrix [R].

4:

Symmetric view factor matrix [F] and conservative radiation matrix [R].

-n:

The first n CHBDYi elements may lose energy to space but the remainder may not. Symmetric exchange factor matrix [F] and nonconservative radiation matrix [R].

Identification numbers for the CHBDYi elements in this radiation cavity. (Integer ≠ 0 or “THRU”)

Remarks: 1. A radiation EIDi list isolates those CHBDYi surface element faces that are to communicate in a radiation enclosure. View-factor calculation and RADMTX formation for an enclosure is performed only for (or among) those faces identified within the same RADCAV. 2. A radiation exchange matrix (RADMTX) can only reference one radiative face list (RADLST). The companion RADCAV, RADLST, and RADMTX must share a unique ICAVITY. 3. For each EIDi, the appropriate CHBDYi element is located, and the proper RADM entry ID field found. Main Index

CHAPTER D Bulk Data Entries

4. If the radiation exchange matrix or any radiation boundary conditions are available from an external source, the RADMTX must be user generated. 5. Multiple RADLST entries may be specified. 6. If any RADLST entry is changed or added on restart then a complete re-analysis may be performed. Therefore, RADLST entry changes or additions are not recommended on restart.

Main Index

361

362

Radiation Boundary Material Property

RADM

Defines the radiation properties of a boundary element for heat transfer analysis. Format: 1 RADM

2

3

4

5

6

7

8

9

RADMID

ABSORP

EMIS1

EMIS2

EMIS3

EMIS4

EMIS5

EMIS6

EMIS7

-etc.-

.45

.33

.29

.20

.17

.13

10

Example: RADM

11

Field

Contents

RADMID

Material identification number. (Integer > 0)

ABSORP

Surface absorptivity or the temperature function curve multiplier if ABSORP is variable. See Remark 2. (0.0 < Real < 1.0)

EMISi

Surface emissivity at wavelength LAMBDAi or the temperature function curve multiplier if EMISi is variable (See the RADBND entry.) (0.0 < Real < 1.0)

Remarks: 1. The RADM entry is directly referenced only by one of the CHBDYE, CHBDYG, or CHBDYP type surface element entries. 2. For radiation enclosure problems, ABSORP is set equal to emissivity. For QVECT loads, absorptivity is specified by ABSORP. 3. If there is more than one EMISi, then:

• There must be a RADBND entry. • The number of EMISi may not exceed the number of LAMBDAi on the RADBND entry.

• The emissivity values are given for a wavelength specified by the corresponding LAMBDAi on the RADBND entry. Within each discrete wavelength band, the emissivity is assumed to be constant.

• At any specific wavelength and surface temperature, the absorptivity is exactly equal to the emissivity. 4. To perform any radiation heat transfer exchange, the user must furnish PARAM entries for:

• TABS to define the absolute temperature scale. • SIGMA ( σ ) to define the Stefan-Boltzmann constant in appropriate units.

Main Index

CHAPTER D Bulk Data Entries

Radiation Boundary Material Property Temperature Dependence

RADMT

Specifies table references for temperature dependent RADM entry radiation boundary properties. Format: 1

2

3

4

5

6

7

8

9

RADMT

RADMI D

T(A)

T( ε 1)

T( ε 2)

T( ε 3)

T( ε 4)

T( ε 5)

T( ε 6)

T( ε 7)

-etc.-

1

2

3

4

5

6

10

Example: RADMT

11

Field

Contents

RADMID

Material identification number. (Integer > 0)

T(A)

TABLEMj identifier for surface absorptivity. (Integer > 0 or blank)

T ( εi )

TABLEMj identifiers for surface emissivity. (Integer > 0 or blank)

Remarks: 1. The basic quantities on the RADM entry of the same RADMID are always multiplied by the corresponding tabular function. 2. Tables T(A) and T ( ε i ) have an upper bound that is less than or equal to one and a lower bound that is greater than or equal to zero. 3. The TABLEMj enforces the element temperature as the independent variable. Blank or zero fields means there is no temperature dependence of the referenced property on the RADM entry.

Main Index

363

364

Radiation Exchange Matrix

RADMTX

Provides the F ji = A j f ji exchange factors for all the faces of a radiation enclosure specified in the corresponding RADLST entry. Format: 1

2

3

4

5

6

7

8

9

RADMTX

ICAVITY

INDEX

Fi,j

Fi+1,j

Fi+2,j

Fi+3,j

Fi+4,j

Fi+5,j

Fi+6,j

-etc.-

2

1

0.0

0.1

0.2

0.2

0.3

0.2

10

Example: RADMTX

Field

Contents

ICAVITY

Unique cavity identification number that links a radiation exchange matrix with its listing of enclosure radiation surface elements. (Integer > 0)

INDEX

Column number in the matrix. (Integer > 0)

Fk,j

If symmetric, the matrix values start on the diagonal (i = j) and continue down the column (k = i + 1, i + 2, etc.). If unsymmetric, the values start in row (i = 1). i refers to EIDi on the RADLST entry. (Real > 0)

Remarks: 1. If the matrix is symmetric, only the lower triangle is input, and i = j = INDEX. If the matrix is unsymmetric, i = 1, and j = INDEX. 2. Only one ICAVITY may be referenced for those faces that are to be included in a unique radiation matrix. 3. Coefficients are listed by column with the number of columns equal to the number of entries in the RADLST. 4. All faces involved in any radiation enclosure must be defined with an CHBDYi element. 5. If any RADMTX entry is changed or added on restart then a complete re-analysis may be performed. Therefore, RADMTX entry changes or additions are not recommended on restart.

Main Index

CHAPTER D Bulk Data Entries

Identifies a Set of Radiation Cavities

RADSET

Specifies which radiation cavities are to be included for radiation enclosure analysis. Format: 1

2

3

4

5

6

7

8

9

RADSET

ICAVITY1

ICAVITY2

ICAVITY3

ICAVITY4

ICAVITY5

ICAVITY6

ICAVITY7

ICAVITY8

ICAVITY9

-etc.-

1

2

3

4

10

Example: RADSET

Field

Contents

ICAVITYi

Unique identification number for a cavity to be considered for enclosure radiation analysis. (Integer > 0)

Remark: 1. For multiple radiation cavities, RADSET specifies which cavities are to be included in the analysis.

Main Index

365

366

Set Definition

SET1

Defines a list of structural grid points for aerodynamic analysis, XY-plots for SORT1 output, and the PANEL entry. Format: 1 SET1

2

3

4

5

6

7

8

9

SID

G1

G2

G3

G4

G5

G6

G7

G8

-etc.-

3

31

62

93

124

16

17

18

10

Example: SET1

19

Alternate Format and Example: SET1

SID

G1

“THRU”

G2

SET1

6

32

THRU

50

Field

Contents

SID

Unique identification number. (Integer > 0)

Gi

List of structural grid point identification numbers. (Integer > 0 or “THRU”; for the “THRU” option, G1 < G2 or “SKIN”; in field 3)

Remarks: 1. SET1 entries may be referenced by the SPLINEi entries, PANEL entries and XYOUTPUT requests. 2. When using the “THRU” option for SPLINEi or PANEL data entries, all intermediate grid points must exist. 3. When using the “THRU” option for XYOUTPUT requests, missing grid points are ignored. 4. When using the “SKIN” option, MSC.Nastran will generate a panel consisting of the structural portion of the fluid-structural boundary. 5. When the SET1 entry is used in conjunction with the ACMODL entry, under rules defined on the ACMODL entry, the Gi may be a list of element IDs.

Main Index

CHAPTER D Bulk Data Entries

Static Scalar Load

SLOAD

Defines concentrated static loads on scalar or grid points. Format: 1 SLOAD

2

3

4

5

6

7

8

SID

S1

F1

S2

F2

S3

F3

16

2

5.9

17

-6.3

14

-2.93

9

10

Example: SLOAD

Field

Contents

SID

Load set identification number. (Integer > 0)

Si

Scalar or grid point identification number. (Integer > 0)

Fi

Load magnitude. (Real)

Remarks: 1. In the static solution sequences, the load set ID (SID) is selected by the Case Control command LOAD. In the dynamic solution sequences, SID must be referenced in the LID field of an LSEQ entry, which in turn must be selected by the Case Control command LOADSET. 2. Up to three loads may be defined on a single entry. 3. If Si refers to a grid point, the load is applied to component T1 of the displacement coordinate system (see the CD field on the GRID entry).

Main Index

367

368

Single-Point Constraint

SPC

Defines a set of single-point constraints and enforced motion (enforced displacements in static analysis and enforced displacements, velocities or acceleration in dynamic analysis). Format: 1 SPC

2

3

4

5

6

7

8

SID

G1

C1

D1

G2

C2

D2

2

32

3

-2.6

5

9

10

Example: SPC

Field

Contents

SID

Identification number of the single-point constraint set. (Integer > 0)

Gi

Grid or scalar point identification number. (Integer > 0)

Ci

Component number. (0 < Integer < 6; up to six Unique Integers, 1 through 6, may be placed in the field with no embedded blanks. 0 applies to scalar points and 1 through 6 applies to grid points.)

Di

Value of enforced motion for all degrees-of-freedom designated by Gi and Ci. (Real)

Remarks: 1. Single-point constraint sets must be selected with the Case Control command SPC = SID. 2. Degrees-of-freedom specified on this entry form members of the mutually exclusive s-set. They may not be specified on other entries that define mutually exclusive sets. See “Degree-of-Freedom Sets” on page 843 for a list of these entries. 3. Single-point forces of constraint are recovered during stress data recovery. 4. From 1 to 12 degrees-of-freedom may be specified on a single entry. 5. Degrees-of-freedom on this entry may be redundantly specified as permanent constraints using the PS field on the GRID entry. 6. For reasons of efficiency, the SPCD entry is the preferred method for applying enforced motion rather than the Di field described here.

Main Index

CHAPTER D Bulk Data Entries

Single-Point Constraint, Alternate Form

SPC1

Defines a set of single-point constraints. Format: 1 SPC1

2

3

4

5

6

7

8

9

SID

C

G1

G2

G3

G4

G5

G6

G7

G8

G9

-etc.-

3

2

1

3

10

9

6

5

2

8

10

Example: SPC1

Alternate Format and Example: SPC1

SID

C

G1

“THRU”

G2

SPC1

313

12456

6

THRU

32

Field

Contents

SID

Identification number of single-point constraint set. (Integer > 0)

C

Component numbers. (Any unique combination of the Integers 1 through 6 with no embedded blanks for grid points. This number must be Integer 0 or blank for scalar points.)

Gi

Grid or scalar point identification numbers. (Integer > 0 or “THRU”; For “THRU” option, G1 < G2.)

Remarks: 1. Single-point constraint sets must be selected with the Case Control command SPC = SID. 2. Enforced displacements are available via this entry when used with the recommended SPCD entry. 3. Degrees-of-freedom specified on this entry form members of the mutually exclusive s-set. They may not be specified on other entries that define mutually exclusive sets. See “Degree-of-Freedom Sets” on page 843 for a list of these entries. 4. Degrees-of-freedom on this entry may be redundantly specified as permanent constraints using the PS field on the GRID entry. 5. If the alternate format is used, points in the sequence G1 through G2 are not required to exist. Points that do not exist will collectively produce a warning message but will otherwise be ignored.

Main Index

369

370

Single-Point Constraint Set Combination

SPCADD

Defines a single-point constraint set as a union of single-point constraint sets defined on SPC or SPC1 entries. Format: 1

2

3

4

5

6

7

8

9

SPCADD

SID

S1

S2

S3

S4

S5

S6

S7

S8

S9

-etc.-

101

3

2

9

1

10

Example: SPCADD

Field

Contents

SID

Single-point constraint set identification number. (Integer > 0)

Si

Identification numbers of single-point constraint sets defined via SPC or by SPC1 entries. (Integer > 0; SID ≠ Si)

Remarks: 1. Single-point constraint sets must be selected with the Case Control command SPC = SID. 2. No Si may be the identification number of a single-point constraint set defined by another SPCADD entry. 3. The Si values must be unique. 4. SPCADD entries take precedence over SPC or SPC1 entries. If both have the same set ID, only the SPCADD entry will be used.

Main Index

CHAPTER D Bulk Data Entries

Enforced Motion Value

SPCD

Defines an enforced displacement value for static analysis and an enforced motion value (displacement, velocity or acceleration) in dynamic analysis. Format: 1 SPCD

2

3

4

5

6

7

8

SID

G1

C1

D1

G2

C2

D2

100

32

436

-2.6

5

9

10

Example: SPCD

2.9

Field

Contents

SID

Set identification number of the SPCD entry. (Integer > 0)

Gi

Grid or scalar point identification number. (integer > 0)

Ci

Component numbers. (0 < Integer < 6; up to six unique Integers may be placed in the field with no embedded blanks.)

Di

Value of enforced motion for at Gi and Ci. (Real)

Remarks: 1. In the static solution sequences, the set ID of the SPCD entry (SID) is selected by the LOAD Case Control command. 2. In dynamic analysis, the selection of SID is determined by the presence of the LOADSET request in Case Control as follows:

• There is no LOADSET request in Case Control SID is selected by the EXCITEID ID of an RLOAD1, RLOAD2, TLOAD1 or TLOAD2 Bulk Data entry that has enforced motion specified in its TYPE field

• There is a LOADSET request in Case Control SID is selected by LID in the selected LSEQ entries that correspond to the EXCITEID entry of an RLOAD1, RLOAD2, TLOAD1 or TLOAD2 Bulk Data entry that has enforced motion specified in its TYPE field. 3. A global coordinate (Gi and CI) referenced on this entry must also be referenced on a SPC or SPC1 Bulk Data entry and selected by the SPC Case Control command. 4. Values of Di will override the values specified on an SPC Bulk Data entry, if the SID is selected as indicated above. 5. The LOAD Bulk Data entry will not combine an SPCD load entry. 6. In static analysis, this method of applying enforced displacements is more efficient than the SPC entry when more than one enforced displacement condition is applied. It provides equivalent answers. Main Index

371

372

7. In dynamic analysis, this direct method of specifying enforced motion is more accurate, efficient and elegant than the large mass and Lagrange multiplier techniques.

Main Index

CHAPTER D Bulk Data Entries

Scalar Point Definition

SPOINT

Defines scalar points. Format: 1

2

3

4

5

6

7

8

9

SPOINT

ID1

ID2

ID3

ID4

ID5

ID6

ID7

ID8

3

18

1

4

16

2

10

Example: SPOINT

Alternate Format and Example: SPOINT

ID1

“THRU”

ID2

SPOINT

5

THRU

649

Field

Contents

IDi

Scalar point identification number. (0 < Integer < 100000000; For “THRU” option, ID1 < ID2)

Remarks: 1. A scalar point defined by its appearance on the connection entry for a scalar element (see the CELASi, CMASSi, and CDAMPi entries) need not appear on an SPOINT entry. 2. All scalar point identification numbers must be unique with respect to all other structural, scalar, and fluid points. However, duplicate scalar point identification numbers are allowed in the input. 3. This entry is used primarily to define scalar points appearing in single-point or multipoint constraint equations to which no scalar elements are connected. 4. If the alternate format is used, all scalar points ID1 through ID2 are defined. 5. For a discussion of scalar points, see “Scalar Elements (CELASi, CMASSi, CDAMPi)” on page 193 of the MSC.Nastran Reference Guide.

Main Index

373

374

Conical Shell Fictitious Support

SUPAX

Defines determinate reaction degrees-of-freedom in free bodies for conical shell analysis. Format: 1 SUPAX

2

3

4

5

6

7

RID1

HID1

C1

RID2

HID2

C2

4

3

2

8

9

10

Example: SUPAX

Field

Contents

RIDi

Ring identification number. (Integer > 0)

HIDi

Harmonic identification number. (Integer > 0)

Ci

Conical shell degree-of-freedom numbers. (Any unique combination of the Integers 1 through 6.)

Remarks: 1. SUPAX is allowed only if an AXIC entry is also present. 2. Up to 12 degrees-of-freedom may appear on a single entry. 3. Degrees-of-freedom appearing on SUPAX entries may not appear on MPCAX, SPCAX, or OMITAX entries. 4. For a discussion of conical shell analysis, see “Conical Shell Element (RINGAX)” on page 155 of the MSC.Nastran Reference Guide.

Main Index

CHAPTER D Bulk Data Entries

Dynamic Load Tabular Function, Form 1

TABLED1

Defines a tabular function for use in generating frequency-dependent and time-dependent dynamic loads. Format: 1

2

3

4

5

6

7

8

9

TABLED1

TID

XAXIS

YAXIS

x1

y1

x2

y2

x3

y3

-etc.-

“ENDT”

6.9

2.0

5.6

3.0

5.6

ENDT

10

Example: TABLED1

32 -3.0

Field

Contents

TID

Table identification number. (Integer > 0)

XAXIS

Specifies a linear or logarithmic interpolation for the x-axis. See Remark 6. (Character: “LINEAR” or “LOG”; Default = “LINEAR”)

YAXIS

Specifies a linear or logarithmic interpolation for the y-axis. See Remark 6. (Character: “LINEAR” or “LOG”; Default = “LINEAR”)

xi, yi

Tabular values. (Real)

“ENDT”

Flag indicating the end of the table.

Remarks: 1. xi must be in either ascending or descending order, but not both. 2. Discontinuities may be specified between any two points except the two starting points or two end points. For example, in Figure 4-9 discontinuities are allowed only between points x2 through x7. Also, if y is evaluated at a discontinuity, then the average value of y is used. In Figure 4-9, the value of y at x=x3 is y = ( y3 + y4 ) ⁄ 2 . If the y-axis is a LOG axis then the jump at the discontinuity is evaluated as y = y3y4 . 3. At least one continuation must be specified. 4. Any xi-yi pair may be ignored by placing the character string “SKIP” in either of the two fields. 5. The end of the table is indicated by the existence of the character string “ENDT” in either of the two fields following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag “ENDT”. 6. TABLED1 uses the algorithm y = yT ( x ) Main Index

375

376

where x is input to the table and y is returned. The table look-up is performed using interpolation within the table and extrapolation outside the table using the two starting or end points. See Figure 4-9. The algorithms used for interpolation or extrapolation are: XAXIS

YAXIS

yT(x)

LINEAR

LINEAR

xj – x x – xi ---------------- yi + ---------------- yj xj – xi xj – xi

LOG

LINEAR

ln ( xj ⁄ x ) ln ( x ⁄ xi ) -------------------------- yi + -------------------------- yj ln ( xj ⁄ xi ) ln ( xj ⁄ xi )

LINEAR

LOG

xj – x x – xi exp ---------------- ln yi + ---------------- ln yj xj – xi xj – xi

LOG

LOG

ln ( xj ⁄ x ) ln ( x ⁄ xi ) exp -------------------------- ln yi + -------------------------- ln yi ln ( xj ⁄ xi ) ln ( xj ⁄ xi )

where xj and yj follow xi and yi. No warning messages are issued if table data is input incorrectly. y

x value Range of Table

Discontinuity Allowed

Discontinuity Not Allowed

Linear Extrapolation of Segment x1-x2

x x1

x2

x3, x4

x5

x6

x7, x8

x Extrapolated

Figure 4-9 Example of Table Extrapolation and Discontinuity 7. Linear extrapolation is not used for Fourier transform methods. The function is zero outside the range of the table. 8. For frequency-dependent loads, xi is measured in cycles per unit time. 9. Tabular values on an axis if XAXIS or YAXIS = LOG must be positive. A fatal message will be issued if an axis has a tabular value < 0.

Main Index

CHAPTER D Bulk Data Entries

Dynamic Load Tabular Function, Form 2

TABLED2

Defines a tabular function for use in generating frequency-dependent and time-dependent dynamic loads. Also contains parametric data for use with the table. Format: 1

2

3

4

5

6

7

8

TABLED2

TID

X1

x1

y1

x2

y2

x3

y3

-etc.-

15

-10.5

1.0

-4.5

2.0

-4.2

2.0

2.8

7.0

SKIP

SKIP

9.0

6.5

ENDT

9

10

Example: TABLED2

Field

Contents

TID

Table identification number. (Integer > 0)

X1

Table parameter. See Remark 6. (Real)

xi, yi

Tabular values. (Real)

6.5

Remarks: 1. xi must be in either ascending or descending order, but not both. 2. Discontinuities may be specified between any two points except the two starting points or two end points. For example, in Figure 4-10 discontinuities are allowed only between points x2 and x7. Also if y is evaluated at a discontinuity, then the average value of y is used. In Figure 4-10, the value of y at x=x3 is y = ( y3 + y4 ) ⁄ 2 . 3. At least one continuation entry must be specified. 4. Any xi-yi pair may be ignored by placing “SKIP” in either of the two fields. 5. The end of the table is indicated by the existence of “ENDT” in either of the two fields following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag “ENDT”. 6. TABLED2 uses the algorithm y = y T ( x – X1 ) where x is input to the table and y is returned. The table look-up is performed using linear interpolation within the table and linear extrapolation outside the table using the two starting or end points. See Figure 4-10. No warning messages are issued if table data is input incorrectly.

Main Index

377

378

y

x value Range of Table

Discontinuity Allowed

Discontinuity Not Allowed

Linear Extrapolation of Segment x1-x2

x x1

x2

x3 x4

x5

x6

x7 x8

x Extrapolated

Figure 4-10 Example of Table Extrapolation and Discontinuity 7. Linear extrapolation is not used for Fourier transform methods. The function is zero outside the range of the table. 8. For frequency-dependent loads, X1 and xi are measured in cycles per unit time.

Main Index

CHAPTER D Bulk Data Entries

Dynamic Load Tabular Function, Form 3

TABLED3

Defines a tabular function for use in generating frequency-dependent and time-dependent dynamic loads. Also contains parametric data for use with the table. Format: 1

2

3

4

TABLED3

TID

X1

X2

x1

y1

x2

62

126.9

30.0

2.9

2.9

3.6

5

6

7

8

y2

x3

y3

-etc.-

4.7

5.2

5.7

ENDT

9

10

Example: TABLED3

Field

Contents

TID

Table identification number. (Integer > 0)

X1, X2

Table parameters. (Real; X2 ≠ 0.0)

xi, yi

Tabular values. (Real)

Remarks: 1. xi must be in either ascending or descending order, but not both. 2. Discontinuities may be specified between any two points except the two starting points or two end points. For example, in Figure 4-11 discontinuities are allowed only between points x2 and x7. Also if y is evaluated at a discontinuity, then the average value of y is used. In Figure 4-11, the value of y at x=x3 is y = ( y3 + y4 ) ⁄ 2 . 3. At least one continuation entry must be present. 4. Any xi-yi pair may be ignored by placing “SKIP” in either of the two fields. 5. The end of the table is indicated by the existence of “ENDT” in either of the two fields following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag “ENDT”. 6. TABLED3 uses the algorithm x – X1 y = y T  -----------------  X2  where x is input to the table and y is returned. The table look-up is performed using interpolation within the table and linear extrapolation outside the table using the two starting or end points. See Figure 4-11. No warning messages are issued if table data is input incorrectly.

Main Index

379

380

y

x value Range of Table

Discontinuity Allowed

Discontinuity Not Allowed

Linear Extrapolation of Segment x1-x2

x x1

x2

x3 x4

x5

x6

x7 x8

x Extrapolated

Figure 4-11 Example of Table Extrapolation and Discontinuity 7. Linear extrapolation is not used for Fourier transform methods. The function is zero outside the range of the table. 8. For frequency-dependent loads, X1, X2, and xi are measured in cycles per unit time.

Main Index

CHAPTER D Bulk Data Entries

Dynamic Load Tabular Function, Form 4

TABLED4

Defines the coefficients of a power series for use in generating frequency-dependent and time-dependent dynamic loads. Also contains parametric data for use with the table. Format: 1

2

3

4

5

6

TABLED4

TID

X1

X2

X3

X4

A0

A1

A2

A3

A4

28

0.0

1.0

0.0

100.

2.91

-0.0329

6.51-5

0.0

-3.4-7

7

8

A5

-etc.-

9

10

Example: TABLED4

ENDT

Field

Contents

TID

Table identification number. (Integer > 0)

Xi

Table parameters. (Real; X2 ≠ 0.0; X3<X4)

Ai

Coefficients. (Real)

Remarks: 1. At least one continuation entry must be specified. 2. The end of the table is indicated by the existence of “ENDT” in the field following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag “ENDT”. 3. TABLED4 uses the algorithm N

y =

∑

x – X1 Ai  -----------------  X2 

i

i = 0

where x is input to the table, y is returned, and N is the number of pairs. Whenever x < X3, use X3 for x; whenever x > X4, use X4 for x. There are N + 1 entries in the table. There are no error returns from this table look-up procedure. 4. For frequency-dependent loads, xi is measured in cycles per unit time.

Main Index

381

382

Material Property Table, Form 1

TABLEM1

Defines a tabular function for use in generating temperature-dependent material properties. Format: 1

2

3

4

5

6

7

8

9

TABLEM1

TID

XAXIS

YAXIS

xI

y1

x2

y2

x3

y3

-etc.-

“ENDT”

6.9

2.0

5.6

3.0

5.6

ENDT

10

Example: 32

TABLEM1

-3.0

Field

Contents

TID

Table identification number. (Integer > 0)

XAXIS

Specifies a linear or logarithmic interpolation for the x-axis. See Remark 6. (Character: “LINEAR” or “LOG”; Default = “LINEAR”)

YAXIS

Specifies a linear or logarithmic interpolation for the y-axis. See Remark 6. (Character: “LINEAR” or “LOG”; Default = “LINEAR”)

xi, yi

Tabular values. (Real)

“ENDT”

Flag indicating the end of the table.

Remarks: 1. xi must be in either ascending or descending order, but not both. 2. Discontinuities may be specified between any two points except the two starting points or two end points. For example, in Figure 4-12 discontinuities are allowed only between points x2 through x7. Also, if y is evaluated at a discontinuity, then the average value of y is used. In Figure 4-12, the value of y at x = x3 is y = ( y3 + y4 ) ⁄ 2 . 3. At least one continuation entry must be specified. 4. Any xi-yi pair may be ignored by placing “SKIP” in either of the two fields. 5. The end of the table is indicated by the existence of “ENDT” in either of the two fields following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag “ENDT”. 6. TABLEM1 uses the algorithm y = yT ( x )

Main Index

where x is input to the table and y is returned. The table look-up is performed using linear interpolation within the table and linear extrapolation outside the table using the two starting or end points. See Figure 4-12. The algorithms used for interpolation or extrapolation are:

CHAPTER D Bulk Data Entries

XAXIS

YAXIS

yT(x)

LINEAR

LINEAR

xy – x x – xi ---------------- yi + ---------------- yj xj – xi xj – xi

LOG

LINEAR

ln ( xj ⁄ x ) ln ( x ⁄ xi ) -------------------------- yi + -------------------------- yj ln ( xj ⁄ xi ) ln ( xj ⁄ xi )

LINEAR

LOG

xj – x x – xi exp ---------------- ln yi + ---------------- ln yj xj – xi xj – xi

LOG

LOG

ln ( xj ⁄ x ) ln ( x ⁄ xi ) exp -------------------------- ln yi + -------------------------- ln yi ln ( xj ⁄ xi ) ln ( xj ⁄ xi )

where xj and yj follow xi and yi. No warning messages are issued if table data is input incorrectly. y

x value Range of Table

Discontinuity Allowed

Discontinuity Not Allowed

Linear Extrapolation of Segment x1-x2

x x1

x2

x3 x4

x5

x6

x7 x8

x Extrapolated

Figure 4-12 Example of Table Extrapolation and Discontinuity 7. Tabular values on an axis if XAXIS or YAXIS = LOG must be positive. A fatal message will be issued if an axis has a tabular value < 0.

Main Index

383

384

Material Property Table, Form 2

TABLEM2

Defines a tabular function for use in generating temperature-dependent material properties. Also contains parametric data for use with the table. Format: 1

2

3

4

5

6

7

8

TABLEM2

TID

X1

x1

yI

x2

y2

x3

y3

-etc.-

15

-10.5

1.0

-4.5

2.0

-4.5

2.0

2.8

7.0

SKIP

SKIP

9.0

6.5

ENDT

9

10

Example: TABLEM2

Field

Contents

TID

Table identification number. (Integer > 0)

X1

Table parameter. (Real)

xi, yi

Tabular values. (Real)

6.5

Remarks: 1. xi must be in either ascending or descending order, but not both. 2. Discontinuities may be specified between any two points except the two starting points or two end points. For example, in Figure 4-13, discontinuities are allowed only between points x2 through x7. Also, if y is evaluated at a discontinuity, then the average value of y is used. In Figure 4-13, the value of y at x = x3 is y = ( y3 + y4 ) ⁄ 2 . 3. At least one continuation entry must be specified. 4. Any xi-yi pair may be ignored by placing “SKIP” in either of the two fields. 5. The end of the table is indicated by the existence of “ENDT” in either of the two fields following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag “ENDT”. 6. TABLEM2 uses the algorithm y = zy T ( x – X1 ) where x is input to the table, y is returned and z is supplied from the MATi entry. The table look-up is performed using linear interpolation within the table and linear extrapolation outside the table using the two starting or end points. See Figure 4-13. No warning messages are issued if table data is input incorrectly.

Main Index

CHAPTER D Bulk Data Entries

y

x value Range of Table

Discontinuity Allowed

Discontinuity Not Allowed

Linear Extrapolation of Segment x1-x2

x x1

x2

x3 x4

x5

x6

x7 x8

x Extrapolated

Figure 4-13 Example of Table Extrapolation and Discontinuity

Main Index

385

386

Material Property Table, Form 3

TABLEM3

Defines a tabular function for use in generating temperature-dependent material properties. Also contains parametric data for use with the table. Format: 1

2

3

4

TABLEM3

TID

X1

X2

x1

y1

x2

62

126.9

30.0

2.9

2.9

3.6

5

6

7

8

y2

x3

y3

-etc.-

4.7

5.2

5.7

ENDT

9

10

Example: TABLEM3

Field

Contents

TID

Table identification number. (Integer > 0)

X1, X2

Table parameters. See Remark 6. (Real; X2 ≠ 0.0)

xi, yi

Tabular values. (Real)

Remarks: 1. Tabular values for xi must be specified in either ascending or descending order, but not both. 2. Discontinuities may be specified between any two points except the two starting points or two end points. For example, in Figure 4-14 discontinuities are allowed only between points x2 through x7. Also, if y is evaluated at a discontinuity, then the average value of y is used. In Figure 4-14, the value of y at x = x3 is y = ( y3 + y4 ) ⁄ 2 . 3. At least one continuation entry must be specified. 4. Any xi-yi pair may be ignored by placing “SKIP” in either of the two fields. 5. The end of the table is indicated by the existence of “ENDT” in either of the two fields following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag “ENDT”. 6. TABLEM3 uses the algorithm x – X1 y = zy T  -----------------  X2  where x is input to the table, y is returned and z is supplied from the MATi entry. The table look-up is performed using linear interpolation within the table and linear extrapolation outside the table using the two starting or end points. See Figure 4-14. No warning messages are issued if table data is input incorrectly. Main Index

CHAPTER D Bulk Data Entries

y

x value Range of Table

Discontinuity Allowed

Discontinuity Not Allowed

Linear Extrapolation of Segment x1-x2

x x1

x2

x3 x4

x5

x6

x7 x8

x Extrapolated

Figure 4-14 Example of Table Extrapolation and Discontinuity

Main Index

387

388

Material Property Table, Form 4

TABLEM4

Defines coefficients of a power series for use in generating temperature-dependent material properties. Also contains parametric data for use with the table. Format: 1

2

3

4

5

6

TABLEM4

TID

X1

X2

X3

X4

A0

A1

A2

A3

A4

28

0.0

1.0

0.0

100.

2.91

-0.0329

6.51-5

0.0

-3.4-7

7

8

A5

-etc.-

9

10

Example: TABLEM4

Field

Contents

TID

Table identification number. (Integer > 0)

Xi

Table parameters. (Real; X2 ≠ 0.0; X3 < X4)

Ai

Coefficients. (Real)

ENDT

Remarks: 1. At least one continuation entry must be specified. 2. The end of the table is indicated by the existence of “ENDT” in the field following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag “ENDT”. 3. TABLEM4 uses the algorithm N

y = z

∑

x – X1 i Ai  -----------------  X2 

i = 0

where x is input to the table, y is returned and z is supplied from the MATi entry. Whenever x < X3, use X3 for x; whenever x > X4, use X4 for x. There are N + 1 entries in the table. There are no error returns from this table look-up procedure.

Main Index

CHAPTER D Bulk Data Entries

Grid Point Temperature Field

TEMP

Defines temperature at grid points for determination of thermal loading, temperature-dependent material properties, or stress recovery. Format: 1 TEMP

2

3

4

5

6

7

8

SID

G1

T1

G2

T2

G3

T3

3

94

316.2

49

219.8

9

10

Example: TEMP

Field

Contents

SID

Temperature set identification number. (Integer > 0)

Gi

Grid point identification number. (Integer > 0)

Ti

Temperature. (Real)

Remarks: 1. In the static solution sequences, the temperature set ID(SID) is selected by the Case Control command TEMP. In the dynamic solution sequences, SID must be referenced in the TID field of an LSEQ entry, which in turn must be selected by the Case Control command LOADSET. There is a maximum of 66 unique temperature SIDs that may be specified. 2. Set ID must be unique with respect to all other LOAD type entries if TEMP(LOAD) is specified in the Case Control Section. 3. From one to three grid point temperatures may be defined on a single entry. 4. If thermal effects are requested, all elements must have a temperature field defined either directly on a TEMPP1, TEMPP3, or TEMPRB entry or indirectly as the average of the connected grid point temperatures defined on the TEMP or TEMPD entries. Directly defined element temperatures always take precedence over the average of grid point temperatures. 5. If the element material is temperature dependent, its properties are evaluated at the average temperature. 6. Average element temperatures are obtained as a simple average of the connecting grid point temperatures when no element temperature data are defined. Gauss point temperatures are averaged for solid elements instead of grid point temperature.

Main Index

7. For steady state heat transfer analysis, this entry together with the TEMPD entry supplies the initialization temperatures for nonlinear analysis. The Case Control command TEMP(INIT) = SID requests selection of this entry. The temperature values specified here must be coincident with any temperature boundary conditions that are specified.

389

390

8. For transient heat transfer analysis, this entry together with the TEMPD entry supplies the initial condition temperatures. The Case Control command IC = SID requests selections of this entry. The temperature values specified here must be coincident with any temperature boundary condition specified. 9. In linear and nonlinear buckling analysis, the follower force effects due to loads from this entry are not included in the differential stiffness. See “Buckling Analysis in SubDMAP MODERS” on page 468 and “Nonlinear Static Analysis” on page 650 of the MSC.Nastran Reference Manual.

Main Index

CHAPTER D Bulk Data Entries

Conical Shell Temperature

TEMPAX

Defines temperature sets for conical shell problems. Format: 1

2

3

4

5

6

7

8

9

TEMPAX

SID1

RID1

PHI1

T1

SID2

RID2

PHI2

T2

4

7

30.0

105.3

10

Example: TEMPAX

Field

Contents

SIDi

Temperature set identification number. (Integer > 0)

RIDi

Ring identification number (see RINGAX entry). (Integer > 0)

PHIi

Azimuthal angle in degrees. (Real)

Ti

Temperature. (Real)

Remarks: 1. TEMPAX is allowed only if an AXIC entry is also present. 2. SIDi must be unique with respect to all other LOAD type entries if TEMP(LOAD) is specified in the Case Control Section. 3. Temperature sets must be selected with the Case Control command TEMP=SID. There is a maximum of 66 unique temperature SIDs that may be specified. 4. One or two temperatures may be defined on each entry. 5. For a discussion of the conical shell problem, see “Restart Procedures” on page 398 of the MSC.Nastran Reference Guide. 6. TEMP(INIT) is not used with this entry.

Main Index

391

392

Grid Point Temperature Field Default

TEMPD

Defines a temperature value for all grid points of the structural model that have not been given a temperature on a TEMP entry. Format: 1 TEMPD

2

3

4

5

6

7

8

9

SID1

T1

SID2

T2

SID3

T3

SID4

T4

1

216.3

10

Example: TEMPD

Field

Contents

SIDi

Temperature set identification number. (Integer > 0)

Ti

Default temperature value. (Real)

Remarks: 1. For structural analysis in the static solution sequences, the temperature set ID (SID) is selected by the Case Control command TEMP. In the dynamic solution sequences, SID must be referenced in the TID field of an LSEQ entry, which in turn must be selected by the Case Control command LOADSET. There is a maximum of 66 unique temperature SIDs that may be specified. 2. SIDi must be unique with respect to all other LOAD type entries if TEMP(LOAD) is specified in the Case Control Section. 3. From one to four default temperatures may be defined on a single entry. 4. If thermal effects are requested, all elements must have a temperature field defined either directly on a TEMPP1, TEMPP3, or TEMPRB entry or indirectly as the average of the connected grid point temperatures defined on the TEMP or TEMPD entries. Directly defined element temperatures always take precedence over the average of grid point temperatures. 5. If the element material is temperature dependent, its properties are evaluated at the average temperature. 6. Average element temperatures are obtained as a simple average of the connecting grid point temperatures when no element temperature data is defined. 7. For steady-state heat transfer analysis, this entry together with the TEMP entry supplies the initialization temperatures for nonlinear analysis. The Case Control command TEMP(INIT) = SID requests selection of this entry. The temperature values specified here must be coincident with any temperatures boundary conditions that are specified.

Main Index

CHAPTER D Bulk Data Entries

8. For transient heat transfer analysis, this entry together with the TEMP entry supplies the initial condition temperatures. The Case Control command IC=SID request selection of this entry. The temperature values specified here must be coincident with any temperature boundary conditions that are specified. 9. In linear and nonlinear buckling analysis, the follower force effects due to loads from this entry are not included in the differential stiffness. See “Buckling Analysis in SubDMAP MODERS” on page 468 and “Nonlinear Static Analysis” on page 650 of the MSC.Nastran Reference Manual. 10. For partitioned Bulk Data superelements and auxiliary models, TEMPD must be specified in all partitioned Bulk Data Sections.

Main Index

393

394

Dynamic Transfer Function

TF

Defines a dynamic transfer function of the form 2

( B0 + B1 ⋅ p + B2 ⋅ p )u d +

∑ ( A0 ( i ) + A1 ( i )p + A2 ( i )p

2

) ui = 0

Eq. 4-3

i

Can also be used as a means of direct matrix input. See Remark 4. Format: 1 TF

2

3

4

5

6

7

SID

GD

CD

B0

B1

B2

G(1)

C(1)

A0(1)

A1(1)

A2(1)

-etc.-

1

2

3

4.0

5.0

6.0

3

4

5.0

6.0

7.0

8

9

10

Example: TF

Field

Contents

SID

Set identification number. (Integer > 0)

GD, G(i)

Grid, scalar, or extra point identification numbers. (Integer > 0)

CD, C(i) B0, B1, B2 A0(i), A1(i), A2(i)

Component numbers. (Integer zero or blank for scalar or extra points, any one of the Integers 1 through 6 for a grid point.) Transfer function coefficients. (Real)

Remarks: 1. Transfer function sets must be selected with the Case Control command TFL = SID. 2. Continuation entries are optional. 3. The matrix elements defined by this entry are added to the dynamic matrices for the problem. 4. The constraint relation given in Eq. 4-3 will hold only if no structural elements or other matrix elements are connected to the dependent coordinate u d . In fact, the terms on the left side of Eq. 4-3 are simply added to the terms from all other sources in the row for u d . 5. See the MSC.Nastran Advanced Dynamic Analysis User’s Guide for a discussion of transfer functions. 6. For each SID, only one logical entry is allowed for each GD, CD combination. 7. For heat transfer analysis, the initial conditions must satisfy Eq. 4-3.

Main Index

CHAPTER D Bulk Data Entries

Transient Response Dynamic Excitation, Form 1

TLOAD1

Defines a time-dependent dynamic load or enforced motion of the form {P(t)} = {A ⋅ F(t – τ)} for use in transient response analysis. Format: 1

2

3

4

5

6

TLOAD1

SID

EXCITEI D

DELAY

TYPE

TID

5

7

LOAD

13

7

8

9

10

Example: TLOAD1

Field

Contents

SID

Set identification number. (Integer > 0)

EXCITEID

Identification number of DAREA or SPCD entry set or a thermal load set (in heat transfer analysis) that defines A. See Remarks 2. and 3. (Integer > 0)

DELAY

Defines time delay τ . (Integer > 0, real or blank) If it is a non-zero integer, it represents the identification number of DELAY Bulk Data entry that defines τ . If it is real, then it directly defines the value of τ that will be used for all degrees of freedom that are excited by this dynamic load entry. See also Remark 9.

TYPE

Defines the type of the dynamic excitation. See Remarks 2. and 3. (Integer, character or blank; Default = 0)

TID

Identification number of TABLEDi entry that gives F ( t ) . (Integer > 0)

Remarks: 1. Dynamic excitation sets must be selected with the Case Control command DLOAD = SID. 2. The type of the dynamic excitation is specified by TYPE (field 5) according to the following table: TYPE

TYPE of Dynamic Excitation

0, L, LO, LOA or LOAD

Applied load (force or moment) (Default)

1, D, DI, DIS, or DISP

Enforced displacement using large mass or SPC/SPCD data

2, V, VE, VEL or VELO

Enforced velocity using large mass or SPC/SPCD data

3, A, AC, ACC or ACCE Enforced acceleration using large mass or SPC/SPCD data Main Index

395

396

3. TYPE (field 5) also determines the manner in which EXCITEID (field 3) is used by the program as described below Excitation specified by TYPE is applied load

• There is no LOADSET request in Case Control EXCITEID may also reference DAREA, static, and thermal load set entries

• There is a LOADSET request in Case Control The program may also reference static and thermal load set entries specified by the LID or TID field in the selected LSEQ entries corresponding to the EXCITEID. Excitation specified by TYPE is enforced motion

• There is no LOADSET request in Case Control EXCITEID will reference SPCD entries. If such entries indicate null enforced motion, the program will then assume that the excitation is enforced motion using large mass and will reference DAREA and static and thermal load set entries just as in the case of applied load excitation.

• There is a LOADSET request in Case Control The program will reference SPCD entries specified by the LID field in the selected LSEQ entries corresponding to the EXCITEID. If such entries indicate null enforced motion, the program will then assume that the excitation is enforced motion using large mass and will reference static and thermal load set entries corresponding to the DAREA entry in the selected LSEQ entries, just as in the case of applied load excitation. 4. EXCITEID may reference sets containing QHBDY, QBDYi, QVECT, QVOL and TEMPBC entries when using the heat transfer option. 5. TLOAD1 loads may be combined with TLOAD2 loads only by specification on a DLOAD entry. That is, the SID on a TLOAD1 entry may not be the same as that on a TLOAD2 entry. 6. SID must be unique for all TLOAD1, TLOAD2, RLOAD1, RLOAD2, and ACSRCE entries. 7. If the heat transfer option is used, the referenced QVECT entry may also contain references to functions of time, and therefore A may be a function of time. 8. If TLOADi entries are selected in SOL 111 or 146 then a Fourier analysis is used to transform the time-dependent loads on the TLOADi entries to the frequency domain and then combine them with loads from RLOADi entries. Then the analysis is performed as a frequency response analysis but the solution and the output are converted to and printed in the time domain. Please refer to “Fourier Transform” on page 176 of the MSC.Nastran Advanced Dynamic Analysis User’s Guide. 9. If DELAY is blank or zero, τ will be zero.

Main Index

CHAPTER D Bulk Data Entries

Transient Response Dynamic Excitation, Form 2

TLOAD2

Defines a time-dependent dynamic excitation or enforced motion of the form  ,  0 {P(t)} =   A ˜t B e C ˜t cos ( 2πF ˜t + P ) , 

t < ( T1 + τ ) or t > ( T2 + τ ) ( T1 + τ ) ≤ t ≤ ( T2 + τ )

for use in a transient response problem, where ˜t = t – T1 – τ Format: 1

2

3

4

5

6

7

8

9

TLOAD2

SID

EXCITEID

DELAY

TYPE

T1

T2

F

P

C

B

4

10

2.1

4.7

12.0

10

Example: TLOAD2

2.0

Field

Contents

SID

Set identification number. (Integer > 0)

EXCITEID

Identification number of DAREA or SPCD entry set or a thermal load set (in heat transfer analysis) that defines A. See Remarks 2. and 3. (Integer > 0)

DELAY

Defines time delay τ. (Integer > 0, real or blank). If it is a non-zero integer, it represents the identification number of DELAY Bulk Data entry that defines τ.. If it is real, then it directly defines the value of τ that will be used for all degrees of freedom that are excited by this dynamic load entry. See also Remark 5.

TYPE

Defines the type of the dynamic excitation. See Remarks 2. and 3. (Integer, character or blank; Default = 0)

T1

Time constant. (Real > 0.0)

T2

Time constant. (Real; T2 > T1)

F

Frequency in cycles per unit time. (Real > 0.0; Default = 0.0)

P

Phase angle in degrees. (Real; Default = 0.0)

C

Exponential coefficient. (Real; Default = 0.0)

B

Growth coefficient. (Real; Default = 0.0)

Remarks: 1. Dynamic excitation sets must be selected with the Case Control command with DLOAD=SID. Main Index

397

398

2. The type of the dynamic excitation is specified by TYPE (field 5) according to the following table: TYPE

TYPE of Dynamic Excitation

0, L, LO, LOA or LOAD

Applied load (force or moment) (Default)

1, D, DI, DIS, or DISP

Enforced displacement using large mass or SPC/SPCD data

2, V, VE, VEL or VELO

Enforced velocity using large mass or SPC/SPCD data

3, A, AC, ACC or ACCE Enforced acceleration using large mass or SPC/SPCD data 3. TYPE (field 5) also determines the manner in which EXCITEID (field 3) is used by the program as described below Excitation specified by TYPE is applied load

• There is no LOADSET request in Case Control EXCITEID may also reference DAREA, static and thermal load set entries

• There is a LOADSET request in Case Control The program may also reference static and thermal load set entries specified by the LID or TID field in the selected LSEQ entries corresponding to the EXCITEID. Excitation specified by TYPE is enforced motion

• There is no LOADSET request in Case Control EXCITEID will reference SPCD entries. If such entries indicate null enforced motion, the program will then assume that the excitation is enforced motion using large mass and will reference DAREA and static and thermal load set entries just as in the case of applied load excitation.

• There is a LOADSET request in Case Control The program will reference SPCD entries specified by the LID field in the selected LSEQ entries corresponding to the EXCITEID. If such entries indicate null enforced motion, the program will then assume that the excitation is enforced motion using large mass and will reference static and thermal load set entries specified by the LID or TID field in the selected LSEQ entries corresponding to the EXCITEID, just as in the case of applied load excitation. 4. EXCITEID (field 3) may reference sets containing QHBDY, QBDYi, QVECT, and QVOL and TEMPBC entries when using the heat transfer option. 5. If DELAY is blank or zero, τ will be zero. 6. TLOAD1 loads may be combined with TLOAD2 loads only by specification on a DLOAD entry. That is, the SID on a TLOAD1 entry may not be the same as that on a TLOAD2 entry. Main Index

CHAPTER D Bulk Data Entries

7. SID must be unique for all TLOAD1, TLOAD2, RLOAD1, RLOAD2, and ACSRCE entries. 8. If the heat transfer option is used, the referenced QVECT entry may also contain references to functions of time, and therefore A may be a function of time. 9. If TLOADi entries are selected in SOL 111 or 146 then a Fourier analysis is used to transform the time-dependent loads on the TLOADi entries to the frequency domain and them combine them with loads from RLOADi entries. Then the analysis is performed as a frequency response analysis but the solution and the output are converted to and printed in the time domain. In this case, B will be rounded to the nearest integer. Please refer to “Fourier Transform” on page 176 of the MSC.Nastran Advanced Dynamic Analysis User’s Guide. 10. The continuation entry is optional.

Main Index

399

400

Parameters for Nonlinear Transient Analysis

TSTEPNL

Defines parametric controls and data for nonlinear transient structural or heat transfer analysis. TSTEPNL is intended for SOLs 129, 159, and 99. Format: 1

2

3

4

5

TSTEPNL

ID

NDT

DT

NO

EPSU

EPSP

EPSW

MAXDIV

MAXBIS

ADJUST

MSTEP

RB

250

100

.01

1

1.E-2

1.E-3

1.E-6

2

5

5

0

0.75

6

7

8

9

KSTEP

MAXITER

CONV

MAXQN

MAXLS

FSTRESS

MAXR

UTOL

RTOLB

2

10

10

2

.02

16.0

0.1

20.

10

Example: TSTEPNL

Main Index

PW

Field

Contents

ID

Identification number. (Integer > 0)

NDT

Number of time steps of value DT. See Remark 2. (Integer > 4)

DT

Time increment. See Remark 2. (Real > 0.0)

NO

Time step interval for output. Every NO-th step will be saved for output. See Remark 3. (Integer > 0; Default = 1)

KSTEP

KSTEP is the number of converged bisection solutions between stiffness updates. (Integer > 0; Default = 2)

MAXITER

Limit on number of iterations for each time step. See Remark 4. (Integer ≠ 0; Default = 10)

CONV

Flags to select convergence criteria. See Remark 5. (Character: “U”, “P”, “W”, or any combination; Default = “PW.”)

EPSU

Error tolerance for displacement (U) criterion. (Real > 0.0; Default = 1.0E-2)

EPSP

Error tolerance for load (P) criterion. (Real > 0.0; Default = 1.0E-3)

EPSW

Error tolerance for work (W) criterion. (Real > 0.0; Default = 1.0E-6)

MAXDIV

Limit on the number of diverging conditions for a time step before the solution is assumed to diverge. See Remark 6. (Integer > 0; Default = 2)

MAXQN

Maximum number of quasi-Newton correction vectors to be saved on the database. See Remark 7. (Integer > 0; Default = 10)

MAXLS

Maximum number of line searches allowed per iteration. See Remark 7. (Integer > 0; Default = 2)

CHAPTER D Bulk Data Entries

Field

Contents

FSTRESS

Fraction of effective stress ( σ ) used to limit the subincrement size in the material routines. See Remark 8. (0.0 < Real < 1.0; Default = 0.2)

MAXBIS

Maximum number of bisections allowed for each time step. See Remark 9. (-9
ADJUST

Time step skip factor for automatic time step adjustment. See Remark 10. (Integer > 0; Default = 5)

MSTEP

Number of steps to obtain the dominant period response. See Remark 11. (10 < Integer < 200; Default = variable between 20 and 40.)

RB

Define bounds for maintaining the same time step for the stepping function during the adaptive process. See Remark 11. (0.1 < Real < 1.0; Default = 0.75)

MAXR

Maximum ratio for the adjusted incremental time relative to DT allowed for time step adjustment. See Remark 12. (1.0 < Real < 32.0; Default = 16.0)

UTOL

Tolerance on displacement or temperature increment below which a special provision is made for numerical stability. See Remark 13. (0.001 < Real < 1.0; Default = 0.1)

RTOLB

Maximum value of incremental rotation (in degrees) allowed per iteration to activate bisection. See Remark 14. (Real > 2.0; Default = 20.0)

Remarks: 1. The TSTEPNL Bulk Data entry is selected by the Case Control command TSTEP = ID. Each residual structure subcase requires a TSTEP entry and either applied loads via TLOADi data or initial values from a previous subcase. Multiple subcases are assumed to occur sequentially in time with the initial values of time and displacement conditions of each subcase defined by the end conditions of the previous subcase. 2. NDT is used to define the total duration for analysis, which is NDT * DT. Since DT is adjusted during the analysis , the actual number of time steps, in general, will not be equal to NDT). Also, DT is used only as an initial value for the time increment. 3. For printing and plotting the solution, data recovery is performed at time steps 0, NO, 2 * NO, ..., and the last converged step. The Case Control command OTIME may also be used to control the output times. 4. The number of iterations for a time step is limited to MAXITER. If MAXITER is negative, the analysis is terminated when the divergence condition is encountered twice during the same time step or the solution diverges for five consecutive time steps. If MAXITER is positive, the program computes the best solution and continues the analysis until divergence occurs again. If the solution does not converge in MAXITER iterations, the process is treated as a divergent process. See Remark 6.

Main Index

401

402

5. The convergence test flags (U = displacement error test, P = load equilibrium error test, W = work error test) and the error tolerances (EPSU, EPSP, and EPSW) define the convergence criteria. All requested criteria (combination of U, P, and/or W) are satisfied upon convergence. Note that at least two iterations are necessary to check the displacement convergence criterion. 6. MAXDIV provides control over diverging solutions. Depending on the rate of divergence, the number of diverging solutions (NDIV) is incremented by 1 or 2. The solution is assumed to diverge when NDIV reaches MAXDIV during the iteration. If the bisection option is used (allowed MAXBIS times) the time step is bisected upon divergence. Otherwise, the solution for the time step is repeated with a new stiffness based on the converged state at the beginning of the time step. If NDIV reaches MAXDIV again within the same time step, the analysis is terminated. 7. Nonzero values of MAXQN and MAXLS will activate the quasi-Newton update and the line search process, respectively. 8. The number of subincrements in the material routines is determined such that the subincrement size is approximately FSTRESS ⋅ σ . FSTRESS is also used to establish a tolerance for error correction in elastoplastic material, i.e., error in yield function
• If ADJUST = 0, then the automatic adjustment is deactivated. This is recommended when the loading consists of short duration pulses.

• If ADJUST > 0, the time increment is continually adjusted for the first few steps until a good value of ∆t is obtained. After this initial adjustment, the time increment is adjusted every ADJUST-th time step only.

• If ADJUST is one order greater than NDT, then automatic adjustment is deactivated after the initial adjustment. Main Index

CHAPTER D Bulk Data Entries

11. MSTEP and RB are used to adjust the time increment during analysis. The recommended value of MSTEP for nearly linear problems is 20. A larger value (e.g., 40) is required for highly nonlinear problems. By default, the program automatically computes the value of MSTEP based on the changes in the stiffness. The time increment adjustment is based on the number of time steps desired to capture the dominant frequency response accurately. The time increment is adjusted as follows: ∆t n + 1 = f ( r )∆t n where 1 2π 1 r = -------------------  ------  --------  MSTEP ω n  ∆t n with f = 0.25 for r < 0.5 ⋅ RB f =

0.5

for 0.5 ⋅ RB ≤ r < RB

f =

1.0

for RB ≤ r < 2.0

f =

2.0

for 2.0 ≤ r < 3.0 ⁄ RB

f =

4.0

for r ≥ 3.0 ⁄ RB

12. MAXR is used to define the upper and lower bounds for adjusted time step size, i.e., DT DT MIN  ---------------------- , ------------------ ≤ ∆t ≤ MAXR ⋅ DT  MAXBIS MAXR 2 13. UTOL is a tolerance used to filter undesirable time step adjustments; i.e., · Un ------------------- < UTOL · U max Under this condition no time step adjustment is performed in a structural analysis (SOL 129). In a heat transfer analysis (SOL 159) the time step is doubled. 14. The bisection is activated if the incremental rotation for any degree-of-freedom ( ∆θ x, ∆θ y, ∆θ z ) exceeds the value specified by RTOLB. This bisection strategy is based on the incremental rotation and controlled by MAXBIS.

Main Index

403

404

View Factor Definition

VIEW

Defines radiation cavity and shadowing for radiation view factor calculations. Format: 1 VIEW

2

3

4

5

6

7

IVIEW

ICAVITY

SHADE

NB

NG

DISLIN

1

1

BOTH

2

3

0.25

8

9

10

Example: VIEW

Field

Contents

IVIEW

Identification number. (Integer > 0)

ICAVITY

Cavity identification number for grouping the radiant exchange faces of CHBDYi elements. (Integer > 0)

SHADE

Shadowing flag for the face of CHBDYi element. (Character, Default = “BOTH”) NONE means the face can neither shade nor be shaded by other faces. KSHD means the face can shade other faces. KBSHD means the face can be shaded by other faces. BOTH means the face can both shade and be shaded by other faces. (Default)

NB

Subelement mesh size in the beta direction. (Integer > 0; Default = 1)

NG

Subelement mesh size in the gamma direction. (Integer > 0; Default = 1)

DISLIN

The displacement of a surface perpendicular to the surface. See Figure 4-15. (Real; Default = 0.0)

Remarks: 1. VIEW must be referenced by CHBDYE, CHBDYG, or CHBDYP elements to be used. 2. ICAVITY references the cavity to which the face of the CHBDYi element belongs; a zero or blank value indicates this face does not participate in a cavity. 3. NB, NG, and DISLIN are used in the calculation of view factors by finite difference or contour integration techniques. They are not used with the VIEW3D entry. 4. A summary of the shadowing conditions can be requested by the PARAM,MESH,YES Bulk Data entry. 5. SHADE references shadowing for CHBDYi elements participating in a radiation cavity, the VIEW calculation can involve shadowing. 6. DISLIN should only be used with LINE type CHBDYE and CHBDYP surface elements. DISLIN > 0.0 means into the cavity. See Figure 4-15.

Main Index

CHAPTER D Bulk Data Entries

n

Relocated Radiation Surface

DISLIN

n

Active Side Location of Element

Figure 4-15 DISLIN Convention 7. NB and NG define the subelement mesh refinement when using the VIEW module (as opposed to the VIEW3D module) for the calculation of view factors. n 3

4

2

1

Figure 4-16 Typical AREA4 surface element where NB=2 and NG=4

Main Index

405

406

View Factor Definition - Gaussian Integration Method

VIEW3D

Defines parameters to control and/or request the Gaussian Integration method of view factor calculation for a specified cavity. Format: 1

2

3

4

5

6

7

8

9

VIEW3D

ICAVITY

GITB

GIPS

CIER

ETOL

ZTOL

WTOL

RADCHK

1

2

2

4

10

Example: VIEW3D

Main Index

1.0E-6

Field

Contents

ICAVITY

Radiant cavity identification number on RADCAV entry. (Integer > 0)

GITB

Gaussian integration order to be implemented in calculating net effective view factors in the presence of third-body shadowing. (Integer 2, 3, 4, 5, 6 or 10; Default = 4)

GIPS

Gaussian integration order to be implemented in calculating net effective view factors in the presence of self-shadowing. (Integer 2, 3, 4, 5, 6 or 10; Default = 4)

CIER

Discretization level used in the semi-analytic contour integration method. (1 < Integer < 20; Default = 4)

ETOL

Error estimate above which a corrected view factor is calculated using the semi-analytic contour integration method. (Real > 0.0; Default = 0.1)

ZTOL

Assumed level of calculation below which the numbers are considered to be zero. (Real > 0.0; Default = 1.E-10)

WTOL

Assumed degree of warpage above which the actual value of F ii will be calculated. (0.0 < Real < 1.0; Default = 0.01)

CHAPTER D Bulk Data Entries

Field

Contents

RADCHK

Type of diagnostic output desired for the radiation exchange surfaces. (Integer; Default = 3) RADCHK = -1, No diagnostic output requested RADCHK = 1, Grid table and element connectivity RADCHK = 2, Surface Diagnostics - Surface type, area, skewness, taper, warpage, grid point sequencing, aspect ratio, and shading flags. RADCHK = 3, Area, view factor, area-view factor product with error estimate, existence flags for partial self-shadowing, third-body shadowing with error estimate, and enclosure summations for view factor. (Default) RADCHK = 0, Same as RADCHK = 1, 2, and 3 RADCHK = 12, Same as RADCHK = 1 and 2 RADCHK = 13, Same as RADCHK = 1 and 3 RADCHK = 23, Same as RADCHK = 2 and 3

Remarks: 1. For ETOL, when the error estimate exceeds the value input for the ETOL entry, the contour method is employed to develop an improved view factor. 2. For ZTOL, the use of a geometry scale that results in small numerical values of A i F ij should be avoided. 3. When WTOL is exceeded, the actual value of F ii will be calculated when using the adaptive view module. Warpage will not be considered in the calculation of F ij . 4. For axisymmetric analysis, RADCHK = -1 or 3 only.

Main Index

407

408

Comment

$

Used to insert comments into the input file. Comment statements may appear anywhere within the input file. Format: $ followed by any characters out to column 80. Example: $ TEST FIXTURE-THIRD MODE Remarks: 1. Comments are ignored by the program. 2. Comments will appear only in the unsorted echo of the Bulk Data.

Main Index

MSC.Nastran Thermal Analysis User’s Guide

APPENDIX

E

View Factor Calculation Methods

■ Calculation of View Factors ■ Fundamentals of View Factor Calculation

Main Index

410

5.1

Calculation of View Factors MSC.Nastran has two independent routines available for the calculation of view factors between gray diffuse surface elements. The default routine, the VIEW module, relies on a user defined combination of area and contour discretization to determine the geometric view factor. The second module, VIEW3D, utilizes Gaussian integration and semi-analytic contour integration to evaluate view factors. In the material that follows, the two methods are compared and contrasted from a user standpoint in an effort to direct their most efficient application.

Main Index

CHAPTER E View Factor Calculation Methods

5.2

Fundamentals of View Factor Calculation 1. View factors can only be determined between surfaces that have been identified with CHBDYi surface elements. 2. Because of the geometric or visual nature of the view factor calculation, it is often necessary to identify both sides of conduction elements with independent surface elements, particularly when third-body shadowing is of concern. Only active surface elements can participate, or be seen, in a view factor calculation. 3. The active side of the surface element is defined relative to the grid point connections. The right hand rule specifies the outward surface normal as one proceeds from G1 to Gn thereby defining the active surface element. 4. The overall quality of the view factor calculated is highly dependent on the surface element mesh model. When the distance between any two elements is reduced below a level on the order of an element length or width, inaccuracies can develop. At the same time, a large number of small elements can create a very computationally intensive problem. 5. There are two types of shadowing which can also reduce the quality of the overall view factor. Self-shadowing reduces the total view factor between two surfaces due simply to their relative orientations in space (Figure 5-1). Third-body shadowing (Figure 5-2) takes into account the reduced view between two surfaces due to other interelement interference surfaces. In this figure, note the existence of both the K and L surfaces. nˆ

nˆ

nˆ

nˆ (NONE)

nˆ (PARTIAL) Figure 5-1 Self-Shadowing

Main Index

nˆ (TOTAL)

411

412

Z 3

J

r 13 K

nK

2 r 12

L

nL Y 1

X

I Figure 5-2 Third Surface Shadowing

6. The CHBDYi element types available for radiation view factor calculation include: POINT LINE REV AREA3 AREA4 AREA6–VIEW3D Module Only AREA8–VIEW3D Module Only All surface elements may be used for radiation enclosure analysis if the appropriate user supplied view or exchange factors are available. 7. MSC.Nastran allows for isolated surface element groupings when performing view factor calculations – multiple radiation cavities. This procedure can eliminate a great deal of needless calculation among surfaces when one group of elements clearly cannot see another group of elements. The surface element groups therefore are arranged by unique cavity IDs. No surface element may reside in more than on cavity. 8. The VIEW entry invokes the calculation of the view factors for the overall thermal analysis. It also separates the CHBDYi surface elements into the desired cavities. The IVIEW field identifies the CHBDYi elements and the ICAVITY field assigns the elements to a cavity.

Using the VIEW Module 1. The geometric integral equation to be solved for the view factor is given below. “Arbitrary Enclosure Radiation Surfaces” on page 413 depicts the pertinent terms. Main Index

CHAPTER E View Factor Calculation Methods

 cos β i cos β j - dA i dA j ∫  ------------------------------2  πr A A ij i j (dimensionless)

1 F ij = ----- ∫ Ai

Eq. 5-1

where F ij is defined as the fraction of the radiant emission leaving surface i which arrives at surface j. Cj z

vj

Aj dA j βj

r

y

r nj ni

vi x

βi

Ai dA i Ci

A i and A j are diffuse emitters and reflectors A i and A j are black. A i and A j are isothermal. Figure 5-3 Arbitrary Enclosure Radiation Surfaces 2. The VIEW Module solves Eq. 5-1 by two methods. The first method discretizes the surface elements into a number of finite subelements and treats the integrals as dual summations over all the subelements on surfaces I and J. This method is often referred to as the finite difference method, but is just an extension of view factor algebra. Consider the surfaces I and II below with subdivision 1 → 8 .

Main Index

413

414

4 1

3

8

2

5

I

7 6

II

From view factor algebra, a.

f 1 – II = f 1 – 5 + f 1 – 6 + f 1 – 7 + f 1 – 8 and similarily for f 2 – II , f 3 – II , and f 4 – II

Reciprocity provides; b.

A1 A 1 f 1 – II = A II f II – 1 ; f II – 1 = ------- f 1 – II A II

c.

Now, f II – I = f II – 1 + f II – 2 + f II – 3 + f II – 4

d. and, A II f II – I = A 1 f 1 – II + A 2 f 2 – II + A 3 f 3 – II + A 4 f f – II

e.

using, a. then A II F II – I = A 1 ( f 1 – 5 + f 1 – 6 + f 1 – 7 + f 1 – 8 ) + A2 ( f2 – 5 + f2 – 6 + f2 – 7 + f2 – 8 ) + A2 ( f3 – 5 + f3 – 6 + f3 – 7 + f3 – + A4 ( f4 – 5 + f4 – 6 + f4 – 7 + f4 – 4

f.

1 so f I – II = ----AI

8

∑ ∑ i = 1j = 5

8) 8)

cos β i cos β j A i A j -----------------------------------------2 ΠR ij

The second method transforms the area integrals into contour integrals and subdivides the perimeter into finite line segments. A similar dual contour summation is then performed around surfaces I and J. This method is commonly referred to as the contour integration method. 3. In general, area integration is faster than contour integration, but does not provide as accurate an answer. Several choices can be made by the user as a result. The RADCAV entry has information fields on it for the control and manipulation of the view factor calculation: NFECI = FD Finite Difference methods are used to calculate the view factors (applies to the VIEW Module only). NFECI = CONT Contour integration methods are used to calculate the view factors (applies to the VIEW Module only). Main Index

CHAPTER E View Factor Calculation Methods

NFECI = blank or 0. This is the default value signifying that the code will make an estimate based on geometry and the field value of RMAX as to whether it will use finite differences or contour integration. Figure 5-4 below illustrates the criteria enforced.

d ij

j

i Figure 5-4

Contour integration is used on any element pair for which; Aj -------------- > RMAX 2 ( d ij ) For example, if A j = 1 , d ij <

10 enforces contour integration.

1. Since the VIEW Module relies on element subdivision in its calculation method, a means of requesting the level of subdivision is made available. The number of element subdivisions are specified on the NB and NG field of the VIEW entry. The subdivision process is illustrated below for the various surface element types. AREA4 G4

Y

G3

G1 G2 X

NB = 3 NG = 4

Main Index

415

416

POINT G1 NB = 2 NG = 4

LINE

G1

G2 NB = 4 NG = 3

REV Z G2 NB = 2 NG = 4 G1 Y X

AREA3 G3 NB = 7 NG = 3

G1 Main Index

G2

CHAPTER E View Factor Calculation Methods

Using the VIEW3D Module - 3D Geometries 1. The VIEW3D Module relies on Gaussian integration techniques for the solution of Eq. 5-1. This view module is accessed by introducing the VIEW3D Bulk Data entry. This view factor calculator is semi-adaptive in that detection of excessive error or shadowing, will automatically invoke semi-analytic contour integration techniques or higher Gaussian integration order to reduce the error. For a general 3D geometry, this procedure is superior in both accuracy and speed to that available with the VIEW module. 2. The VIEW3D Module is designed for the calculation of view factors for general 3D and axisymmetric geometries. Planar view factors must be calculated with the VIEW routine. 3. There is no surface subdivision available with VIEW3D, therefore a responsible initial mesh is required for good results. Accuracy levels can be substantially controlled by requesting the use of various integration orders. 4. This module is requested by including the Bulk Data entry VIEW3D. The VIEW3D entry contains specific fields for defining the various integration orders desired for unobstructed view factors, self and third-body shadowing view factors, and improved view factors when excessive error is detected. 5. The view factor error is defined as: ERROR = F ij ⋅ ( RMAX ⁄ RMIN ) In this equation, F ij is the initially calculated view factor (always an integration order of 2 by 2) and RMAX and RMIN represent the largest and smallest integration point (surface I) to integration point (surface J) vector lengths. Surface proximity and orientation are reflected in this value. 6. When a large number of surfaces are involved in an enclosure (1000+), it may be advisable to reduce the values of the field data for GITB, GIPS, and CIER to the value of (2). 7. Because view factors solely involve geometry, it is important to work in dimensions/units that do not lead to machine accuracy problems. In particular, in transformed space, the view factor equation has an integration point to integration point distance raised to the fourth power in the denominator.

Using the VIEW3D Module - Axisymmetric Geometries 1. Axisymmetric geometries have their radiative surfaces modeled with CHBDYG elements of TYPE=REV. These are necessarily attached to CTRIAX6 conduction elements. 2. The module is designed to build an internal geometry composed of a 3D representation of the axisymmetric model. This computational model represents approximately onehalf of a full 3D geometry. The number of elements employed in the computational models is set by the user through the value NREV in field 9 of the RADCAB Bulk Data entry. Every REV element in a given cavity then must generate the same number of Main Index

417

418

computation elements. It is recommended to set NREV to a level which will result in approximately square computation elements being created. To guarantee this for every element then, all REV elements would need to be about the same length. This may not be practical for many problems. 3. Although there are considerable numbers of computational elements, the liberal use of symmetry eliminates the need to calculate many of the individual view factors in the internal half-model representation. In the absence of any third body shadowing, the axisymmetric calculation should be much faster than the equivalent 3D calculation. 4. The general specification of shadowing conditions for axisymmetric geometry can be complicated. For simple geometries, the user can save considerable calculation effort by setting the NONE, KSHD, and KBSHD flags on the shade field of the VIEW Bulk Data entry. When in doubt, it is safest to use the designation BOTH.

Miscellaneous View Factor Capabilities (VIEW or VIEW3D) 1. Shadowing calculations absorb considerable resources while calculating view factors. If the geometry is such that no shadowing can occur, it is recommended to turn off the calculation process by utilizing the SHADOW field on the RADCAV entry. A NO declaration will eliminate any shadowing calculations. The default value is YES. If a limited subset of surfaces in a problem are involved in shadowing, the most efficient calculation will result if the SHADE field of the VIEW Bulk Data entry is appropriately identified. 2. If a complete radiation enclosure is being analyzed, small inaccuracies in the individual view factors may lead to view factor sums that exceed 1.0 by a small (1 or 2 percent) amount. In this case, the view factors can be scaled to provide a sum of exactly 1.0 by utilizing the SCALE field on the RADCAV entry. 3. If an incomplete enclosure is being analyzed and it is desirable to complete the enclosure with a dummy or space element, this can be facilitated by using the ELEAMB field of the RADCAV entry. The ambient element must be an existing surface element of the problem, however, it is not used explicitly in the determination of the view factors. Subsequent to the view factor calculations, the view factor 1.0 – SUMMATION is assigned to the space element for each individual enclosure surface element. 4. View factor output can be controlled through the PRTPCH field of the RADCAV entry. 5. We define a global view factor as the view factor that exists between one group of surface elements and another group of surface elements. If global view factors are of interest, perhaps for some system level analysis, these can be determined while executing the VIEW module. The SET ij fields on the RADCAV entry reference the desired surface element sets.

Main Index

MSC.Nastran Thermal Analysis User’s Guide

APPENDIX

F

Radiation Enclosures

■ Method of Poljak ■ Method of Poljak - Radiation Exchange in Matrix Format ■ Transformation from Element Heat Flows to Grid Point Heat Flows ■ Example of Element/Grid Transformation ■ Two Element Example for Radiant Exchange ■ Resistive Network Approach to the Two Surface Problem ■ Radiation Enclosure Analysis

Main Index

420

6.1

Method of Poljak N

∑

A k q i, k =

Eq. 6-1

A j q o, j f j – k

j = 1

Eq. 6-2

Aj fj – k = Ak fk – j N

∑

q i, k =

Eq. 6-3

f k – j q o, j

j = 1 4

q o, k = ε k σT k + ( 1 – ε k )q i, k

Eq. 6-4

N 4

∑

q i, k =

f k – j ( ε k σT k + ( 1 – ε k )q i, k )

Eq. 6-5

j = 1 N

∑

N 4 f k – j ε k σT k

∑

f k – j ( 1 – ε k )q i, k

Eq. 6-6

N N   4   q i, k 1 – ∑ f k – j ( 1 – ε k ) = ∑ f k – j ε k σT k     j = 1 j = 1

Eq. 6-7

q i, k =

j = 1

+

j = 1

N    q i, k = ∑ 1 – ∑ f k – j ( 1 – ε k )    j = 1 j = 1 N

–1 4

f k – j ε k σT k

Eq. 6-8

where: A = elemental areas f = basic view factors N = number of element in enclosure q i, k = heat flux into surface element k q o, j = heat flux leaving surface element j Similarly for q o, k , then Nε T

qk

Main Index

= q i, k – q o, k

Eq. 6-9

CHAPTER F Radiation Enclosures

or Nε T

Qk

Main Index

= A k ( q i, k – q o, k )

Eq. 6-10

421

422

6.2

Method of Poljak - Radiation Exchange in Matrix Format IN

[ A ] { q }e OUT

{ q }e

OUT

= [ F ] { q }e

(compare to Eq. 6-1) IN

4

= σ [ ε ]{ ue } + [ I – ε ] { q }e

Eq. 6-11

(compare to Eq. 6-4)

Eq. 6-12

where: = diagonal matrix of element areas

\ A \ IN

{ q }e

= irradiation

[ F ] = matrix of exchange coefficients ( A i f ij ) OUT

{ q }e

= radiosity

σ = Stephan-Boltzmann constant = diagonal matrix of surface emissivities

\ ε \

= diagonal matrix of surface absorptivities

\ α \

Substituting Eq. 6-12 into Eq. 6-11 yields: IN

{ q }e OUT

{ q }e

= σ[(A – F(I – α))

–1

4

Fε ] { u } e

= σ[ε + (I – α)(A – F(I – α )) IN

OUT

{ Q }e = [ A ] ( { q }e – { q }e

–1

Eq. 6-13 4

Fε ] { u } e 4

) ≡ –[ Re ] { u }e

Eq. 6-14

Substituting Eq. 6-13 into Eq. 6-14 yields: [ R e ] = σ [ Aε – Aα ( A – F ( I – α ) ) [ R e ] = radiation exchange matrix. If ε = α and F SYM then [ R e ] . SYM

Main Index

–1

Fε ]

Eq. 6-15

CHAPTER F Radiation Enclosures

6.3

Transformation from Element Heat Flows to Grid Point Heat Flows MSC.Nastran solves the system equations for the grid point temperatures. The view factors, however, are calculated between geometric surface elements. Therefore, the introduction of radiation exchange into the system equations requires the transformation of the radiation exchange matrix from an element based representation to a grid point based representation. T

{ Q }g = [ G ] { Q }e

Eq. 6-16

where: [G]

T

= matrix of constant coefficients constructed from the fraction of the element area associated with the connecting grid points.

then: 4

{ u }e = [ G ] { ug + Ta }

4

Eq. 6-17

and T

[ R ]g = [ G ] [ R ]e [ G ] [ R ]g

SYM

if [ R ] e

Eq. 6-18 Eq. 6-19

SYM

{ Q }e = –σ [ R ]e [ G ] { ug + Ta } { Q }g = – σ [ R ]g { u g + Ta }

Main Index

4

4

Eq. 6-20 Eq. 6-21

423

424

6.4

Example of Element/Grid Transformation G3 G4

G7

G2 G6

1 G1

G8

2 G5

[ R ]e =

R 11 R 12 R 21 R 22

   4  R 11 R 12  u 1   Q1    = –σ   R 21 R 22  u 4   Q2  e  e  2 e Q   1 Q   2 Q   3    Q4    =  Q5     Q6     Q7     Q8   g

AF1 AF2 AF3 AF4 0 0 0 0

0 0 0 0 AF5 AF6 AF7 AF8

   Q1     Q2   e

Eq. 6-22

Eq. 6-23

Eq. 6-24

Comparing Eq. 6-24 to Eq. 6-16 then, [G] =

AF1 AF2 AF3 AF4 0 0 0 0 0 0 0 0 AF5 AF6 AF7 AF8

Eq. 6-25

Where AFi ( i = 1, 8 ) is the fractional area of the element associated with grid point Gi. T

[ R ]g = [ G ] [ R ]e [ G ]

Main Index

Eq. 6-26

CHAPTER F Radiation Enclosures

[ R ]g =

AF1 AF2 AF3 AF4 0 0 0 0

0 0 0 0 AF5 AF6 AF7 AF8

R 11 R 12 R 21 R 22

e

AF1 AF2 AF3 AF4 0 0 0 0 0 0 0 0 AF5 AF6 AF7 AF8

AF1R 11 AF1 AF1R 11 AF2 AF2R 11 AF1 AF2R 11 AF2 [ R ]g =

Main Index

AF1R 12 AF8

AF3R 11 AF1 AF3R 11 AF2 AF4R 11 AF1

AF8R 21 AF1

Eq. 6-27

Eq. 6-28

AF8R 22 AF8

425

426

6.5

Two Element Example for Radiant Exchange

A1 2 1

D

A2

[ R ] e = σ [ Aε – Aα ( A – F ( I – α ) )

[F] =

( A – F( I – α ) )

–1

=

=

A1 0

Fε ]

Eq. 6-29

[f]

A

Eq. 6-30

0

A 1 f 12

A 2 f 21

0

–

0 A2

–1

0 1 – ε1 0 1 – ε2

– A 1 f 12 ( 1 – ε 2 ) – A 2 f 21 ( 1 – ε 1 ) A2 A1

–1

–1

Eq. 6-31

For ease of illustration (and manipulation) let surfaces 1 and 2 be black bodies, then ε 1 = ε 2 = 1.0 then

( A – F( I – α ) )

[ R ]e = σ

A1 0 0 A2

–

=

A1 0

[ R ]e = σ

Main Index

–1

0 A2

1 ------ 0 A1

Eq. 6-32

1 0 -----A2

1 ------ 0 A1 1 0 -----A2

A1

– A 1 f 12

– A 2 f 21

A2

0

A 1 f 12

A 2 f 21

0

Eq. 6-33

Eq. 6-34

CHAPTER F Radiation Enclosures

{ Q }e = –σ

A1

– A 1 F 12

– A 2 F 21

A2

 4  u1   4   e  u2  e

Eq. 6-35

To further define a specific problem, let A 1 = A 2 = D = 1.0, T 1 = 1000 and T 2 = 0.0 . For this geometry then, f 12 = f 21 ≅ .20 . The resulting heat flows are: 4

Q 1 = – σ ( 1000 – .2 ( 0 ) ) = – σ ( 1000 ) 4

4

Q 2 = – σ ( – .2 ( 0 ) – .2 ( 1000 ) ) = .2σ ( 1000 )

4

Eq. 6-36

Note: Since the exchange matrix [ R ] is not conservative, we recognize that the MSC.Nastran e default condition assumes a third exchange surface representing a loss to space. Therefore, the loss to space is: Q 1 + Q 2 + Q 3 = 0.0 Q 3 = .8σ ( 1000 )

Main Index

4

Eq. 6-37

427

428

6.6

Resistive Network Approach to the Two Surface Problem E b1

J1 1 – ε1 --------------ε1 A1

1 -------------A 1 f 12

(surface resistance)

E b2

J2 1 – ε2 --------------ε2 A2

E b = σT

4

is the emissive power of a block body, and J is referred to as a radiosity node.

(surface (space resistance) resistance)

The heat flow then is; 4

4

σ ( T1 – T2 ) Q 1 – 2 = -------------------------------------------------------------1 – ε1 1 – ε2 1 --------------- + -------------- + --------------ε1 A1 ε2 A2 A 1 f 12

Eq. 6-38

Using the same example problem considered in the exchange matrix development, ε 1 = ε 2 = 1.0 A 1 = A 2 = 1.0 f 12 = .20 4

4

Q 1 – 2 = σA 1 f 12 ( T 1 – T 2 ) = – Q 2 – 1 = .2σ ( 1000 )

4

Eq. 6-39

in a matrix format,  4 A 1 f 12 – A 1 f 12  u 1  { Q }e = –σ   – A 1 f 12 A 1 f 12  u 4   2 Note: There is no exchange with the environment in these equations.

Main Index

Eq. 6-40

CHAPTER F Radiation Enclosures

6.7

Radiation Enclosure Analysis Radiation Matrix Formation - General The basic exchange relationship for a radiation enclosure is given in Eq. 6-41 { Q }n = [ R ]n { u + T a }

4

where: [ R ] n = σ [ Aε – Aα [ A – F ( I – α ) ] – 1 Fε ] n

( α = ε for radiation enclosure)

{ Q } n = Vector of net elemental heat flows from radiant exchange for cavity n [ R ] n = Radiation exchange matrix for cavity n { u } = Vector of grid point temperatures σ = Stefan-Boltzmann constant = Diagonal matrix of surface element areas

\ A \

= Identity matrix

\ I \

= Diagonal matrix of surface emissivities

\ ε \

= Diagonal matrix of surface absorptivities

\ α \

[ F ] n = Lower triangular matrix of exchange coefficients ( A j f ji ) for cavity n T a = Scale factor to correct for absolute temperature User supplied data: σ = Supplied on the PARAM,SIGMA Bulk Data entry T a = Supplied on the PARAM,TABS Bulk Data entry = Calculated from the input data for CHBDYi surface elements

\ A \ Main Index

Eq. 6-41

429

430

[ F ] = Supplied from the RADLST/RADMTX Bulk Data entries or calculated internally using the VIEW or VIEW3D modules = Supplied from the RADM Bulk Data entries

\ ε

, \

\ α \

Radiation Matrix Formation Using MSC.Nastran View Factors As described in “View Factor Calculation Methods” on page 409, MSC.Nastran can calculate diffuse grey geometric view factors (stored as A j ⋅ f ji ) to be used in radiation enclosure analysis. Those view factors are used in Eq. 6-41 to generate a total radiation exchange matrix. This matrix is symmetric and generally non-conservative in the sense that the column summations will not be equal to zero. This would imply that in an isothermal enclosure, there would exist net heat flow. This could be the result of an incomplete enclosure with resultant energy loss to space. If a complete enclosure is desired, an ambient element can be requested. The total view factor summations can also be scaled to exactly equal 1.0 for any summations exceeding 1.0. These options are discussed beginning on “View Factor Calculation Methods” on page 409. Control over the form of the radiation matrix can be effected by specifying the matrix type (MTXTYP) on the RADLST Bulk Data entry. Once these entries are generated by the VIEW or VIEW3D module, the matrix type can either remain as MTXTYP = 1, or it can be changed to a MTXTYP = 4. In this case, the radiation matrix will have its diagonal terms adjusted to provide a column sum of exactly zero. This is referred to as a conservative radiation matrix.

Radiation Matrix Formation Using User-Supplied Exchange Factors It may be desirable to input the radiation exchange matrix directly. In this case the user provides exchange factors with the RADLST/RADMTX Bulk Data entries. Exchange factors can be used to account for specular effects, transmissive surface character, and enclosure gas absorption. When used in this fashion, the input represents the following system: “SCRIPT-F”

RADMTX [ R ] = –σ * “SCRIPT-F”

( Off Diagonal Terms)

MTXTYP = 2 – Symmetric – Conservative RADLST MTXTYP = 3 – Unsymmetric – Conservative Main Index

CHAPTER F Radiation Enclosures

In this instance CONSERVATIVE means that the diagonal terms of [ R ] are adjusted to make the column summations equal to 0.0. Since all the radiation matrix values are user supplied, no control over the system can be effected by the view factor module. A user warning message is issued if Eq. 6-42 is satisfied.

∑ A i f ij > A i . ( 1.001 ) i

where: i = Column in view factor matrix j = Row in view factor matrix A = Surface element area f = View Factor

Main Index

calculated for each j

Eq. 6-42

431

432

Main Index

MSC.Nastran Thermal Analysis User’s Guide

APPENDIX

G

Radiation Exchange – Real Surface Approximation

■ Real Surface Approximation and Radiation Exchange

Main Index

434

7.1

Real Surface Approximation and Radiation Exchange In the most general sense, radiative surface properties can vary with absorption and emission angle, surface temperature, and spectral distribution of incident and emitted radiation. For an enclosure analysis, the many reflections and re-reflections tend to smooth out directional behavior. Additionally, it may be difficult if not impossible to acquire good directional, temperature, or wavelength dependent surface properties. Based on this, many radiation problems are approximated at the first level of analysis with surfaces which exhibit diffuse gray absorption and emission radiative character. MSC.Nastran allows for a second level of analysis which presumes that radiation surface interaction is diffuse, but admits emissivity and absorptivity to be functions of temperature and/or wavelength. The concept of a diffuse view factor is still applicable for this type of analysis since it is a simple geometric construct. The basic notion involved here is to consider the energy transport associated with separate wavelength intervals (wavebands). Numerically, this can be implemented with a method known as the band-energy approximation. Figure 7-1 illustrates the hemispherical spectral emissivity for tungsten. Figure 7-2 depicts a potential waveband approximation for the hemispherical spectral emissivity for input to MSC.Nastran.

Figure 7-1 Hemispherical Spectral Emissivity of Tungsten*

Main Index

CHAPTER G Radiation Exchange – Real Surface Approximation

Figure 7-2 Band Approximations to Hemispherical Spectral Emissivity of Tungsten* *From Siegel and Howell, Thermal Radiation Heat Transfer, Second Edition.

Radiation Exchange Relationship for Diffuse Spectral Surface Behavior { Qe } =

∑ { Q eλ } λ

{ Q eλ } in { q eλ }

=

in

 λ  [ A ]   qe   

out

 λ –  qe   

  

= σ[(A – F(I – α( λ) ))

–1

\ Fε ( λ ) ]

{ Ue }

fe

4

\ out { q eλ }

= σ[ε( λ ) + ( I – α(λ ))(A – F(I – α( λ) ))

–1

\ Fε ( λ ) ]

{ Ue }

fe

4

\ { fe } =

   FRAC 0 – λ U – FRAC 0 – λ U  2 e 1 e 

f e = Fraction of the total radiant output of a black body that is contained in the nth wavelength band where ∆λ = λ 2 – λ 1 . U e = Elemental temperatures FRAC 0 – λU = 15 e -----4 π Main Index

∑

m = 1, 2, …

e – mν ------------ { [ ( mν + 3 )mν + 6 ] mν + 6 }, ν ≥ 2 m4

435

436

FRAC 0 – λU = e

2

4

ν = PLANCK2 ---------------------------- , where PLANCK2 = λU e

[ R eλ ] n { Q eλ } n

6

8

 ν ν ν 15 3  1 ν ν 1 – ------ ν  --- – --- + ------ – ------------ + ------------------ – ------------------------ , ν < 2 4  3 8 60 5040 272160 13305600  π  o 25898 µm R  ( TYP )  o 14388 µm K 

=σ [ Aε ( λ ) – Aα ( λ ) ( A – F ( I – α ( λ ) ) ) – 1 Fε ( λ ) ] n

= λ –[ Re ] n

\ { Ue }

fe

4

\ net { Q eλ }

=

λ net

–[ Re ]

{ Ue }

4

where, n max NET [ R eλ ]

=

∑ n = 1

λ [ Re ]n

\ fe \ n

Key Points regarding Spectral Radiation Band Analysis within MSC.Nastran 1. Only one RADBND (wavelength break point) entry can be specified with any input file. This does not mean that all surfaces of all cavities must display spectral surface behavior. For any surfaces which are to remain as grey or blackbody, each waveband emissivity value associated with its RADM entry can be given the same emissivity value resulting in a constant emissivity over all wavelengths. Recall that radiation material surface properties are associated with the CHBDYi surface element description, so every element in every cavity can potentially exhibit its own radiative character. 2. Temperature and/or wavelength dependent radiative surface properties can be applied to radiation enclosure analyses as well as the radiation boundary condition. 3. Within each waveband the emissivity must be a constant value. Each discontinuity (vertical jump) in the emissivity vs. wavelength piecewise linear curve must be input as a waveband of zero width. 4. The necessary inputs for spectral exchange in MSC.Nastran are given in “Thermal Capabilities” on page 5. Main Index

CHAPTER G Radiation Exchange – Real Surface Approximation

Input Example - Real Surface Behavior,

ε(λ)

ε( λ) .90 .40 λ2 λ

λ1

0

∞

RADBND

5

25898.

2.0

2.0

9.0

RADM

1

1.0

.40

.90

0.0

ε( λ) .90

λ1

0

λ2

RADBND

3

25898.

2.0

RADM

1

1.0

.90

λ

∞

9.0

ε(λ) .90 .40

0

Main Index

λ1

λ2

RADBND

4

25898.

2.0

2.0

RADM

1

1.0

.90

.40

9.0

437

438

Main Index

439

I

N

D

E

X

MSC.Nastran Thermal Analysis User’s Guide

I N D E X MSC.Nastran Thermal Analysis User’s Guide

Symbols $ 38 $ Bulk Data entry specification of 279, 408

A Absolute temperature 21 Absorptivity 138, 204, 228, 429 Ambient element 148, 150 Ambient nodes 88 Ambient temperature 166, 228 ANALYSIS 61, 70 Axisymmetric elements 127 Axisymmetric modeling 127 Axisymmetric surface elements 127

B Band-energy approximation 434 BDYOR 277, 278 BDYOR Bulk Data entry specification of 280 BEGIN BULK 35, 38 BFGS 66 Bisection of loads 60 Blackbody 138 Boundary conditions 16, 88 CONV 16 CONVM 16 RADBC 16 RADSET 16 Bulk Data 277, 278 Bulk Data entries 38, 276

C

Main Index

Case Control 13, 19, 84, 114, 166, 167, 172, 185, 277 Case Control commands 35 Case Control Section 12 CBAR 7, 277

CBEAM 7, 277 CBEND 7, 277 CDAMP1 Bulk Data entry specification of 281 CDAMP2 Bulk Data entry specification of 282 CDAMP3 Bulk Data entry specification of 283 CDAMP4 Bulk Data entry specification of 284 CDAMP5 Bulk Data entry specification of 285 CDAMPi 8 CELAS1 Bulk Data entry specification of 286 CELAS2 Bulk Data entry specification of 287 CELAS3 Bulk Data entry specification of 288 CELAS4 Bulk Data entry specification of 289 CELASi 8, 29, 193 CEND 35 CEND Executive Control statement specification of 231 CHBDY 88, 100, 105, 111, 204 CHBDYE 8, 17, 19, 127, 277, 278 CHBDYE Bulk Data entry specification of 290 CHBDYG 8, 15, 24, 26, 127, 144, 277, 278 AREA3 8 AREA4 8 AREA6 8 AREA8 8 REV 8 CHBDYG Bulk Data entry specification of 293 CHBDYi 21, 22, 23, 25, 26, 142, 193, 200, 204, 412

Index

440 INDEX

CHBDYP 8, 20, 108, 277, 278 ELCYL 8 FTUBE 8 LINE 8 POINT 8 TUBE 8 CHBDYP Bulk Data entry specification of 296 CHEX1 277 CHEX2 277 CHEXA 7, 163, 166, 277 Comment 38, 408 Comment Bulk Data entry specification of 279 Conduction matrix 59 Conductivity 105, 158 CONROD 7, 277 Control node 112, 116, 158, 177, 204 Control node for forced convection 20 Control node for free convection 17 Control node for radiation boundary condition 21 CONV 16, 17, 88, 278 CONV Bulk Data entry specification of 301 Convection 166 Convergence criteria 62 energy error 63 load error 63 temperature error 62 CONVM 16, 19, 158, 278 CONVM Bulk Data entry specification of 303 Correction vector 59 Courant number 20, 214 CPENTA 7, 277 CQUAD4 7, 17, 144, 277 CQUAD8 7, 277 CROD 7, 277 CTETRA 7, 277 CTRIA3 7, 277 CTRIA6 7, 277 CTRIAX6 7, 127, 277 CTUBE 7, 277 Cutoff wavelength 139 Index

D

Main Index

DELAY 13, 15, 19, 167, 277 DELAY Bulk Data entry specification of 304 Density 10, 228

DIAG 50 66, 185 DIAG 51 66, 185 DIAG Executive Control statement specification of 232 Directional solar heat flux 133 DLOAD 12, 13, 15, 19, 166, 167, 176, 277 DLOAD Bulk Data entry specification of 305 DMI Bulk Data entry specification of 306 DMIG Bulk Data entry specification of 310 DPHASE Bulk Data entry specification of 313 Dynamic viscosity 10, 158, 228

E ECHO Executive Control statement specification of 236 Element connectivity 84 Elements 7 conduction elements 7 special elements 8 surface elements 7 Emissivity 105, 106, 142, 228, 429 Enclosure radiation 24, 148 Enclosure radiation exchange 22 ENDDATA 38 ENTHALPY 185 Enthalpy 185, 228 Exchange factors 430 Execution of MSC.Nastran 33 Executive Control statements 35

F File Management statements 35 Files generated 39 .dat 39 .DBALL 39 .f04 39 .f06 39 .log 39 .MASTER 39 .pch 39 .plt 39 .USROBJ 39 .USRSOU 39 .xdb 39 miscellaneous scratch files 39

INDEX

Film node 95, 100, 111, 112, 158 Film node for free convection 17 Finite difference view factor 25 Fluid elements 158 Flux load 130 Forced convection 16, 19, 158, 214 Free and forced convection 278 Free convection 16, 17, 18, 88, 95, 177, 181 Free convection exponent 111 Free convection film nodes 122 Free convection forms 116, 122 Free convection heat transfer coefficient 10, 112, 228

G Gaussian integration 142, 410 Gaussian integration view factor 26 Grashof's number 88, 228 GRID 277, 278 Grid point 84

H Heat capacitance 158 Heat transfer coefficient 158

I IC 30, 71, 277 ID Executive Control statement specification of 237 INCLUDE 22 INCLUDE Bulk Data entry specification of 314 Initial conditions 30, 163 steady state analysis 30 transient analysis 30 Input data 34 Input File structure of 33 Internal heat generation 114, 172 Internal volumetric heat generation 112 Iteration scheme 59

J JCL 38

Main Index

441

K Kinematic viscosity 88, 228

L Latent heat 10, 185 Line search method 60 LOAD 12, 15, 277 Load 84, 114 LOAD Bulk Data entry specification of 315 Load set identification (SID) 12 Loads 111, 116 Lower temperature limit for phase change 10 Lumped heat capacitance 193 Lumped thermal capacitance 8

M MAT4 10, 11, 17, 18, 20, 90, 91, 164, 174, 277, 278 MAT4 Bulk Data entry specification of 316 MAT4/MATT4 114, 158 MAT4/MATT4/TABLEM2 97 MAT5 10, 277, 278 MAT5 Bulk Data entry specification of 318 Material properties 84 MATT4 10, 11, 17, 18, 20, 277, 278 MATT4 Bulk Data entry specification of 319 MATT4/TABLEMi 95 MATT5 10, 277, 278 MATT5 Bulk Data entry specification of 320 MPC 29, 100, 102, 210, 277 MPC Bulk Data entry specification of 321 MPCADD Bulk Data entry specification of 322 MSC.Aries 40 MSC.Nastran input file, structure of 33 MSC.Nastran Quick Reference Guide 84 MSC.XL 40 Multiple loads 176, 200

Index

442 INDEX

N NASPLT 40 NASTRAN definition(s) 35 NDAMP 187, 214 Newton's method 59 NLPARM 35, 36, 60, 62, 64, 66, 85, 92, 277 NLPARM Bulk Data entry specification of 323 NOLIN 210 NOLIN1 13, 277 NOLIN1 Bulk Data entry specification of 329 NOLIN2 13, 277 NOLIN2 Bulk Data entry specification of 331 NOLIN3 14, 210, 277 NOLIN3 Bulk Data entry specification of 333 NOLIN4 14, 277 NOLIN4 Bulk Data entry specification of 335 NONLINEAR 13, 277 Nu 215 Numerical damping 185, 187, 214 Nusselt's number 88, 228

O operation commands 47 Output requests ENTHALPY 37 FLUX 36, 37 HDOT 37 OLOAD 36, 37 SORT1 37 SORT2 37 SPCF 36, 37 THERMAL 36, 37

P PARAM Bulk Data entry specification of 337 PARAM,POST 40 PARAM,SIGMA 429 PARAM,TABS 429 Parameter 21 SIGMA 21 TABS 21 PBAR 277 PBEAM 277

Index

Main Index

PBEND 277 pch 39, 40 PCONV 17, 18, 90, 91, 278 PCONV Bulk Data entry specification of 338 PCONVM 278 PCONVM Bulk Data entry specification of 340 PDAMP Bulk Data entry specification of 342 PDAMP5 Bulk Data entry specification of 343 PELAS Bulk Data entry specification of 344 Phase change 185, 187 PHBDY 277, 278 PHBDY Bulk Data entry specification of 345 Planck's second constant 25, 228 Plotting 41 TEKPLT 41 X-Y plotting 47 plt 40 Pr 214 Prandtl's number 20, 88, 228 PROD 277 PSHELL 277 PSOLID 277 PTUBE 277 Punch file 147, 150, 152, 155, 157

Q QBDY1 13, 68, 277 QBDY1 Bulk Data entry specification of 347 QBDY2 13, 68, 277 QBDY2 Bulk Data entry specification of 348 QBDY3 13, 68, 277 QBDY3 Bulk Data entry specification of 349 QBDYi 35 QHBDY 13, 35, 68, 277 QHBDY Bulk Data entry specification of 350 Quasi-Newton 60 Quasi-Newton (BFGS) updates 60 QVECT 11, 13, 15, 22, 35, 68, 133, 138, 200, 277 QVECT Bulk Data entry specification of 352

INDEX

QVOL 13, 35, 68, 111, 114, 172, 174, 277 QVOL Bul Data entry specification of 355

R RADBC 11, 16, 21, 278 RADBC Bulk Data entry specification of 356 RADBND 25, 138, 140, 277, 278, 436 RADBND Bulk Data entry specification of 357 RADCAV 25, 26, 142, 148, 153, 278, 418 Radiation 278 Radiation ambient element 148 Radiation boundary condition 105, 106, 130, 133, 200, 278 Radiation cavities 153, 412 Radiation cavity/enclosure 142 Radiation exchange 142 Radiation exchange with space 16 Radiation exchange within an enclosure 16 Radiation matrix 430 Radiation to space 21, 130 RADLST 22, 23, 24, 278 RADLST Bulk Data entry specification of 360 RADLST/RADMTX 22, 25, 142, 430 RADLST/RADMTX punch files 148 RADM 10, 15, 21, 22, 24, 25, 133, 138, 142, 277, 278 RADM Bulk Data entry specification of 362 RADM/RADBND 21 RADM/RADMT 21 RADM/RADMT/RADBND 23, 25, 26 RADMT 10, 15, 25, 277, 278 RADMT Bulk Data entry specification of 363 RADMTX 23, 24, 278 RADMTX Bulk Data entry specification of 364 RADSET 11, 16, 23, 24, 25, 26, 27, 142, 153, 278 RADSET Bulk Data entry specification of 365 RADVAC Bulk Data entry specification of 358 Re 214 Reference enthalpy 10 Residual vector 59 Main Index

443

Restart LOOPID 36 SUBID 36 Restarts 37 LOOPID 37 SLOOPID 37 STIME 37 Reynolds' number 20, 228

S SCR 39 SCR (scratch) command 39 Self-shadowing 411 SET1 Bulk Data entry specification of 366 Shadowing 142, 144 SID 172 SIGMA 21, 23, 26, 108 SLOAD 13, 193, 277 SLOAD Bulk Data entry specification of 367 SOL 153 35 SOL 159 36 SOL Executive Control statement specification of 238 Solar flux 200 Solar load 130, 138 SPC 28, 64, 85, 163, 166, 193, 277, 278 SPC Bulk Data entry specification of 368 SPC1 277 SPC1 Bulk Data entry specification of 369 SPCADD Bulk Data entry specification of 370 SPCD 277 SPCD Bulk Data entry specification of 371 SPCs 85 Specific heat 10, 88, 158, 228 Spectral emissivity 434 Spectral radiation 138 Spectral radiation exchange 25 SPOINT 176, 277 SPOINT Bulk Data entry specification of 373 Steady State 15

Index

444 INDEX

Steady state analysis 12, 30, 61 Bulk Data 30 Case Control 30 convergence criteria 62 equilibrium equation 61 iteration control 64 iteration output 66 residual vector 61 SOL 153 61 Steady state heat transfer 35 LOAD 35 MPC 36 output requests 36 restarts 36 SORT1 36 SORT2 36 SPC 36 TEMP(INIT) 36 Stefan-Boltzmann 429 Stefan-Boltzmann constant 21, 228 Streamwise-upwind Petrov-Galerkin Element (SUPG) 19 Structural plotting 41 parameter definition commands 42 plot set selection 41 thermal contour plots 44 undeformed structural plots 44 SUPAX Bulk Data entry specification of 374 SUPG element 19 Surface elements 88, 144

T

Index

Main Index

TABLED1 13, 176, 277 TABLED1 Bulk Data entry specification of 375 TABLED2 19, 277 TABLED2 Bulk Data entry specification of 377 TABLED3 277 TABLED3 Bulk Data entry specification of 379 TABLED4 277 TABLED4 Bulk Data entry specification of 381 TABLEDi 167 TABLEM 122 TABLEM1 277, 278 TABLEM1 Bulk Data entry specification of 382 TABLEM2 15, 17, 18, 24, 277, 278

TABLEM2 Bulk Data entry specification of 384 TABLEM3 277, 278 TABLEM3 Bulk Data entry specification of 386 TABLEM4 277, 278 TABLEM4 Bulk Data entry specification of 388 TABLEMi 10, 11, 25 TABS 21, 23, 26, 108 Tangential matrix update strategy 60 Tangential stiffness matrix 59 TEMP 30, 62, 71, 277 TEMP Bulk Data entry specification of 389 TEMP(ESTI) 277 TEMP(INIT) 30, 62 TEMPAX Bulk Data entry specification of 391 TEMPBC 19, 28, 166, 176, 193, 277 TEMPD 30, 62, 71, 277 TEMPD Bulk Data entry specification of 392 Temperature boundary conditions and constraints 28 CELASi 29 MPC 29 SPC 28 TEMPBC 28 Temperature range for phase change 10 TEMPP1 277 TEMPP2 277 TEMPRB 277 TF 277 TF Bulk Data entry specification of 394 TFL 277 Thermal conductivity 10, 88, 228 Thermal loads 12, 13 NOLIN1 13 NOLIN2 13 NOLIN3 14 NOLIN4 14 QBDY1 13 QBDY2 13 QBDY3 13 QHBDY 13 QVECT 13 QVOL 13 SLOAD 13 Thermostat control 210 Third surface shadowing 412

INDEX

Third-body shadowing 153 TIME Executive Control statement specification of 242 Time-varying loads 172 TLOAD 176 TLOAD1 13, 15, 176, 277 TLOAD1 Bulk Data entry specification of 395 TLOAD2 277 TLOAD2 Bulk Data entry specification of 397 TLOADi 12, 176 Transient 15 Transient analysis 12, 30, 69 automatic time stepping 72 boundary temperatures 79 bulk data 30 case control 30 convergence criteria 79 equilibrium equation 69 fixed time step 79 initial temperatures 79 integration and iteration control 73 iteration equation 70 iteration output 75 Newmark's method 70 Newmark's method with adaptive time stepping 69 numerical stability 79 PARAM,NDAMP 70 residual vector 70 SOL 159 70 tangential stiffness matrix 70 time step size 78 Transient heat transfer 36 DLOAD 36 DMIG 36 IC 37 MPC 36 NONLINEAR 37 output requests 37 SPC 36 TEMP 37 TEMPBC (of TRAN type) 37 TEMPD 37 TF 36 TSTEPNL 36 Transient solution 163 Transient temperature specification 163 TSTEPNL 60, 71, 73, 164, 277 TSTEPNL Bulk Data entry specification of 400 Main Index

445

U Units 185, 417

V VIEW 25, 26, 142, 153, 278, 410, 412, 413, 415, 418, 430 VIEW Bulk Data entry specification of 404 View Factor 411 View factor 25, 142, 148, 153, 228, 278, 418, 430 View factor calculation 26 VIEW3D 26, 142, 410, 412, 417, 418, 430 VIEW3D Bulk Data entry specification of 406 Volume coefficient of expansion 89, 228 Volumetric internal heat generation 10

W Waveband 434, 436 Wavelength 138 Wavelength break points 25

X X-Y plotting 47, 48, 49 curve request 51 curve type 50 operation 50 operation command 47 parameter definition commands 47 subcase list 51 X-Y plots for SORT1 output 54 X-Y plotter terminology 47

Index