Md Nastran R3 Release Guide

MD Nastran R3 Release Guide

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Corporate MSC.Software Corporation 2 MacArthur Place Santa Ana, CA 92707 USA Telephone: (800) 345-2078 Fax: (714) 784-4056

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Worldwide Web www.mscsoftware.com

Disclaimer 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 © 2008 MSC.Software Corporation. Printed in U.S.A. All Rights Reserved. This notice shall be marked on any reproduction of this documentation, in whole or in part. Any reproduction or distribution of this document, in whole or in part, without the prior written consent of MSC.Software Corporation is prohibited. This software may contain certain third-party software that is protected by copyright and licensed from MSC.Software suppliers. MSC, MD, Dytran, Marc, MSC Nastran, MD Nastran, Patran, MD Patran, the MSC.Software corporate logo, and Simulating Reality are trademarks or registered trademarks of the MSC.Software Corporation in the United States and/or other countries. NASTRAN is a registered trademark of NASA. PAMCRASH is a trademark or registered trademark of ESI Group. SAMCEF is a trademark or registered trademark of Samtech SA. LS-DYNA is a trademark or registered trademark of Livermore Software Technology Corporation. ANSYS is a registered trademark of SAS IP, Inc., a wholly owned subsidiary of ANSYS Inc. ABAQUS is a registered trademark of ABAQUS Inc. All other brand names, product names or trademarks belong to their respective owners. PCGLSS 6.0, Copyright © 1992-2005, Computational Applications and System Integration Inc. All rights reserved. PCGLSS 6.0 is licensed from Computational Applications and System Integration Inc. oÉîáëáçå=MK=^éêáä=OQI=OMMU jak^WoPWwWwWwWa`Jobi

Main Index

Contents MD Nastran R3 Release Guide jp`=k~ëíê~å=OMMT= oÉäÉ~ëÉ=dìáÇÉ

Table of Contents

Preface to the MD Nastran R3 Release Guide A Word About Prerelease Features List of Books

1

xiv

xv

xvi

Technical Support

xvii

Internet Resources

xix

Overview of MD Nastran R3 Overview 2 Local Adaptive Meshing 2 Advanced Integrated Nonlinear (SOL 400) 2 Contact 3 Explicit Nonlinear (SOL 700) 4 MD Adams Integration 4 Optimization 4 Aeroelasticity 5 SCA User Defined Services 5 Symbolic Subsitution 5 List of Errors Resolved 6 List of Example Problems for the MD Nastran R3 Release 6 List of MD Nastran Documents Released with MD Nastran R3

2

Adaptive Meshing Local Adaptive Mesh Refinement 10 Introduction 10 The Adaptive Mesh Refinement Loop 14 Refinement by Regular Subdivision 15 Location of New Grid Points 20 Hanging Nodes and Multipoint Constraints on Hanging Nodes Selection of Elements to Refine 27 Refinement Criteria 28 Propagation of Refinement 37

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7

23

iv MD Nastran R3 Release Guide ==

Transference of Analysis Data Between Unrefined and Refined Meshes 42 Detection of Geometric Features and Material and Superelement Interfaces 49 User Interface 55 Output 68 Guidelines and Limitations 71

3

Advanced Integrated Nonlinear and Contact SOL 400 Performance Enhancements

76

SOL 400 Advanced Heat Transfer 77 Outline of New SOL 400 Heat Transfer Capabilities BCONTACT=ALLBODY Introduction 95 Benefits 95 Input 95 Output 95 Limitation 95 Example 95

77

95

Linear Perturbation and Brake Squeal Analyses in SOL 400 Introduction 98 Input 98 Output 99 Guidelines and Limitations 100 Examples - Examples of Case Control Approaches 100 Examples of Linear Perturbation and Brake Squeal Analyses SOL 400 Materials and Elements 109 Introduction 109 Benefits 110 Advanced Integrated Nonlinear Analysis Input 111 Output 113 Guidelines and Limitations 113

111

Enhancements to Connector Elements 118 Introduction 118 CBUSH Enhancements in SOL 400 118 Inputs 119 Outputs 119 Example 119 Nonlinear CWELD and CFAST Elements in SOL 400

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120

98

102

Contents v

Inputs 121 Outputs 121 Supported Output Requests Limitations 122 Example 122

122

Adaptive Time Stepping Scheme Enhancements for Quasi-Static Analysis 128 NLADAPT Bulk Data Entry 128 Results Output 131 Contact and Adaptive Time Stepping Enhancements for Transient Dynamic Analysis 133 Enhancements for Dynamic Contact 133 Enhancements for Dynamic Time-Stepping 136 Progressive Failure Analysis with a Micromechanical Module Introduction 138 Definition of a Composite 138 Output 140

138

3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge 141 Introduction 141 Benefits 142 Moment Carrying Glue 142 Input 142 Limitations 142 Examples 143 Improved Flexibility in Contact (for Shell only in MD Nastran R3) 145 Input 146 Examples 147 In-Plane Shell Edge-to-Edge Glue 147 Input 147 Limitations 147 Examples 147 Beam-to-Beam Contact 151 Input 151 Examples 152 General Shell Edge(-to-Edge and -to-Surface) Contact 155 Input 155 Limitations 155 Examples 155 Optimize Contact Constraints 157 Input 158

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vi MD Nastran R3 Release Guide ==

Limitations 158 Examples 158 GLUE Control 158 Input 158 Limitations 159 Breaking Glue 159 Input 159 Limitations 160 Miscellaneous Items

160

Explicit Nonlinear - SOL 700 162 Introduction 162 New Capabilities in Explicit Nonlinear - SOL 700 162 Advanced Fluid Structure Interaction (FSI) 162 Parallel FSI 165 Advanced Composites 166 Smooth Particle Hydrodynamics (SPH) Method 167 Sheet Metal Forming (SMF) with Spring-back 167 Integrated Fan Blade Out (FBO) and Rotor Dynamics (RD) simulation Analysis Chaining 172 New Materials and Elements 174 Support for FAA Hybrid II and III Dummy Models 174 New SOL 700 Bulk Data Entries and Parameters 175 Arc-Length Methods (Pre-release) Introduction 183 Benefits 183 Method and Theory 183 Inputs 184 Outputs 184 Limitations 184

183

Analysis Chaining 189 Introduction 189 Input 189 Analysis Type 189 Examples 190 Legal Chaining Type 193 Limitations 194

4

Implicit Nonlinear Implicit Nonlinear - SOL 600 196 Support of Large Grid and Element IDs

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196

169

Contents vii

Multiple RFORCE Entries in the Same Subcase 196 BCONTACT Case Control Command Clarification 197 Generalized Alpha Dynamic Integration Method 202 MATVP Material Property Entry 202 MATSMA Shape Memory Alloy Material Property Entry 203 Nonlinear Elastic Orthotropic Materials 203 Composite Integration Methods to Reduce Computer Time 203 New SOL 600 Bulk Data Entries and Parameters 205

5

NVH and Acoustics NVH Enhancements 208 ACMS with Acoustic External Superelement Creation 208 Multiple RANDOM Looping 208 Sparse OUTPUT4 Format for External Superelement Creation Binary op2 and op4 Compatibility Robustness 208 Merged Superelement Results 209

208

Enhancements to the Frequency Response Function (FRF) and FRF Based Assembly (FBA) Feature 210 Introduction 210 Names for FRF Components 210 Interchangeable COMPID/COMPNAME Fields in All Bulk Data Entries Meant for FBA Use 210 User Load Specification in the FBA Process 210 Responses to Unit Loads and User Specified Loads 210 Connection of Scalar Points and Explicit Connection of Coincident Grid Points 212 Flexible Connection of Degrees-of-Freedom 212 Release of Connection Degrees-of-Freedom 212 Grounding of Connection Degrees-of-Freedom 212 Handling of Displacement (or Local) Coordinate Systems at Connection Grid Points of FRF Components in the FBA Process 213 FRFs for PLOTEL Grid Points 213 Summary of the Enhancements 213 Enhancements to ADAMSMNF Case Control Command

6

Numerical Methods and High Performance Computing Linear and Nonlinear Contact Analysis Introduction 216 Benefits 216

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214

216

viii MD Nastran R3 Release Guide ==

Inputs 216 Guidelines and Limitations 216 Demonstration Example 217 High Performance Iterative Solver Now Available for Nonlinear Transient Analysis 219 Introduction 219 Benefits 219 Inputs 219 Outputs 219 Guidelines and Limitations 219 Matrix Based Iterative Solver Now Available for Nonlinear Static Analysis 221 Introduction 221 Benefits 221 Method and Theory 221 Inputs 222 Outputs 222 Guidelines and Limitations 222 Demonstration Examples 222 Factor Matrix Caching for Lanczos and Nonlinear Transient Analysis with NLAUTO 225 Introduction 225 Benefits 225 Method and Theory 225 Inputs 225 Outputs 225 Guidelines and Limitations 226 Demonstration Examples 226 New TAUCS Indefinite Solver Improves Lanczos Performance Introduction 228 Benefits 228 Method and Theory 228 Inputs 228 Outputs 228 Guidelines and Limitations 228 Demonstration Examples 229

228

Shared Memory Parallel (SMP) Scalability Improvements for Static Analysis 230 Introduction 230 Benefits 230

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Contents ix

Method and Theory 230 Inputs 230 Outputs 230 Guidance and Limitations 230 Demonstration Examples 231 New MAXRATIO Information Output Introduction 232 Benefits 232 Method and Theory 232 Inputs 232 Outputs 232 Guidelines and Limitations 233 Demonstration Example 233 Example Input Data 233 Example Output 235

232

New SPARSESOLVER MDTSTATS Information Output Introduction 236 Benefits 236 Method and Theory 236 Inputs 236 Outputs 236 Guidelines and Limitations 237 Demonstration Example 237 Example Input Data 237 Example Output 239

7

Upward Compatibility TEMPERATURE Case Control Command Improvements in Fluid Eigenvalue Analysis FLUID GRID Points and Partitioning

242 244

245

Distributed Memory Parallel (DMP) Diagnostic Messages System Information Message (SIM) 6916

8

Optimization Enhancements in DRESP3 Introduction 250 Benefits 250

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236

250

248

247

x MD Nastran R3 Release Guide ==

User Inputs 250 Output 255 Guidelines and Limitations Examples 257

255

Topometry Optimization 260 Introduction 260 Benefits 260 Input 261 Output 263 Guidelines and Limitations 263 Example 1 - Three-bar Truss (tomex1.dat) Input 265 Output 267 Example 2 – Car Model Topometry Design

263

267

Topography (Bead or Stamp) Optimization Introduction 269 Benefits 269 Input 269 Outputs 272 Guidelines and Limitations 273 Example 3 – A Square (togex1.dat) 273 Input 274 Output 274

269

Permanent Glued Contact Modeling in SOL 200 Input 275 Example 4 - A Solid Beam (topoug5.dat) 275 Input 276 Output 277 Randomization of an Input Data File Introduction 278 Benefits 278 Input 278 Output 279 Guidelines and Limitations 279 Random Elimination of Element Types Introduction 280 Benefits 280 Input 280 Output 280 Guidelines and Limitations 280

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278

280

275

Contents xi

Enhancements in SOL 200 Optimization Introduction 281 Benefits 281 Input 281 Example 282 Output 284 Guidelines 286 Limitations 286

281

Optimization of Nonlinear Structural Responses (Pre-release) Introduction 290 Benefits 291 Theory 291 Implementation 294 Input 295 Outputs 298 Examples 302 References 307

9

Aeroelasticity and Rotor Dynamic Improvements A New Aerodynamic Interpolation Method Introduction 310 Inputs 310 Outputs 310 Guidelines and Limitations 310 Examples 311 External Spline Server 313 Introduction 313 Inputs 313 API Changes 313 Sparse Matrix Format 314 Upgrading an Existing Spline Server Blade Vibration Analysis

10

SCA User Services User Defined Services Introduction 318 Example 318 Requirements 320

Main Index

315

318

314

310

290

xii MD Nastran R3 Release Guide ==

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The 2005 New Template

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å Preface to the MD Nastran R3 Release Guide å A Word About Prerelease Features å List of Books å Technical Support å Internet Resources

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xiv MD Nastran R3 Release Guide Preface to the MD Nastran R3 Release Guide

Preface to the MD Nastran R3 Release Guide This Release Guide contains descriptions for both the MD Nastran R3 and MD Nastran R2.1 versions, and supersedes the MD Nastran R2.1 Release Guide.

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Preface xv

A Word About Prerelease Features MD Nastran R2.1 contains a number of features that have been labeled as “prerelease.” A prerelease feature or enhancement is defined as a feature or enhancement that has not yet completed MSC’s exhaustive verification and validation (V and V) testing and qualification process. Therefore, prerelease features are to be used at the client’s own risk.

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xvi MD Nastran R3 Release Guide List of Books

List of Books Below is a list of some of the MD Nastran and MSC Nastran documents. You may order any of these documents from the MSC.Software BooksMart site at http://store.mscsoftware.com/.

fåëí~ää~íáçå=~åÇ=oÉäÉ~ëÉ=dìáÇÉë ç Installation and Operations Guide ç Release Guide

oÉÑÉêÉåÅÉ=_ççâë ç Quick Reference Guide ç DMAP Programmer’s Guide ç Reference Manual

rëÉêÛë=dìáÇÉë ç Getting Started ç Linear Static Analysis ç Basic Dynamic Analysis ç Advanced Dynamic Analysis ç Design Sensitivity and Optimization ç Thermal Analysis ç Numerical Methods ç Aeroelastic Analysis ç Superelement ç User Modifiable ç Toolkit ç Implicit Nonlinear (SOL 600) ç Explicit Nonlinear (SOL 700) ç MD User’s Guide - Application Examples ç Topology Optimization ç SCA Service Guide ç User Defined Services

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Preface xvii

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.

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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, training courses, and documentation updates at the MSC.Software Training, Technical Support, and Documentation web page.

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United States Telephone: Fax:

(800) 732-7284 (714) 784-4343

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(44) (1276) 60 19 00 (44) (1276) 69 11 11

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Madrid, Spain Telephone: Fax:

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(34) (91) 5560919 (34) (91) 5567280

xviii MD Nastran R3 Release Guide Technical Support

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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.

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qê~áåáåÖ 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 markets. 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.

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Preface xix

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.

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xx MD Nastran R3 Release Guide Internet Resources

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Chapter 1: Overview of MD Nastran R3

1

Overview of MD Nastran R3 

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MD Nastran R3 Release Guide

Overview

2 MD Nastran R3 Release Guide Overview

Overview MSC Software is proud to release MD Nastran R3. This release of MD Nastran significantly advances the multidiscipline capabilities available to you. The following sections briefly describe some of the major and minor enhancements to MD Nastran R3.

Local Adaptive Meshing MD Nastran R3 introduces adaptive remeshing in linear statics (SOL 101) and Advanced Nonlinear (SOL 400). This enhancement allows you to specify a region of the mesh to remesh during the simulation based on various criteria. If any of the activated remeshing criteria is met, the element, and possibly some neighboring elements, will be subdivided. The results from the original mesh will be mapped on to the new mesh and the analysis will continue. The three basic remeshing criteria are: • Error Estimate – this criterion uses an estimation of the stress error in an element and compares it

to a maximum allowable value. • Regional – in this case, a sphere or cube is defined and any element that is within the sphere or

cube is remeshed. • Contact Status – this criterion monitors the contact status of an element. If contact is detected,

the element will be subdivided. Remeshing can provide you with an automated way to refine your mesh in areas of stress concentration and contact. The result is much more accurate results without the need for multiple models of various refinements. More information on the local adaptive meshing capabilities can be found in Adaptive Meshing (Ch. 2).

Advanced Integrated Nonlinear (SOL 400) MD Nastran’s Advanced Integrated Nonlinear module is designed as the multidiscipline solution sequence. Unlike the traditional MSC Nastran solution sequences, this module can host multiple analyses to perform a full event simulation, such as brake squeal analysis or engine thermal cycling. The basic solver requirements for these event simulations are the ability to chain individual analyses together where the results of one analysis are used as the initial conditions for a subsequent analysis. Examples of this are thermal analyses and structural analyses and the ability to perform perturbation analyses at any point during the event to extract required information such as frequency response. With this release, SOL 400’s analysis chaining capabilities include the following types of analyses:

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• Linear static analysis

(New)

• Nonlinear static analysis

(Released in R2)

• Nonlinear transient analysis

(Released in R2)

• Normal modes analysis

(New)

CHAPTER 1 3 Overview of MD Nastran R3

• Direct complex eigenvalue analysis

(New)

• Modal complex eigenvalue analysis

(New)

• Brake Squeal Analysis (BSQUEAL Command)

(New)

• Steady state heat transfer analysis

(New)

• Transient heat transfer analysis

(New)

In addition to extending the analysis capabilities of MD Nastran, there has also been a focus to enhance the performance. With MD Nastran R3, new adaptive time-stepping routines have been implemented in the nonlinear solutions. These routines both increase the robustness of the solution and also reduce the number of steps taken for a complete step. Numerical Methods has always been a focus for MD Nastran. In the first two releases, new numerical solvers were integrated. The MD Nastran R3 release continues this focus by making the CASI solver available for nonlinear transient analyses and implementing a new matrix-based solver for unsymmetric problems. Examples are, heat transfer with advection and structural analysis with friction, damping, or follower forces. For structural analyses with composites, a new optional module is available in SOL 400 for progressive failure analysis. You can now calculate micro-mechanical damage for both the matrix and fiber directly from MD Nastran. More detailed information on these enhancements to SOL 400 can be found in Advanced Integrated Nonlinear and Contact (Ch. 3).

Contact The general 3D contact capabilities released in MD Nastran R2 included iterative touching contact in Linear Statics (SOL 101) and the Advanced Nonlinear (SOL 400) and glued contact in all linear solution sequences. For MD Nastran R3, the contact capabilities have been enhanced to include beam-to-beam, shell edge-to-edge, and moment-carrying glue contact. With beam-to-beam contact, beam element contact is detected and load transfer is passed from one beam to the other. You can also specify a beam “radius” to increase the displacement accuracy. This functionality is critical in many industries including the biomedical field where devices such as pacemakers are modeled with wire leads using beam elements. The shell edge-to-edge and moment-carrying glue options are included to ease the process of assembly modeling. The edge-to-edge contact option works with both touching and gluing contact. With edgeto-edge gluing, surfaces defined using shell elements do not need to have mesh congruency at the boundary. This dramatically reduces the amount of model pre-processing required to create complex assemblies. The moment carrying glue option allows shell-to-shell, shell-to-solid, beam-to-shell, and beam-to-solid connections. Using this technique, moments generated on one mesh will be transferred through to the other mesh automatically.

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4 MD Nastran R3 Release Guide Overview

In addition to the advanced contact functionality, enhancements have been made to increase solver performance with contact models. The adaptive time-stepping routines have been implemented for dynamic analyses and there are also new computational tools and procedures for all contact analyses. More detailed information on these enhancements to SOL 400 can be found in Advanced Integrated Nonlinear and Contact (Ch. 3) and Numerical Methods and High Performance Computing (Ch. 6).

Explicit Nonlinear (SOL 700) As a complement to the Advanced Integrated Nonlinear solution for multidiscipline analysis, MD Nastran also includes an integrated LS-Dyna based explicit solver. This solution was officially released in MD Nastran R2. For MD Nastran R3, the Eulerian solver used in MSC.Software’s Dytran solver has been fully integrated into MD Nastran’s SOL 700. This combination of LS-Dyna and MSC.Software technology provides a best-in-class solution for traditional impact and crash problems involving fluid-structure interaction. This FSI solution has also been implemented for high performance computing using the distributed memory parallel technique. Through the use of SOL 700 analysis chaining, you can now model complex problems including: • Pre-stress structures such as engine fan for bird strike (Implicit-to-Explicit) • Event simulations involving multiple drop tests (Explicit-to-Explicit) • Manufacturing processes with spring back (Explicit-to-Implicit)

For crash analysis, MD Nastran R3 adds the FAA Hybrid Dummies to the previous dummy models included in the R2 release. Micromechanical progressive failure analysis components are included MD Nastran’s SOL 700. Other enhancements to MD Nastran’s Explicit Nonlinear solution are described in Advanced Integrated Nonlinear and Contact (Ch. 3).

MD Adams Integration The integration of Motion and Structural analysis continues with MD Nastran R3. With this release, you can save your flexible body model and mode information directly in the MD Nastran database for import into MD Adams. This new storage mode eliminates the need to save an intermediate Modal Neutral File (MNF) file. More information on the MD Adams integration can be found in Enhancements to ADAMSMNF Case Control Command (Ch. 5).

Optimization MD Nastran has had very powerful optimization routines since it was released in 2006. The functionality in that release included shape, sizing, and basic topology optimization. MD Nastran R2 introduced

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CHAPTER 1 5 Overview of MD Nastran R3

manufacturing and symmetry constraints for topology optimization. MD Nastran R3 extends this functionality in the areas of topography and topometry optimization. In topography optimization, the nodes on a surface mesh are moved normal to the surface during the optimization loop to arrive at an optimal shape. In contrast, topometry optimization considers each element in a design region to have a unique property and it will be modified to achieve an optimal design. Additional optimization enhancements include: • Design optimization solution permanent glued contact for design optimization studies, • Automatic randomization of input variables rapid stochastic analysis set-up, • Random element elimination for sensitivity studies of spot welds and connectors, • A pre-release of a nonlinear response optimization routine based on equivalent static loads.

More information on these optimization enhancements can be found in Optimization (Ch. 8).

Aeroelasticity MD Nastran R2.1 introduced an external spline evaluation capability. This capability has been enhanced in R3 to support storage of the spline matrix in sparse format. This change allows larger models to fit into memory. MD Nastran R3 also introduces new capabilities for aeroelasticity analyses. There is a new aerodynamic interpolation method that interpolates each term in the generalized aerodynamic matrix individually. Examples for using this new interpolation method are given in Aeroelasticity and Rotor Dynamic Improvements (Ch. 9).

SCA User Defined Services As a result of the new MD Nastran architecture, MD Nastran R3 introduces the ability to include user defined services as part of the MD Nastran analyses. For this release of MD Nastran, nonlinear force elements are equipped with an external implementation allowing you to define a nonlinear squeeze film damper. This element type is critical in the rotordynamic analysis of aircraft engines. More detailed information on the SCA User Defined Services can be found in SCA User Services (Ch. 10).

Symbolic Subsitution Using the new Symbolic Substitution feature, you can run multiple analyses on an input file, while modifying fields automatically. Using Symbolic Substitution you specify a special symbol in the input file that identifies the location where changes are to be made. When you run your job, you specify a replacement symbol value that replaces the special symbol in your input file, but only for that job. You can then make several runs, each with a different value, without having to make any additional modifications to the input file.

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6 MD Nastran R3 Release Guide Overview

For more information, please see Symbolic Substitution (App. A) in the MD Nastran Installation and Operations Guide.

List of Errors Resolved The list of errors resolved in this release can be found at: http://www.mscsoftware.com/support/prod_support/nastran/errorlist/files/error2008.lst

List of Example Problems for the MD Nastran R3 Release The table below is a list of the example problems in this release guide and the associated file name that can be found in the test problem library, or in the documentation directory in your MD Nastran R3 installation.

Example Problems

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File Name

2D composite heat transfer element page 79

2d_comp.dat

3D composite heat transfer element page 80

3d_pcomp.dat

Quartz lamp model page 82

quartz_lamp_hemi.dat

2D Transient Thermal Analysis page 86

vtest8_pc.dat

Chaining page 93

hs_chain1.dat

Transient analysis in 2-D contact page 95

nlc021a.dat

Rotating Fan-Blade Model page 102

nlrot103.dat

Brake Squeal Model page 104

nlbsql01.dat

Beam-to-Solid page 143

nlcmc01.dat

Shell-toSolid page 144

nlcmc02c.dat

Four Co-plane Shell Bodies Edge-to-Edge page 148

nlc025a.dat

Five Irregular Shell Bodies Edge-to-Edge page 148

nlc026a.dat

Five Irregular Shell Bodies Edge-toEdge Glue plus the 6th Shell Body as a “Footplate” page 150

nlc026c.dat

Crossed Beams page 153

nlc027a.dat

Coiled Beams page 154

nlc027b.dat

Shell Free Edge Contact page 155

nlc028a.dat

Thin-Wall Square Boxed Free Edges Contact page 156

nlc028b.dat

Imperfect Spherical Shell page 185

nla011b.dat

Three-bar Truss page 263

tomex1.dat

A Square page 273

togex1.dat

CHAPTER 1 7 Overview of MD Nastran R3

Example Problems

File Name

A Solid Beam page 275

topoug5.dat

Exterior Acoustic as Design Constraints page 288

d200exac.dat

Fluid Modes as Design Constraints page 288

d200fmd1.dat

10 Bar Truss page 302

deslo.dat

List of MD Nastran Documents Released with MD Nastran R3 Along with this Release Guide, the following documents are updated for the MD Nastran R3 release: • MD Nastran Installation and Operations Guide • MD Nastran Quick Reference Guide • MD Nastran User’s Guide - Application Examples • MD Nastran User’s Guide - Explicit Nonlinear (SOL 700) • MD Nastran User’s Guide - SCA Service Guide • MD Nastran User’s Guide - Topology Optimization • MD Nastran User’s Guide - User Defined Services Guide

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8 MD Nastran R3 Release Guide Overview

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Chapter 2: Adaptive MeshingMD Nastran R3 Release Guide

2

Adaptive Meshing 

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Local Adaptive Mesh Refinement

10 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Local Adaptive Mesh Refinement Introduction MD Nastran R3 introduces a new Local Adaptive Mesh Refinement capability to the linear structural solution sequences in both SOL 101 and SOL 400, possibly in situations involving contact and/or superelements. Adaptive mesh refinement is an automatic mechanism for altering and controlling locally the size of the finite element mesh. Beginning with an initial mesh provided by the user, a sequence of new meshes is automatically generated. Each new mesh of this sequence is an offspring of the previous, coarser mesh and is obtained by refining (by subdivision) a subset of their elements. The following figures illustrate this mechanism in three examples: the compression of an 2D L-shaped elastic panel (Figure 2-1), 2D elastic analysis of a Mode-I fracture specimen (Figure 2-2) and an 3D elastic analysis of a pinched cylindrical body (Figure 2-3 ) and (Figure 2-4).

Figure 2-1

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Adaptive analysis of an L-shaped elastic panel subjected to compression

CHAPTER 2 11 Adaptive Meshing

Figure 2-2

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2D Elastic analysis of a mode-I fracture specimen

12 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-3

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3D Elastic analysis of a pinched cylindrical body

CHAPTER 2 13 Adaptive Meshing

Figure 2-4

3D Elastic analysis of a pinched cylindrical body

Adaptive mesh refinement can be applied to meshes that combine elements of different types (triangular or quadrilateral surface elements, tetrahedral, pentahedral or hexahedral volume elements), different interpolation orders (linear or quadratic), different dimensionality (line, surface or volume elements), or models substructured into different superelements. The following elements are supported: • Line elements: CBEAM, CBEAM3 (with no offsets or warping), CBEND, CBAR (with no

offsets), CONROD, CROD, CTUBE, CVISC. • Surface elements: CTRIA3, CTRIAR, CTRIA6, CQUAD4, CQUADR, CQUAD8 • Volume elements: CTETRA, CPENTA, CHEXA.

This new adaptive mesh refinement capability shouldn’t be confused with the existing p-adaptive analysis or p-version adaptivity capability available in linear static (SOL 101) and normal modes (SOL 103) analysis (see the MD Nastran Reference Manual). While p-adaptivity is an automatic mechanism to altering the polynomial degree of the underlying finite element interpolating functions defined over a fixed size mesh, adaptive mesh refinement (or h-adaptivity) attempts to change the

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14 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

element size while keeping interpolation order unaltered. For the current release both types of adaptive analysis cannot be combined.

The Adaptive Mesh Refinement Loop During the adaptive mesh refinement process, a sequence of analysis supported over a sequence of different finite element meshes is sequentially performed within an automatic loop (Figure 2-5).

Figure 2-5

The adaptive mesh refinement loop

This adaptive mesh refinement loop can be summarized as follows: 1. The user inputs an initial, preferably coarse, finite element mesh. 2. An analysis is run and a finite element solution (supported on the current mesh) is computed. 3. Some elements of the previous mesh are scheduled or marked for refinement. These elements are chosen according to a user specified adaptivity criterion and implicit refinement propagation rules. 4. The elements scheduled for refinement are refined and a new finite element mesh with new elements and grid points are thus created. 5. Element properties, boundary conditions, constraints and loads are transferred or mapped from the previous mesh to the new mesh. 6. Steps 2 to 5 are repeated until a termination criterion is met. Table 2-1 schematically illustrates the first two iterations of the adaptive mesh refinement loop. Elements

scheduled for refinement due to the user specified adaptivity criterion are depicted in green. Notice that there are neighboring elements that are also refined during the process (yellow elements). Implicit rules

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CHAPTER 2 15 Adaptive Meshing

to propagate the refinement from elements meeting the user specified criterion to their neighbors are explained in Propagation of Refinement, 37. Table 2-1

First two iterations of the adaptive mesh refinement loop First Iteration

Second Iteration

...

...

1. Initial Mesh

2. Analysis 3. Mark for refinement

4. Refine

5. Transfer

...

Refinement by Regular Subdivision Mesh refinement in MD Nastran R3 is accomplished by the so-called regular or isotropic subdivision of a subset of parent elements into offspring or children sub-elements. Figure 2-6 illustrates the subdivision rules for individual elements of the different types:

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16 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Line Elements CTRIA*

CQUAD*

CHEXA

CTETRA

CPENTA

Figure 2-6

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Regular (isotropic) subdivision rules for individual elements of different types

CHAPTER 2 17 Adaptive Meshing

These subdivision rules are called regular or isotropic because all edges in the boundary of a refined element are subdivided into the same number of segments (two) as opposed to, for example, the subdivision of a quadrilateral or a triangular element by bisection (Figure 2-7).

Figure 2-7

Isotropic vs. Anisotropic subdivision of a quadrilateral and a triangular element

For a tetrahedron, there are three possible regular subdivision schemes into eight children tetrahedra. These three schemes are obtained as follows: first, each edge is bisected. This defines four corner tetrahedra and an internal octahedron. Then, the latter might be subdivided into four additional tetrahedra in three different ways, according to each of its three diagonals. In MD Nastran, the diagonal selected to subdivide the internal octahedron is the one connecting node 7 (mid-node of the edge 1-3) to node 9 (mid-node of edge 2-4) as depicted in Figure 2-8. Furthermore, corner nodes of the children tetrahedra are numbered according to the special rule illustrated in Figure 2-8. This special labeling convention of nodes along with the selection of the diagonal connecting nodes 7 to 9 to subdivide the inner octahedron ensures minimization of element distortion with successive refinements.

Figure 2-8

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Labeling convention for corner nodes of children tetrahedra

18 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

During subdivision, the following properties are preserved: 1. Preservation of element type: Quadrilateral elements are subdivided into quadrilateral elements, triangular elements into triangular elements, etc., as opposed to, for example, subdivision of a quadrilateral into triangles or subdivision of a triangle into quadrilaterals (Figure 2-9).

Figure 2-9

Preservation of element type during subdivision

2. Preservation of element orientation (Figure 2-10): The outlining nodes of children elements will be listed in clockwise (respectively counterclockwise) order when the father element have been defined in clockwise (respectively counterclockwise) order.

Figure 2-10

Preservation of orientation during subdivision

3. Preservation of interpolation order: Linear (4-noded) quadrilateral elements (CQUAD4, CQUADR) will be subdivided into four 4-noded quadrilateral elements whereas quadratic (8noded) quadrilateral elements (CQUAD8) will be subdivided into four quadratic (8-noded) quadrilateral elements (Figure 2-11). The linear case requires the creation of 5 new grid points whereas the quadratic case demands the creation of 13, two on each edge, two on each internal edge and one in the centroid of the element.

Figure 2-11

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Preservation of interpolation order in quadrilateral elements during subdivisions

CHAPTER 2 19 Adaptive Meshing

Similarly, linear (3-noded) triangular elements (CTRIA3, CTRIAR) will be subdivided into four linear (3-noded) triangular elements whereas quadratic (6-noded) triangular elements will be subdivided into four quadratic triangular elements (Figure 2-12). The linear case requires the creation of 3 new grid points whereas the quadratic case involves the creation of 9 new grid points, two on each edge and one on each internal edge.

Figure 2-12

Preservation of interpolation order in triangular elements during subdivision

The same rule applies to 3D elements (CTETRA, CPENTA, CTRIA), i.e., a linear tetrahedron (4-noded), pentahedron (6-noded) or hexahedron (8-noded) will be respectively subdivided into eight linear tetrahedra, pentahedra or hexahedra requiring respectively the creation of 6, 12 and 19 new grid points (Figure 2-13).

Figure 2-13

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Preservation of interpolation order in 3D linear elements during subdivision

20 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Equivalently, a fully quadratic tetrahedral (10 nodes), pentahedral (15 nodes) and hexahedral (20 nodes) element will be subdivided into eight fully quadratic tetrahedra, pentahedra or hexahedra. This requires the creation of two new grid points per external and internal edge, five new grid points per quadrilateral face and one new grid point in the bulk of the hexahedral element, a total of 38 new grid points for CTETRA, 48 new grid points for CPENTA and 55 new grid points for CHEXA. For incomplete quadratic 3D elements, i.e., 3D elements created with a number of grid points greater than 4 and less than 10 for CTETRA, greater than 6 and less than 15 for CPENTA and greater than 8 and less than 20 for CHEXA, only a minimum number of new grid points will be created during subdivision to avoid the generation of redundant degrees of freedom. For example, an hexahedron defined with 10 grid points (two quadratic edges and 6 linear edges) will be subdivided into eight quadratic hexahedra with only a few quadratic edges and new grid points (Figure 2-14).

Figure 2-14

A variable number of new grid points is created during subdivision of incomplete quadratic 3D elements

Location of New Grid Points In linear elements, new edge nodes are placed at the mid-side of the (straight) edge. Similarly, new face nodes of linear quadrilateral surface elements (CQUAD4, CQUADR) or quadrilateral faces of linear pentahedral and hexahedral elements (6-noded CPENTA or 8-noded CHEXA) or new internal nodes of linear tetrahedral or hexahedral elements (4-noded CTETRA or 8-noded CHEXA) are placed at the baricenter of the surface element, face or 3D element, i.e., at the position obtained by averaging the position of the corner nodes (Figure 2-15).

Figure 2-15

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Location of new mid-edge and mid-face nodes in a linear element. Mid-edge nodes are placed at the mid-side of the straight edge, mid-face nodes at the baricenter of the face and internal nodes at the baricenter of the element.

CHAPTER 2 21 Adaptive Meshing

In quadratic elements new nodes are positioned by making use of the isoparametric mapping. The parametric space of the element is uniformly bisected and mid-edge and mid-face nodes are mapped back to the physical space using the element (isoparametric) shape functions (Figure 2-16).

Figure 2-16

Uniform subdivision of the parametric domain and resulting subdivision in physical space

No special provisions are taken during refinement of very distorted quadratic elements. In this case, the user should expect distorted children elements (Figure 2-17).

Figure 2-17

Subdivision of a distorted quadratic (quadrilateral) element

The default method of placement of mid-edge nodes on mid-side edges might render inaccurate solutions when the initial mesh provided by the user is very coarse and the boundary of the domain of analysis is therefore poorly approximated.

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22 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

For example, consider the analysis of a circular planar shell subjected to compression and initially discretized with very few elements as illustrated in Figure 2-18. If mid-edge nodes are placed on the midside of edges, inaccurate results are obtained because the circular domain remains poorly approximated during all mesh refinement cycles.

Figure 2-18

Compression of a circular planar shell. Default location for mid-edge nodes is on the mid-side of edges

To address this inaccuracy, the user can request to place mid-edge nodes on a smooth approximation of the analysis domain boundary interpolated from the initial mesh. Given the initial mesh, a smooth curve is interpolated using the nodes located on the mesh boundary to approximate the analysis domain boundary. Then, mid-edge nodes are projected onto this smooth approximation. Figure 2-19 depicts this alternative for the case of the compressed circular shell example shown in Figure 2-18.

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CHAPTER 2 23 Adaptive Meshing

Figure 2-19

Compression of a circular planar shell. Projection of mid-edge nodes onto a smooth approximation of the geometric boundary interpolated from the initial mesh

It’s important to note that the smooth approximation of the boundary is computed using the boundary nodes of the initial mesh provided by the user and that the accuracy of this approximation is determined by the coarseness of this initial mesh. The success and accuracy of this smooth boundary approximation depends also on appropriate detection of corners and edges. In order to identify corners and edges, the initial mesh is preprocessed using an automatic Geometric Feature Detection Algorithm, see Detection of Geometric Features and Material and Superelement Interfaces, 49. The alternative method of projecting edge-nodes onto a smooth approximation of the mesh boundary is available only for edge nodes belonging to edge-boundaries of 2D and 3D geometries. However, no repositioning for edge and face nodes belonging to 3D surfaces and face-boundaries of 3D geometries is supported for the current release.

Hanging Nodes and Multipoint Constraints on Hanging Nodes When an element is refined (subdivided) but its adjacent elements are not refined a non conforming mesh is generated. Nodes created on the boundary between a refined and a non refined element are referred to as hanging-nodes (Figure 2-20).

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24 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-20

Hanging node

Displacement on hanging nodes need to be constrained or tied to the displacement of corner nodes to avoid a discontinuity in the displacement field, as illustrated in Figure 2-21:

Figure 2-21

Displacement field over an incompatible mesh created due to the presence of an unconstrained hanging node

In MD Nastran R3, all degrees of freedom (1 to 6) associated to a hanging node are automatically constrained using internal Multipoint Constraint (MPC) equations derived from the isoparametric mapping. Figure 2-22 and Figure 2-23 depicts the MPC equation for hanging nodes laying respectively on a linear

and a quadratic edge. Notice that in the linear case, the MPC equation ties each component of the hanging node displacement U M with those corresponding to the corner nodes 1 and 2 whereas in the quadratic case each components of the hanging node displacements U M needs to be tied to the corresponding displacements of both the corner nodes 1, 2 and the mid-edge node 3.

Figure 2-22

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Constraint equations for hanging nodes laying on a linear edge

CHAPTER 2 25 Adaptive Meshing

Figure 2-23

Constraint equations for hanging nodes laying on a quadratic edge

Figure 2-24 and Figure 2-25 show the MPC equations for hanging nodes laying respectively on a linear and a quadratic face. In the linear case, the MPC equation ties each component of the hanging node displacement with those corresponding to the corner nodes 1, 2, 3 and 4 whereas in the quadratic case, each component of the hanging node displacements needs to be tied to the corresponding displacements of both the corner nodes 1, 2, 3, 4 and the mid-edge nodes 5, 6, 7 and 8.

Figure 2-24

Constraint equation for hanging nodes laying on a linear face

Figure 2-25

Constraint equation for hanging nodes laying on a quadratic face

An example illustrating the need of enforcing constraints on hanging nodes is depicted in Figure 2-26, Figure 2-27, and Figure 2-28 concerning the deformation of a cylindrical shell subjected to a central

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26 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

concentrated load. Figure 2-26 shows the finite element mesh after the third iteration in the adaptive mesh refinement loop along with the hanging nodes involved in MPC equations. Figure 2-27 and Figure 2-28 compare the deformed configuration and von Mises stresses obtained when the hanging node constraints are enforced (left) or not enforced (right). Notice when the hanging node constraints are not enforced, an incompatible configuration is obtained.

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Figure 2-26

Multipoint constraints on hanging nodes

Figure 2-27

Compatible (left) and incompatible (right) deformations obtained when multipoint constraints are enforced (left) or not (right)

CHAPTER 2 27 Adaptive Meshing

Figure 2-28

Compatible (left) and incompatible (right) von Mises stresses obtained when multipoint constraints are enforced (left) or not (right)

Selection of Elements to Refine Elements that will be refined during a given iteration in the adaptive loop are selected in two steps; first, all elements meeting the user specified adaptivity criterion are searched for and scheduled for refinement. Second, some of the elements adjacent to the latter are also scheduled for refinement according to a set of implicit propagation rules. If no elements meeting the user specified criterion are found, the adaptivity loop is terminated. MD Nastran R3 currently supports four refinement criteria (see Refinement Criteria, 28): 1. Error indicator based criterion 2. Nodes within a spherical spatial region criteria 3. Nodes within an orthogonal spatial region criteria 4. Nodes in contact criteria The set of implicit refinement propagation rules are the following (see Propagation of Refinement, 37): 1. Horizontal propagation (2-to-1 rule) 2. Horizontal propagation from inner to outer children in triangular and tetrahedral elements 3. Vertical propagation 4. Propagation across superelement boundaries.

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28 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Refinement Criteria The mesh refinement criteria available in MD Nastran R3 are the following: Error Indicator Based Criterion In this case an error indicator element is refined if 2

E e ≥ fE

Ee

is computed over each element ‘e’ in the finite element mesh. Then, an

2

where f is a scalar factor such that 0 ≤ f ≤ 1 and chosen by the user (as part of the Bulk Data entry HADACRI) and E is the quadratic mean of the error indicator defined as:

E

2

1 Z JJJJ N

N

∑

2

Ee

e Z 1

with N the total number of elements in the element set where element ‘e’ belongs, Thus, an element is refined if its estimated error is larger than a fixed percentage of the quadratic mean. Figure 2-29 schematically depicts a mesh with its corresponding elemental error indicator (blue) and quadratic mean (red). Only those elements with error indicator above a fixed percentage of the quadratic mean will be refined.

Figure 2-29

Error indicator distribution over a 1-D mesh (blue) with N elements and corresponding quadratic mean (red). Only those elements for which E e is above a fixed percentage of will be refined.

The factor f is specified by the user in the F1 field of the HADACRI Bulk Data entry (see User Interface, 55 or the Bulk Data entry HADACRI (p. 1733) in the MD Nastran Quick Reference Guide). The error indicator E e is a scalar, elemental magnitude that provides a relative measure of the discretization error, i.e., the error between the finite element solution and the analytical solution of the underlying differential equations of the problem under analysis. It is computed using the grid point stresses and element stress discontinuity following the procedure utilized by the ELSDCON Case Control

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CHAPTER 2 29 Adaptive Meshing

command and described in the MD Nastran Reference Manual, Section 8.3. This procedure can be summarized as follows: Na

• Let σ aij Z

∑

e

e

W a σ ai j

be the weighted average over all elements ‘e’ concurrent to a given node

e Z 1

‘a’ of each component ‘ij’ of the grid point stresses σ ea ij where W e is a weighting factor assigned to element ‘e’ and Na is the number of elements connected to the given node ‘a’. • An estimate of the error in a particular component of stress ‘ij’ at a grid point ‘a’ is then be N

computed as

2

E ai j Z

∑

e

W a ( σ a ij Ó σ ai j )

2

e Z1

Averaging the latter over the different stress components, ‘ij’, over the different shell fibers (for shell elements) and over the different grid points ‘a’ connected by a given element ‘e’ the elemental, scalar error indicator E e is obtained. Figure 2-30 shows an example using the error indicator based adaptivity criterion involving the analysis of a 2D mode-I fracture specimen. Notice that this criterion tends to cluster the refinement near areas of stress concentration. This is due to the fact that stress gradients (and therefore element stress discontinuities and error indicators) are considerably higher in those zones than in the rest of the mesh.

Figure 2-30

Analysis of a 2D mode-I fracture specimen

This refinement criterion is available for any of the surface or volume elements, namely CTRIA3, CTRIAR, CTRIA6, CQUAD4, CQUADR, CQUAD8, CTETRA, CPENTA, CHEXA. It is not available

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30 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

however for the family of line elements. The latter might be subdivided either by using any other criteria of the remaining refinement criterion, or because they are connected to the boundary of a surface or volume element (see Vertical Propagation, 40). Elements Within a Spatial Spherical Region Criterion In this criteria, the user defines a spherical region in space by specifying its center in basic coordinate system ( X 0, Y 0, Z 0 ) and its radius R. Then, all elements with at least one node with basic coordinates ( X, Y, Z ) within the spherical region (i.e., such that

( ( X, Y , Z ) Ó ( X 0, Y 0, Z 0 ) < R ) ||

will be refined.

Figure 2-31 shows the mesh obtained in an example involving a 3D cylindrical body using this criterion. Figure 2-32 shows a detail of the mesh obtained after the fourth refinement cycle along with the spatial

spherical region selected for refinement.

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CHAPTER 2 31 Adaptive Meshing

Figure 2-31

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Sequence of meshes obtained on a 3D cylindrical body using the “elements within a spherical region” adaptivity criterion

32 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-32

Mesh obtained after the third refinement cycle of 3D cylindrical body using the “elements within a spherical region” adaptivity criterion. Only the bottom half of the cylinder is shown in the right picture.

Elements Within a Spatial Orthogonal Region Criterion In this refinement criterion, the user defines an hexahedral region in space or box aligned with the basic coordinates system by specifying the basic coordinates of opposite corners ( X 0, Y 0, Z 0 ) and ( X 1, Y 1, Z 1 ) of the box. Then, all elements with at least one node with basic coordinates ( X, Y, Z ) within the specified hexahedral region (i.e., such that X 0 ≤ X ≤ X1 , Y 0 ≤ Y ≤ Y 1 and Z 0 ≤ Z ≤ Z 1 ) will be refined. Figure 2-33 shows the mesh obtained in the same 3D cylindrical body used in Figure 2-31 but with the nodes within a box refinement criterion. A detail of the mesh obtained after the third refinement along with the orthogonal refinement region is shown in Figure 2-34.

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CHAPTER 2 33 Adaptive Meshing

Figure 2-33

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Sequence of meshes obtained on a 3D cylindrical body using the “elements within an orthogonal region” adaptivity criterion

34 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-34

Mesh obtained after the third refinement cycle of 3D cylindrical body using the “elements within an orthogonal (box) region” adaptivity criterion. Only the bottom half of the cylinder is shown in the right picture.

Elements in Contact Criterion In this criterion, all touching elements with at least one node involved in contact and touched elements with at least one face in contact will be refined. MD Nastran R3 supports glued contact, rigid-todeformable body contact, and deformable-to-deformable body contact situations. Figure 2-35 shows the initial mesh of two 3D deformable bodies composed exclusively of linear hexahedral elements and brought into contact after a vertical displacement is applied on the top body.

Figure 2-35

Two 3D deformable bodies in contact

Figure 2-36 shows the sequence of meshes obtained during the mesh refinement process.

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CHAPTER 2 35 Adaptive Meshing

Figure 2-36

Sequence of meshes during adaptive mesh refinement process using the “Nodes in Contact” criterion on two 3D deformable bodies in contact

Figure 2-37 and Figure 2-38 depict the sequence of meshes obtained during mesh refinement using the

“Nodes in Contact” refinement criterion in a situation involving 3D rigid-to-deformable contact with 8noded CHEXA elements and 3D glue contact between two deformable bodies with 10-noded CTETRA elements respectively.

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36 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-37

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Sequence of meshes during adaptive mesh refinement process using the “Nodes in Contact” criterion on a Rigid-to-Deformable body contact setting

CHAPTER 2 37 Adaptive Meshing

Figure 2-38

Sequence of meshes during adaptive mesh refinement process using the “Nodes in Contact” criterion on a glue contact problem

Propagation of Refinement Once elements meeting the refinement criteria are scheduled for refinement, the refinement is propagated to some of their adjacent elements according to a set of implicit propagation rules. These rules are the following: Horizontal Propagation (2 to 1 rule) The first refinement propagation rule is the 2-to-1 rule. The 2-to-1 rule restricts the number of hanging nodes on each edge to one, see Hanging Nodes and Multipoint Constraints on Hanging Nodes, 23. To this end, all the edge-neighbors of elements scheduled for refinement are selected for refinement as well. This is illustrated in Figure 2-39. When one element scheduled for refinement (green element) is refined, two hanging nodes are created on its adjacent edges. To restrict the number of hanging nodes to one the refinement is propagated to its edge-neighbors (yellow elements).

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38 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-39

The green element has been scheduled for refinement due to the user specified refinement criteria. The refinement must be propagated to the edge neighbors (yellow elements) to avoid the creation of more than one hanging node per edge.

Notice that in 3D meshes, there might be more than one edge-neighbor per edge as illustrated in Figure 2-40.

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CHAPTER 2 39 Adaptive Meshing

Figure 2-40

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Propagation of refinement from an element meeting the user’s specified refinement criterion (green element) to its edge-neighbors (yellow elements) to enforce the 2-to-1 propagation rule. In 3D, there might be more than one neighbor per edge.

40 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Horizontal Propagation in Triangles and Tetrahedra Consider a refined triangular or tetrahedral element. If the internal triangle or internal tetrahedra are scheduled for a second refinement, then the external triangle or tetrahedral are automatically selected for refinement as well. This is to avoid the creation of redundant degrees of freedom on internal edges or faces that would otherwise be constrained with no net gain of mesh resolution (Figure 2-41).

Figure 2-41

If the internal (green) triangle of a refined triangular element is further refined, no net addition of degrees-of-freedom is obtained (top row). To avoid this redundancy, the refinement is automatically propagated to all external (yellow) triangles of the refined triangular element (bottom row).

Vertical Propagation Consider a line element (CBEAM, CBEAM3, CBEND, CBAR, CONROD, CROD, CTUBE, CVISC) attached to an edge of a surface element (CQUAD4, CQUADR, CQUAD8, CTRIA3, CTRIAR, CTRIA6) of a surface element attached to the face of a 3D element (CTETRA, CPENTA, CHEXA). Then, if the element of higher dimensionality is scheduled for refinement, then the element of lower dimensionality attached to its face is automatically selected for refinement as well (Figure 2-42).

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CHAPTER 2 41 Adaptive Meshing

Figure 2-42

The refinement is automatically propagated from elements of higher dimensionality selected for refinement (green) to elements of lower dimensionality attached to their boundary (yellow).

The same rule applies in the opposite direction: if an element of lower dimensionality attached to the boundary of another element of higher dimensionality is scheduled for refinement, then the latter is automatically selected for refinement (Figure 2-43).

Figure 2-43

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The refinement is automatically propagated from elements of lower dimensionality selected for refinement (green) and attached to elements of higher dimensionality (yellow) to the latter.

42 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Propagation of Refinement Across Partitioned Superelement Boundaries Hanging nodes cannot occur at partitioned superelement boundaries because their corresponding degrees of freedom cannot belong simultaneously to two different Degree-of-Freedom Sets (see Degree-ofFreedom Set Definitions (Ch. 7) in the MD Nastran Quick Reference Guide). In order to prevent this condition, the refinement is automatically propagated across superelement boundaries. In this way, hanging nodes are moved from the boundary to the interior of the affected superelements (Figure 2-44).

Figure 2-44

When elements on a given superelement are scheduled for refinement (green elements), the refinement is propagated into the neighboring superelement (yellow elements) to avoid the creation of hanging nodes on the superelement boundaries.

Transference of Analysis Data Between Unrefined and Refined Meshes Once a refined mesh is obtained by subdividing selected elements from the previous mesh, analysis data must be communicated or transferred from the old mesh to the new mesh in order set up the next analysis on the new mesh. Analysis data to transfer includes element properties, shell thicknesses, material orientations, pressure loads and permanent and single point constraints (displacement boundary conditions). The rules to transfer this data are the following: Transference of Element Properties Children elements created after refinement inherit their parent’s property ID. In surface elements (CQUAD4, CQUADR, CQUAD8, CTRIA3, CTRIAR, CTRIA6) with nonuniform shell thicknesses, the thickness for corner nodes in the children elements are linearly interpolated from the corner nodes of the parent element (Figure 2-45).

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CHAPTER 2 43 Adaptive Meshing

Figure 2-45

Transference of non-uniform shell thickness data from the parent to the children elements

Furthermore, children elements inherit the material orientation angle (see THETA field on the CQUAD4, CQUADR, CQUAD8, CTRIA3, CTRIAR, CTRIA6 entries). The orientation angle THETA for children element is computed using the equations given in Figure 2-46. This takes into account that THETA is defined as the angle between the edge joining nodes 1 and 2 of the element and the material direction and, therefore, might not be uniform within children elements. Notice that uniform material orientation does not imply uniform angle THETA.

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44 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-46

Transference of material orientation angle from the parent of the children elements. The blue arrow points in the direction of the material orientation which is conserved during refinement. Notice that this does not imply the conservation of the THETA angle.

Transference of Distributed Loads and Concentrated Forces Pressure loads (PLOAD, PLOAD2, PLOAD4) distributed over parent elements are automatically redistributed over children elements. Thus, a uniform pressure load distributed over a quadrilateral surface element (PLOAD, PLOAD2) is copied over children elements and redistributed with same magnitude and direction over their smaller area.

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CHAPTER 2 45 Adaptive Meshing

Similarly, the magnitude of non-uniform pressure loads distributed over surface elements faces of 3D elements or faces of surface elements (PLOAD4) are not just copied over but interpolated linearly from corner pressures (Figure 2-47) and applied to children elements with the same direction.

Figure 2-47

Transference of PLOAD4 applied to the face of a 3D (CHEXA) element. Midedge and mid-face pressures are linearly interpolated from corner values

No special provisions are taken regarding transference of concentrated forces or moments. Thus, no concentrated loads will be created or new grids created for refinement but just carried over existing grid points in the old mesh to the same grid points in the new mesh. Transference of Displacement Coordinate System, Displacement Boundary Conditions and Constraints Displacement coordinate systems, permanent single point constraints, single point constraints and multipoint constraints on the new grid point c created during refinement are internally enforced according to the following rules: • If the coordinates systems defined on corner grid points (specified on the CD field in the GRID

Bulk Data entry) are identical, then the same displacement coordinate system is assigned for a new mid-edge or mid-face node created during refinement. Furthermore, for edges of surface or volume elements, each degree of freedom associated to the new mid-node created on the edge is either permanently constrained (assigned to degree-of-freedom set SG), or explicitly constrained via an internal Single point constrain SPC (assigned to the degree-of-freedom set SB) or constrained to corner nodes via an internal Multipoint Constraints M (see Degree-of-Freedom Set Definitions (Ch. 7) in the MD Nastran Quick Reference Guide) depending upon the degreeof-freedom set where the corner nodes. For faces of volume elements, each degree-of-freedom of a new mid-face node created during refinement is also either permanently constrained, or explicitly constrained (via internal SPC) or tied to corner nodes (via internal MPC) according to the permanent constraints, enforced displacement or multipoint constraints defined on the corner nodes.

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46 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

The specific constraints to be enforced internally for mid-edge or mid-face nodes are: • If permanent constraints have been defined on a degree of freedom i at both corner nodes, then

a permanent constraint is also assigned to the degree of freedom i at the mid-edge of mid-face node. For example (Figure 2-48), if both corner nodes a and b on an edge have been permanently constrained in all degrees-of-freedom (by defining P S a Z 123456 and P S b Z 123456 on the PS field in the GRID Bulk Data entry), then node c will be also constrained permanently in all degrees-of-freedom (by defining P S c Z 123456 internally).

Figure 2-48

Coordinate systems ( C D a and C D b ) defined on corner node a and b (using the CD field in the Grid Bulk Data entry) must match in order for constraints to be enforced on mid-edge node c. Permanent constraints (PS field on the GRID Bulk Data entry) on each degree-of-freedom are then carried over the mid-edge node.

• If single point constraints have been defined on a degree of freedom i for all corner nodes, then

the degree of freedom i on the mid-edge or mid-face node will be tied internally to the corner nodes according to the same multipoint constraint equations used for hanging nodes on straight edges (see Hanging Nodes and Multipoint Constraints on Hanging Nodes, 23, Figure 2-22 and Figure 2-24). Notice that this is equivalent to imposing an SPC on the midedge node, degree-of-freedom i, with a value for enforced displacement averaged from the value at corner nodes. For example, if a displacement with value U a along direction 1 is enforced on node a (by defining an SPC on node a, direction 1) and a displacement in the same direction with value U b is enforced on node b (by defining another SPC on node b, direction 1), then a multipoint constrain for node c (direction 1) is internally defined such that U c Z 1 ⁄ 2 ( U a H U b ) (Figure 2-49).

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CHAPTER 2 47 Adaptive Meshing

Figure 2-49

If displacement is enforced on a given degree-of-freedom on corner nodes a and b (using SPC or SPC1 entries), then a multipoint constraint that ties the mid-edge node c with both corner nodes is internally enforced, provided that displacement coordinate systems for all corner nodes coincide (CD field in the GRID entry).

• The same multipoint constraint equation is applied on the mid-edge node c (in a given

direction i) if one of the corner nodes has been constrained permanently and the other corner node has been constrained via a Single Point Constraint (SPC) on the same direction i. For example, if a displacement with value U a along direction 1 is enforced on node a (by defining an SPC on node a, direction 1) and a permanent constraint in the same direction has been enforced for corner node b (by defining P S b Z 1 on the PS field in its GRID Bulk Data entry), then a multipoint constraint for node c (direction 1) is internally defined such that U c Z 1 ⁄ 2 ( U a H U b ) Z 1 ⁄ 2 ( U a H 0 ) Z 1 ⁄ 2 U a (Figure 2-50).

Figure 2-50

Main Index

If a displacement is enforced on a given degree-of-freedom on corner node a (using SPC or SPC1 entries) and a permanent constraint is enforced on the same degree-of-freedom on corner node b (PS=1 on its GRID Bulk Data entry), then a multipoint constraint that ties the mid-edge node c with both corner nodes is internally enforced, provided that displacement coordinate systems for all corner nodes coincide (CD field in GRID entry).

48 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

• Similarly, the same multipoint constraint is applied on the mid-edge or mid-face nodes (in a

given degree-of-freedom i) if some of the corner nodes are involved in a permanent constraint (PS field in the GRID Bulk Data entry) or single point constraint (SPC or SPC1 Bulk Data entry) and the others corner nodes are involved in a multipoint constraint (MPC Bulk Data entry) on the same degree of freedom i. • If the corner nodes are involved in contact, either as touching nodes or touched element faces

or edges, then the mid-edge nodes are regarded as nodes potentially in contact. Therefore, constraints on any of the degrees-of-freedom associated to the latter are determined by the contact detection algorithm. The set of relations just outlined is summarized in the following table: corner node a

corner node b

mid-node c

SG

SG

SG

SB

SB

M

SG SB

SB SG

M

SG or SB M

M SG or SB

M

Node in contact

Node in contact

Node potentially in contact

• If the displacement coordinate system defined on corner nodes on an edge or face are different,

then the displacement coordinate system for the mid-node on the edge or face is set to the basic coordinate system. Furthermore, no constraints are enforced on any of its associated degrees-offreedom independently of the constraints that might have been imposed on corner nodes (Figure 2-51).

Figure 2-51

Main Index

If coordinate systems ( C D a and C D b ) defined on corner nodes a and b (using the CD field in the GRID Bulk Data entry) are different then the mid-edge node c is left free and its displacement coordinate system is set to the basic.

CHAPTER 2 49 Adaptive Meshing

Detection of Geometric Features and Material and Superelement Interfaces Prior to the initiation of the adaptive mesh refinement loop, the initial mesh provided by the user is preprocessed using an automatic Geometric Feature and Material interface Detection Algorithm aimed to identify: • Geometric features such as: • Sharp corners and edges • Non-manifold edges and vertices, i.e., edges joining more than two surfaces (in 3D) or

vertices joining more than two curves in 2D or 3D. • Other interfaces such as: • Interfaces between mesh regions with different property IDs. • Interfaces between superelements.

Detection of Geometric Features The Geometric Feature Detection Algorithm identifies edges and corners by comparing the angle between each pair of adjacent elements with the “Feature Angle” VARPHI. The feature angle is a scalar parameter specified by the user (PARAM,VARPHI) that defines how sharp a mesh edge or vertex should be in order to be considered as a geometric feature. More precisely, face outward normal vectors N 1, N 2 of each pair of adjacent mesh faces and the edge oriented tangents T 1, T 2 of each pair of adjacent mesh edges are computed (Figure 2-52) by the geometric feature detection algorithm. If the angle between N 1 and N 2 for mesh faces, or between T 1 and T 2 for mesh edges is larger than the feature angle VARPHI then the common edge or vertex will be considered a splitting edge or vertex where surfaces or lines are broken and a geometric feature is thus defined.

Figure 2-52 Mesh faces and elements are preprocessed to ensure consistent orientation and that the appropriate sign of face normal vectors and edge tangents will be accounted for during the computation of their mutual angle.

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50 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-53, Figure 2-54, Figure 2-55, and Figure 2-56 show the edges identified by the Geometric Feature detection algorithm on a surface mesh (Figure 2-53) and three 3D volume meshes (Figure 2-53, Figure 2-54, Figure 2-55).

Main Index

Figure 2-53

Edges detected by the geometric feature detection algorithm in a surface mesh of triangular elements of a mechanical part with a non-manifold edge

Figure 2-54

Edges detected by the geometric feature detection algorithm in a 3D hexahedral mesh of a cylindrical body

CHAPTER 2 51 Adaptive Meshing

Figure 2-55

Edges detected by the geometric feature detection algorithm in a 3D hexahedral mesh of an engine cup

Figure 2-56

Edges detected by the geometric feature detection algorithm in a 3D hexahedral mesh of an engine cylinder head

Adequate identification of geometric features (by appropriately adjusting the feature angle VARPHI) is essential to ensure the convergence of the mesh refinement process to expected results. Thus, if the error indicator based refinement criterion is selected and sharp edges are not properly identified by the geometric feature detection algorithm, the refinement might cluster indefinitely in the neighborhood of the undetected sharp edges (Figure 2-53). This anomaly occurs mainly on sharp intersections between shells due to the fact that the error indicator indirectly measures membrane stress jumps between adjacent elements and the latter might be very high due to the abrupt change in shell normal directions at sharp intersections. Figure 2-57 and Figure 2-58 depict two orthogonal planar shells joined on a common edge and subjected

to a vertical displacement on the top. The feature angle must be chosen smaller than π ⁄ 2 in order for the joining edge to be detected and the error estimator to ignore (or filter) the large membrane stress discontinuity across this edge (Figure 2-57). If the feature angle is not appropriately chosen, then the

Main Index

52 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

geometric feature algorithm will fail to identify the joining edge and the mesh refinement will cluster in its neighborhood (Figure 2-58).

Figure 2-57

An adequate value of the VARPHI parameter ( π ⁄ 4 in this case) will ensure that the sharp edge shared by both planar shells is detected by the geometric feature detection algorithm and the big membrane stress jumps occurring at the edge are filtered out.

Figure 2-58

The geometric feature detection algorithm fails to detect the sharp edge shared by both planar shells because the VARPHI parameter is too large. As a consequence, the big membrane stress jumps occurring at the edge are not filtered out and the refinement clusters in the neighborhood of the sharp edge.

The adequate identification of corners is also required to improve the smooth approximation of the analysis domain boundary constructed by interpolating the mesh boundary nodes and used as a method to place new mid-edge nodes during refinement (see Location of New Grid Points, 20) alternative to the default location at the mid-side of the edge.

Main Index

CHAPTER 2 53 Adaptive Meshing

Figure 2-59 and Figure 2-60 compare the two edge-node placement methods (mid-side placement and

projection of mid-edge nodes onto a smooth approximation of the boundary) in an example involving a 2D treble shaped planar shell subjected to compression. The boundary of this mesh exhibits three sharp corners located at the intersection of each pair of circular leaves. The mesh is refined everywhere (uniform refinement). This is accomplished by selecting the “nodes within a spatial sphere” refinement criteria (see Refinement Criteria, 28) with a spherical refinement region big enough to contain the whole mesh.

Figure 2-59

Main Index

Mid-edge nodes are placed in the mid-side of edges

54 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-60

Projection of mid-edge nodes onto a smooth approximation of the geometric boundary interpolated from the initial mesh

Notice that the three sharp corners are appropriately detected by the Geometric Feature Detection Algorithm and kept as hard points during the mesh refinement process. By contrast, sharp corners might become smeared out if the geometric feature detection algorithm is not successful due to an inadequate selection of the feature angle (parameter VARPHI) (Figure 2-61).

Figure 2-61

Main Index

Corners might be smeared out if they are not appropriately detected by the automatic geometry feature detection algorithm. Corner detection can be controlled by the user adjusting the VARPHI parameter.

CHAPTER 2 55 Adaptive Meshing

Detection of Material and Superelement Interfaces Interfaces between mesh regions with different properties IDs or superelement IDs are also automatically detected during the preprocessing phase prior to the beginning of the adaptive mesh refinement loop. Different properties or superelement may reference different materials or different shell thicknesses. Therefore, stress of different order of magnitude are expected in areas with different properties or superelements. This type of discontinuities must be filtered out by the error indicator (which averages stress jumps across interelement boundaries) in order to be able to capture the discontinuities introduced by the finite element discretization exclusively.

User Interface Local adaptive mesh refinement is activated by the new Case Control command HADAPT and controlled by the two new Bulk Data entries HADAPTL and HADACRI along with the optional feature angle parameter VARPHI (Figure 2-62). • The Case Control command HADAPT must reference the Bulk Data entry HADAPTL. • The Bulk Data entry HADAPTL provides an interface to control the number of iterations in the

adaptive mesh refinement loop (REPEAT field), the refinement criteria (CRITID field), (see Refinement Criteria, 28) which must reference a Bulk Data entry HADACRI, the refinement region where the latter will be applied (WHEREMETHOD and WHEREID fields), the placement method for new mid-edge nodes (SNAPMETHOD field), (see Location of New Grid Points, 20), and the maximum levels of refinements permitted to any individual element in the mesh (MAXLEVEL field). • The Bulk Data entry HADACRI provides an interface for the specification of the refinement criterion along with criteria specific parameters (see Refinement Criteria, 28). • The parameter VARPHI, (feature angle) can be optionally adjusted when corners and edges are

not satisfactory detected to control how sharp a mesh edge or vertex should be in order to be consider a split edge or vertex between two otherwise continuous curves or surfaces (see Detection of Geometric Features and Material and Superelement Interfaces, 49). • Different mesh refinement criteria might be applied to different refinement regions by

combining two pairs of Bulk Data entries HADAPTL and HADACRI. Furthermore, mesh refinement can be driven by a combined error indicator based on stresses arising from multiple load cases.

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56 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-62

User interface to activate and control the new adaptive mesh refinement capability

Selection of Refinement Region Adaptive mesh refinement can be either requested for all elements in the mesh or for a subset of elements. Two different mesh refinement subsets are supported: • elements sharing a given property ID •

elements belonging to a given superelement.

The refinement region can be specified by the user via the pair of fields (WHEREMET,WHEREID) in the HADAPTL Bulk Data entry as follows: • If mesh refinement must be restricted to all elements sharing a given property identified with

property ID “PID”, then the WHEREMET field must be set to the keyword “PROP” and WHEREID field must be set to the integer PID: N HADAPTL

Main Index

2 1

3

4

5

6

7

8

101

PROP

PID

9

10

CHAPTER 2 57 Adaptive Meshing

• If mesh refinement must be restricted to a particular superelement identified with superelement

ID “SEID”, then the WHEREMET field must be set to the keyword “SUPER” and the WHEREID field must be set to the integer SEID: N

2

HADAPTL

3

4

5

1

6

7

8

101

SUPER

SEID

9

10

• Finally, if mesh refinement is requested for all elements in the mesh, then the field

WHEREMET must be set to the keyword “ALL” and the WHEREID field is ignored. N

2

HADAPTL

1

3

4

5

6

7

101

ALL

8

9

10

Consider by way of example a cylindrical shell subjected to a concentrated force as depicted in (Figure 2-63). Two different properties (labeled with IDs 1 and 2) have been assigned to the top and bottom halves of the shell. The concentrated force is applied on the center node of the shell (located at the interface between both regions) and in the direction normal to the shell.

Figure 2-63

Main Index

Pinched cylindrical shell. Different properties have been assigned to elements in the top and bottom halves of the shell.

58 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Mesh refinement using the error indicator based criterion have been requested for the bottom half (property 2): N

2

3

HADAPTL

1

HADACRI

101

1

4

5

6

7

8

101

PROP

2

9

10

0.9

Figure 2-64 shows the sequence of meshes and deformed configuration obtained during the adaptive mesh refinement process. Notice that even though the refinement is mainly confined to the bottom half, it also propagates a few layers into the top half due to the 2-to-1 rule (see Propagation of Refinement, 37).

Figure 2-64

Pinched cylindrical shell. Sequence of meshes and deformed configuration obtained during the mesh refinement process.

Selection of Refinement Criterion The refinement criterion that will be applied to the refinement region is selected by specifying a refinement criteria ID on the CRITID field in the HADAPTL Bulk Data entry: N HADAPTL

Main Index

2 1

3

4

5

6

7

CRITID

ALL

8

9

10

CHAPTER 2 59 Adaptive Meshing

along with a corresponding HADACRI Bulk Data entry, N HADACRI

2

3

4

5

6

7

8

9

CRITID

TYPE

F1

F2

F3

F4

F5

F6

10

The particular refinement criteria is specified using the TYPE field in the HADACRI Bulk Data entry. Four different refinement criteria (see Refinement Criteria, 28), can be selected, namely:

TYPE

Name of Mesh Refinement Criterion

1

Error indicator based criterion

2

Element within a spatial spherical region criterion

3

Elements within a spatial cubic region criterion

4

Elements in contact criterion.

The fields F1 to F6 are parameters required to control each specific refinement criterion as follows: N

2

3

4

5

6

7

8

9

CRITID

TYPE

F1

F2

F3

F4

F5

F6

Error Indicator based criteria

1

f

Nodes within a sphere criteria

2

X0

Y0

Z0

R

Nodes within a box criteria

3

X1

Y1

Z1

X2

Y2

Z2

Nodes in contact criteria

4

HADAPTL

10

• For the error indicator refinement criteria (see Error Indicator Based Criterion, 28), an element is

refined if the elemental error indicator

Ee

is smaller than a fixed percentage f (with

the quadratic mean of the error indicator, namely Fields F2 to F6 are ignored.

2

Ee ≥ f E

2

0≤f≤1)

of

. In this case the field F1 is the factor f.

• For the nodes within a spherical spatial region criteria (see Elements Within a Spatial Spherical Region Criterion, 30), an element is refined if any of its connected nodes lay within a spatial

spherical region with center ( X 0, Y 0, Z 0 ) (in basic coordinate system) and radius R. In this case the fields (F1,F2,F3) specify the sphere center ( X 0, Y 0, Z 0 ) and the field F4 specifies the radius R. Fields F5 and F6 are ignored.

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60 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

• For the nodes within a spatial orthogonal region criteria (see Elements Within a Spatial Orthogonal Region Criterion, 32), an element is refined if any of its connected nodes lay within a

spatial orthogonal region or box with diagonally opposed corners ( X 1, Y 1, Z 1 ) and ( X 2, Y 2, Z 2 ) (in basic coordinate system). In this case the fields (F1, F2, F3) specify the box corner ( X 1, Y 1, Z 1 ) and the fields (F4, F5, F6) specify the opposite corner ( X 2, Y 2, Z 2 ) . The coordinates and ( X 1, Y 1, Z 1 ) must be chosen such that X 1 < X 2 , Y 1 < Y 2 and Z 1 < Z 2 .

( X 1, Y 1, Z 1 )

• For the nodes in contact criteria (see Elements in Contact Criterion, 34), elements connected to

nodes involved in contact are refined. In this case all fields F1 to F6 are ignored. Different Criteria in Different Regions Different refinement criteria might be applied to different refinement regions. This can be accomplished by superposing two different HADAPTL entries with the same ID (and referenced from a unique Case Control command HADAPT) and pointing to two different HADACRI entries on two different refinement regions. Consider by way of example a cylindrical body subjected to a concentrated forces as depicted in (Figure 2-65). Two different properties (labeled with IDs 1 and 2) have been designated for the top and bottom halves of the body. The nodes-within a spherical region criterion (TYPE=2) is requested for the top half and the Nodes-within an orthogonal region criterion (TYPE=3) is demanded for the bottom half.

Figure 2-65

Main Index

Two different refinement criteria are applied to two different refinement regions. The top region is refinement criterion type 2 (nodes within a sphere) while the bottom region is subjected to refinement criterion type 3 (nodes within a box). The refinement regions are defined using different property IDs.

CHAPTER 2 61 Adaptive Meshing

Two different HADAPTL entries (with the same ID) referencing two different HADACRI entries with two different refinement regions (defined by two different pairs of values in the fields (WHEREMET,WHEREID)) are thus required: SUBCASE 1

... HADAPT =

1

BEGIN BULK

... HADAPTL

1

HADAPTL

4

1

HADACRI

111

2

X0

HADACRI

222

3

X1

111

PROP

1

222

PROP

2

Y0

Z0

R

Y1

Z1

X2

Y2

Z2

... ENDDATA

Each HADACRI requests different refinement criteria (TYPE=2 and TYPE=3) with different criteria specific parameters. Figure 2-66 shows the sequence of meshes obtained during the adaptive mesh refinement process. Notice that even though the refinement is mainly confined to the specified refinement regions, some elements away from these regions might also be refined due to the 2-to-1 rule (see Propagation of Refinement, 37).

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62 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-66

Main Index

Sequence of meshes obtained with two different refinement criteria are applied to two different refinement regions. The top region is subjected to refinement criterion type 2 (nodes within a sphere) while the bottom region is subjected to refinement criterion type 3 (nodes within a box).

CHAPTER 2 63 Adaptive Meshing

Different Criteria in the Same Region Different refinement criteria can be applied also to the same refinement region. As in the previous case, two different pairs of HADAPTL and HADACRI entries are required. In this case both HADAPTL entries should request refinement within the same refinement region (using identical specifications for the fields WHEREMET and WHEREID). Both HADAPTL entries should be identified with the same label (ID) and referenced from a unique case control entry HADAPT. Consider for example the case of a cylindrical shell subjected to a concentrated force (Figure 11-5). Mesh refinement is requested everywhere in the mesh (WHEREMET=ALL) using two different refinement criteria: the error indicator based criterion (TYPE=1) and the nodes-within an orthogonal region criterion (TYPE=3). Two different HADAPTL entries (with the same ID) referencing two different HADACRI entries with the same refinement regions are thus required: SUBCASE 1

... HADAPT =

1

BEGIN BULK

... HADAPTL

1

111

ALL

HADAPTL

1

222

ALL

HADACRI

111

1

f

HADACRI

222

3

X1

Z1

X2

Y1

Y2

Z2

... ENDDATA

Each HADACRI requests different refinement criteria (TYPE=1 and TYPE=3) with different criteria specific parameters. Figure 2-67 shows the sequence of meshes obtained during the adaptive mesh refinement process. Notice that both refinement criteria are combined to produce one single refined mesh.

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64 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-67

Different refinement criteria applied to the same refinement region

Combination of Subcases (SOL 101) or Static Steps (SOL 400) with Error Indicator Based Criterion The error indicator is computed using the finite element stresses and measures indirectly the stress discontinuity across interelement boundaries. When multiple load cases are defined, multiple finite element stress solutions are obtained (one for each load case) and therefore, multiple instances of the error indicator are computed. In this case, the user can select any individual instance of the computed error indicator or any combination of instances to create a refined mesh. To this end, multiple Case Control commands HADAPT (one for each load case) referencing a single HADAPTL Bulk Data entry with its corresponding HADACRI Bulk Data entry are required. Consider by way of example the analysis of a cylindrical shell under the action of two different load cases, each consisting of a concentrated force applied at different heights (Figure 2-68, Figure 2-69, Figure 2-70). The error indicator might be computed using either the first load case only (Figure 2-68), the second load case only (Figure 2-69), or the combination of both load cases (Figure 2-70).

Main Index

CHAPTER 2 65 Adaptive Meshing

Every load case that should be considered for the computation of the error indicator must include an HADAPT Case Control command referencing a unique HADAPTL Bulk Data entry:

Error Indicator Based on Load Case 1 (Figure 2-68)

Error Indicator Based on Load Case 2 (Figure 2-69)

Error Indicator Based on the Combination of Load Case 1 and Load Case 2 (Figure 2-70)

SUBCASE 1 … HADAPT = 1 SUBCASE 2 …

SUBCASE 1 …

SUBCASE 1 … HADAPT = 1 SUBCASE 2 … HADAPT = 1

SUBCASE 2 … HADAPT = 1

BEGIN BULK

... HADAPTL

1

111

ALL

HADAPTL

1

222

ALL

ENDDATA

One single pair of Bulk Data entries HADPTL and HADACRI are required. The unique HADAPTL entry must be referenced either by an HADAPT Case Control command included as part of the first load case (Figure 2-68), or included as part of the second load case (Figure 2-69), or included at both load cases (Figure 2-70). Figure 2-68, Figure 2-69 and Figure 2-70 show the sequence of meshes obtained during the adaptive

mesh refinement process on the cylindrical shell subjected to two independent load cases on each one of these three possibilities.

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66 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-68

Main Index

Sequence of meshes and deformed configuration obtained using the error indicator based criterion applied to the first load case

CHAPTER 2 67 Adaptive Meshing

Figure 2-69

Main Index

Sequence of meshes and deformed configuration obtained using the error indicator based criterion applied to the second load case

68 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Figure 2-70

Sequence of meshes and deformed configuration obtained using the error indicator based criterion applied to both the first and second load cases

Output User Information Messages (.f06 File) The output requests for displacements, stresses, forces, etc., are automatically honored for each and all the iterations of the adaptive mesh refinement loop (Figure 2-71). Thus, for example, if DISPLACEMENT=ALL is specified in the case control section of the input file, then the grid point displacements will be written to the .f06 file not only for the initial mesh, but for all the subsequent meshes created during the mesh refinement process. At the end of each refinement cycle in the adaptive mesh refinement loop (Figure 2-71) the following user information message is printed to the .f06 file to signal the end of the analysis supported on the current mesh and beginning of a new analysis supported on the refined mesh obtained from the previous: -----------------------------------------------------* * * E N D O F A N A L Y S I S #: 2 * * * ------------------------------------------------------

Main Index

CHAPTER 2 69 Adaptive Meshing

The total number of elements meeting the user’s specified criterion and the total number of elements actually refined is reported to the .f06 at the end of each successful refinement instance (step 3 and 4 in Figure 2-71) and prior to the transference of analysis data between unrefined and refined meshes (step 5 in Figure 2-71).

Figure 2-71

User information messages reporting the progress of the adaptive mesh refinement loop

Notice that the number of elements actually refined will be in general different from the number of elements meeting the refinement criterion because the refinement is propagated from the latter to the neighbors according to the set of implicit propagation rules described in Propagation of Refinement, 37. When the error indicator based criterion is selected, a user message is printed to the .f06 file informing the total number of elements scanned for the computation of the error indicator, the mean square average over the whole mesh of the local error indicator and the relative change of this magnitude with respect to the previous iteration in the adaptive mesh refinement loop:

-----------------------------------------------------GLOBAL NUMBER OF ELEMENTS: 64 AVERAGE ERROR INDICATOR: 3.522044E+04 CHANGE IN AVERAGE ERROR INDICATOR: 1.389418E+01 % ------------------------------------------------------

It bears emphasis that the error indicator is not an error estimator in the sense that its numerical value does not measure the actual (absolute) error but gives rather a relative assessment of where the mesh should be refined.

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70 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

If no elements meet the user specified criterion or no elements are actually refined, the adaptive mesh refinement loop is terminated and corresponding messages are printed to the F06 file. Output Files for Postprocessing in MD Patran or SimX A request for the creation of post processing files (“.xdb” using PARAM,POST,0 or “.op2” using PARAM,POST,-2) is automatically honored for each and all analysis instances in the adaptive mesh refinement loop. Different postprocessing files are automatically created in the same directory and with the same name as the input file and with the extension “i.xdb” or “i.op2” where i is the iteration counter in the adaptive mesh refinement loop. Thus, for example, if the input file is fender.dat, then, PARAM,POST,0 will create the sequence of files fender.xdb fender.1.xdb fender.2.xdb fender.3.xdb … fender.i.xdb … while the sequence of files created via PARAM,POST,-2 will be called. fender.op2 fender.1.op2 fender.2.op2 fender.3.op2 … fender.i.op2 … The first file in the sequence will contain postprocessing data corresponding to the initial mesh and analysis results and subsequent files will contain postprocessing information for each refined mesh created during the adaptive mesh refinement process. All files are assigned to the same logical FORTRAN units which are internally closed at the end of each mesh refinement cycle and renamed with the appended extensions “i.xdb” or “i.op2” prior to the beginning of the subsequent cycle. When using PARAM,POST,0, the user can specify a non default logical FORTRAN unit number to write postprocessing data (using the parameter GEOMU) and assign a non default physical file name to this user specified logical FORTRAN unit (using the ASSIGN statement in the File Management Section). Similarly, when using PARAM,POST,-2, the user can request the use of a non-default logical FORTRAN unit number to write postprocessing data (using the parameter OUNIT2) and assign a non default physical file name to this users specified logical FORTRAN unit. In these cases, the user’s specified logical FORTRAN unit and physical file name will be used (with the appended extension “i.xdb” or “i.op2”) in the creation of the sequence of postprocessing files.

Main Index

CHAPTER 2 71 Adaptive Meshing

Bulk Data File Images of the Sequence of Refined Meshes During the adaptive mesh refinement process, new elements, new grid points, new boundary conditions, new multipoint constraints and new pressure loads are created automatically. Furthermore, contact bodies are internally redefined to subtract refined elements and replace them by their children elements. Bulk data file images containing the new mesh and analysis data created after each refinement cycle is automatically generated prior to the beginning of each analysis cycle. Each bulk data file image is created in the same directory and with the same name as the input file and with the extension “.seid.i.bdf” where seid is the superelement ID (0 for models with no superelements) and i is the iteration counter in the adaptive mesh refinement loop. Thus, for example, if the input file is fender.dat and contains no upstream superelements (only the residual structure, i.e. SEID=0), then the sequence of bulk data files created automatically will be named: fender.0.1.bdf fender.0.2.bdf fender.0.3.bdf … fender.0.i.bdf … If, for example, an input file engine.dat contains three upstream superelements labeled with SEID 7 and 24 (in addition to the residual structure with SEID=0) then the following sequence of bulk data file images will be created: engine.0.1.bdf engine.0.2.bdf engine.0.3.bdf … engine.0.i.bdf …

engine.7.1.bdf engine.24.1.bdf engine.7.2.bdf engine.24.2.bdf engine.7.3.bdf engine.24.3.bdf engine.7.i.bdf engine.24.i.bdf

These bulk data file images might be used as the starting point for the creation of a new analysis input files supported on any of the refined mesh obtained during the adaptive mesh refinement cycle.

Guidelines and Limitations Modeling Guidelines • The number of elements created during refinement grows exponentially. If on each refinement iteration i , a fraction f i of the total number of elements N i is refined by subdividing each element of this fraction into M children elements (with M Z 2 for line elements, M Z 4 for surface elements and M Z 8 for volume elements), then, the total number of element at iteration i H 1 will be: Ni H 1 Z Ni Ó fi Ni H fi Ni ⋅ M Z Ni ( 1 H fi ( M Ó 1 ) )

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72 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Therefore, if the fraction f i remains approximately constant during the mesh refinement process, i.e., if f i ≅ f with f a constant independent of i , then the number of elements at iteration i will be given by the estimate Ni Z N0 ( 1 H f( M Ó 1) )

i

where N 0 is the number of elements in the initial mesh (the mesh provided by the user). For example, in a surface mesh ( M Z 4 ) and if approximately 1/3 of the elements are refined on each refinement iteration ( f Z 1 ⁄ 3 ) , then the number of elements at iteration i will be roughly i 3 N i Z N 0 2 . Thus an initial structure with thousands of shell elements ( N 0 Z O ( 10 ) ) will be refined 6 into millions of shell elements ( N 0 Z O ( 10 ) ) in about 10 iterations. In a 3D mesh ( M Z 8 ) , and if approximately 1/3 of the elements are refined on each iteration, the total number of elements expected at iteration i will be approximately N i Z N 0 ( 10 ⁄ 3 ) i . Thus, a mesh with thousands of 3D elements will be refined into millions of 3D elements in about 6 iterations. • Exponential growth of the number of elements implies that adaptive mesh refinement is memory

intensive. As a rough estimate, each refinement iteration i requires on the order of 100 ⋅ N i integer words of memory where N i is the number of elements of the mesh created during refinement iteration i . • Instead of the traditional modeling practice, the user should start the process with an initial mesh

preferably coarse which will be refined automatically and selectively according to the refinement criterion. • The effectiveness of the refinement process depends on an appropriate detection of geometric

corners, creases and edges and interfaces between elements of different properties. Detection of geometric features requires the selection of a proper value for the Geometric Feature parameter (PARAM,VARPHI), (see Location of New Grid Points, 20 and Detection of Geometric Features and Material and Superelement Interfaces, 49). • When the initial mesh is very coarse and the boundary of the structure under analysis is poorly

approximated, it is recommended to activate the automatic projection of mid-edge nodes onto a smooth approximation of the mesh boundary using SNAPMETH=1 (see Detection of Geometric Features and Material and Superelement Interfaces, 49). Convergence of the mesh refinement process might be dramatically improved using this method. • The user should avoid the use of MPC sets 90000000 to 99999999 which are reserved for hanging nodes constraints generated during the adaptive mesh refinement process (Hanging Nodes and Multipoint Constraints on Hanging Nodes, 23) • When mesh refinement is restricted to a specific mesh refinement region (by selecting

WHEREMET=PROP or WHEREMET=SUPER in the HADAPTL Bulk Data entry), the user should expect refinement also in a few layers away from the refinement region due to the enforced implicit propagation ruleMs (see Propagation of Refinement, 37). • In partitioned superelements, the HADAPT entry must be specified in the main bulk data

section. Entries specified in the Bulk Data Section corresponding to individual parts (sections beginning with BEGIN SUPER) will be ignored.

Main Index

CHAPTER 2 73 Adaptive Meshing

• When using regular superelements, the Bulk Data Section must begin with BEGIN SUPER as

opposed to BEGIN BULK in order to the refinement to be appropriately propagated across superelement boundaries. If BEGIN BULK is used, grid points on the superelement boundaries will be duplicated and not shared by the joining superelements. • In SOL 400 (ANALYSIS=STATICS), multiple load cases should be listed in different STEP

entries and within one single SUBCASE entry. By contrast, in SOL 101, multiple load cases should be listed under multiple SUBCASE entries. Limitations • The error indicator based refinement criterion can be used with surface or volume elements, but not with line elements. The latter can be subdivided with any other of the refinement criteria, or when they are attached to the boundary of a surface or volume elements • Refinement of CBEAM, CBEAM3 with offsets or warping are not supported. Refinement of

CBAR with offsets is not supported. • Temperature loads are not supported. Similarly, the HEATSTAT=YES option in SOL 101 that

runs a preliminary thermal analysis to compute thermal loads for a subsequent structural analysis is not supported. • For the current release, a mesh can be refined but not unrefined. • Adaptive Mesh refinement cannot be combined with p-adaptivity. • Adaptive Mesh refinement can be used either in structural linear analysis in SOL 101 or linear

structural analysis in SOL 400 (ANALYSIS=STATICS). It cannot be used in any other analysis type in SOL 400. • In SOL 400, an adaptive linear analysis cannot be chained with any other analysis and should be

run as an independent and unique SUBCASE, possibly with multiple STEPS to enforce different load cases. All STEPS must be preceded by ANALYSIS=STATIC.

Main Index

74 MD Nastran R3 Release Guide Local Adaptive Mesh Refinement

Main Index

Chapter 3: Advanced Integrated Nonlinear and Contact

3

Main Index

MD Nastran R3 Release Guide

Advanced Integrated Nonlinear and Contact 

SOL 400 Performance Enhancements



SOL 400 Advanced Heat Transfer



BCONTACT=ALLBODY



Linear Perturbation and Brake Squeal Analyses in SOL 400



SOL 400 Materials and Elements



Enhancements to Connector Elements



Adaptive Time Stepping Scheme Enhancements for Quasi-Static Analysis



Contact and Adaptive Time Stepping Enhancements for Transient Dynamic Analysis



Progressive Failure Analysis with a Micromechanical Module



3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-toSurface and Edge-to-Edge



Explicit Nonlinear - SOL 700



Arc-Length Methods (Pre-release)



Analysis Chaining

76 MD Nastran R3 Release Guide SOL 400 Performance Enhancements

SOL 400 Performance Enhancements Dramatic performance improvements have been made to SOL 400 for the MD Nastran R3 release. For specific details on these improvements, please see Linear and Nonlinear Contact Analysis (Ch. 6).

Main Index

CHAPTER 3 77 Advanced Integrated Nonlinear and Contact

SOL 400 Advanced Heat Transfer Outline of New SOL 400 Heat Transfer Capabilities • Added new nonlinear elements such as composite thermal elements 3D. Composite thermal 2D

using PCOMP or PCOMPG. • The performance for the hemi-cube view factor increases proportionally as the model size

increases. A speed up of 33 times has been observed in the test case. • New output added for multiple layers of output for composite thermal element. • Transient thermal analysis using SPCD and SPC1 • Chaining analysis is now available from the thermal analysis step into the structure analysis step

in a single run. • Minimal Input test file change from previous existing test file in SOL 153 or SOL 159 into

SOL 400 SOL 400 is the most comprehensive thermal solver that exists in the MSC product line. It has integrated the existing nonlinear steady state thermal SOL 153 and nonlinear transient thermal SOL 159 and all its functionalities. In addition, 21 new finite heat transfer elements that included rod, planar 2D, membrane 2D element., Shell 3D element, and solid elements have been implemented. Also we have the 2D composite heat transfer elements with multiple layers using either PCOMP or PCOMG that referenced the MAT4 and MAT5 entries. The advantage of using 2D composite heat transfer is that the user can have 3D thermal analysis simulated on the 2D structure.

Nastran Type ROD

Req Nodes

Type Code

INT Code

NL_PROP

2

ROD

L

PRODN1

CQUAD4

4

DCT

L

PSHLN1

CQUAD8

8

DCT

Q

PSHLN1

CTRIA3

3

DCT

L

PSHLN1

CQUAD4

4

PLST

L

PSHLN2

CTRIA3

3

PLST

L

PSHLN2

CQUAD8

8

PLST

Q

PSHLN2

CTRIA6

6

PLST

Q

PSHLN2

CQUAD4

4

COMP

L

PLCOMP

CQUAD8

8

COMP

Q

PLCOMP

Shell(3D)

Planar(2D)

Planar Composite

Main Index

78 MD Nastran R3 Release Guide SOL 400 Advanced Heat Transfer

Nastran Type

Req Nodes

Type Code

INT Code

NL_PROP

Membrane element CQUAD4

4

MB

L

PSHLN1

CTRIA3

3

MB

L

PSHLN1

CQUAD8

8

MB

Q

PSHLN1

CTRIA6

6

MB

Q

PSHLN1

CHEXA

8

SOLI

L

PSLDN1

CHEXA

20

SOLI

Q

PSLDN1

CTETRA

4

SOLI

L

PSLDN1

CTETRA

10

SOLI

Q

PSLDN1

CPENTA

6

SOLI

L

PSLDN1

Solid Element

Solid Composite elements

N PSHLN1

CHEXA

8

SLCO

L

PLCOMP

CHEXA

20

SLCO

Q

PLCOMP

2

3

PID

MID1

4

5

6

7

8

9

10

ANALY

C3

BEH3H

INT3H

C4

BEH4H

INT4H

C6

BEH6H

INT6H

C8

BEH8H

INT8H

Let us say you want to use the SHELL 3D element. CQUAD4,101,1,9,10,12,11 PSHELL,1,5,0.1 PSHLN1,1,5,,,IH ,C4,,,DCT,L MAT4,5,20.0 Here is an example using the nonlinear extension for the CHEXA element. psldn1,1,1,,,ih PSOLID 1 CHEXA 5958

Main Index

1 1 7357

0 391 7356

3742

3743

422

7355

7358

CHAPTER 3 79 Advanced Integrated Nonlinear and Contact

N PSLDN1

2 PID

3

4

5

MID1

6

7

8

9

10

ANALY

C4

BEH4H

INT4H

C6

BEH6H

INT6H

C8

BEH8H

INT8H

C10

BEH10H

INT10H

C20

BEH20H

INT20H

The following is an example using a 2D composite heat transfer element: MD Nastran test file: 2d_comp.dat Boundary conditions: 1. Heat flux of 50 Btu/hr/inch2 impose on the top surface 2. Edge is held at 20 degree F The PID of the CQUAD4 points to the PCOMP Bulk Data entry, and a PSHLN1 with ID 1 and PCOMP specify number of layers, material ID and ply angles. In this case we have a total of three layers with -45, 90,0 degree ply angles with call out to MAT5 ID of 1,2,1 respectively. pshln1,1,1,,,ih PCOMP,1 ,1,0.1,-45.0,,2,0.1,90.0 ,2,0.1,0.0 $ CQUAD4 1 1 CQUAD4 2 1 CQUAD4 3 1 CQUAD4 4 1 MAT5 1 .2 MAT5 2 1.

Main Index

1 2 4 5

4 5 7 8

5 6 8 9 .5 2.

2 3 5 6 .6 3.

80 MD Nastran R3 Release Guide SOL 400 Advanced Heat Transfer

NLSTRESS=all will give you the following new output.

0

SUBCASE 1

LOAD STEP =

1.00000E+00

G R A D I E N T S ELEMENT ID 1

PLY ID 1

2

3

A N D

INTEG. POINT ID 1 2 3 4 1 2 3 4 1 2 3 4

TOTAL AVERAGE

F L U X E S

F O R

L A Y E R E D

E L E M E N T S

A D I E N T S----------------F L U X E S----------------T E M PT-Y T-Z F-X F-Y F-Z T 1.142E+02 0.000E+00 -1.692E+01 -3.988E+01 0.000E+00 3.206E+01 1.126E+02 0.000E+00 -1.668E+01 -3.931E+01 0.000E+00 3.189E+01 1.142E+02 0.000E+00 -1.636E+01 -3.963E+01 0.000E+00 6.503E+01 1.126E+02 0.000E+00 -1.612E+01 -3.907E+01 0.000E+00 6.439E+01 1.142E+02 0.000E+00 1.175E+00 -1.142E+02 0.000E+00 3.206E+01 1.126E+02 0.000E+00 1.175E+00 -1.126E+02 0.000E+00 3.189E+01 1.142E+02 0.000E+00 4.387E+00 -1.142E+02 0.000E+00 6.503E+01 1.126E+02 0.000E+00 4.387E+00 -1.126E+02 0.000E+00 6.439E+01 1.142E+02 0.000E+00 5.877E-01 -2.284E+02 0.000E+00 3.206E+01 1.126E+02 0.000E+00 5.877E-01 -2.252E+02 0.000E+00 3.189E+01 1.142E+02 0.000E+00 2.193E+00 -2.284E+02 0.000E+00 6.503E+01 1.126E+02 0.000E+00 2.193E+00 -2.252E+02 0.000E+00 6.439E+01

-1.391E+00

1.134E+02

-1.646E+00 -5.061E+01 0.000E+00 -4.116E+00 -1.265E+02

Using the 3D composite heat transfer element: MD Nastran test file: 3d_pcomp.dat pcompls,1,-1,,,ih ,c20,,,slco,q

Main Index

C O M P O S I T E

-------G R T-X -5.877E-01 -5.877E-01 -2.193E+00 -2.193E+00 -5.877E-01 -5.877E-01 -2.193E+00 -2.193E+00 -5.877E-01 -5.877E-01 -2.193E+00 -2.193E+00

0.000E+00 0.000E+00

4.834E+01

STEP 1

CHAPTER 3 81 Advanced Integrated Nonlinear and Contact

,101,1,0.001 ,102,1,0.001 CHEXA 1 768 769

1 771 772

23 22 777

21 14 770

1 2 776

composite group number 1 number of layers 12 solid composite layer direction -1 allowable interlaminar bond shear stress 0.0000 actual layer thickness is given below layer layer id mat id thickness ply angle 1 112 1 1.000E-03 0.000E+00 2 111 1 1.000E-03 0.000E+00 3 110 1 1.000E-03 0.000E+00 4 109 1 1.000E-03 0.000E+00 5 108 1 1.000E-03 0.000E+00 6 107 1 1.000E-03 0.000E+00 7 106 1 1.000E-03 0.000E+00 8 105 1 1.000E-03 0.000E+00 9 104 1 1.000E-03 0.000E+00 10 103 1 1.000E-03 0.000E+00 11 102 1 1.000E-03 0.000E+00 12 101 1 1.000E-03 0.000E+00

Main Index

3 15 775

773 774

766 767

82 MD Nastran R3 Release Guide SOL 400 Advanced Heat Transfer

The following is a quartz lamp model. Boundary Conditions: • The volumetric heating for the center lamp is 50 watt/cubic cm. • There is view factor calculation for the complete enclosure including the third-body shading of

the inner Quartz lamp • Free convection to air at 20 degrees C occurs on the outer surface with h=5 watt/cm**2*C

MD Nastran test file: quartz_lamp_hemi.dat

Main Index

CHAPTER 3 83 Advanced Integrated Nonlinear and Contact

Hemicube: 321.3 cpu sec Gaussian (VIEW3D): 10751.9 cpu sec A speed up of 33 times.

Main Index

84 MD Nastran R3 Release Guide SOL 400 Advanced Heat Transfer

Number of CHBDYG Elements

Hemicube

Gaussian I

1440

48.3 sec

182.6 sec

19594

321.3 sec

10751.9 sec

76243

4851.9 sec

259251 sec

We can see that the performance is 4 times faster for this medium size model. The HEMICUBE method is selected by this NLMOPTS,HEMI,1 SOL 400 CEND ANALYSIS = HSTAT TITLE = MSC/NASTRAN job created on 29-Oct-98 at 16:46:24 ECHO = NONE MAXLINES = 999999999 TEMPERATURE(INITIAL) = 1 $ Direct Text Input for Global Case Control Data SUBCASE 1 $ Subcase name : Default SUBTITLE=Default NLPARM = 5 SPC = 1 LOAD = 2 THERMAL(SORT1,PRINT)=ALL FLUX(SORT1,PRINT)=ALL $ Direct Text Input for this Subcase BEGIN BULK nlmopts,hemi,1 PARAM POST 0 PARAM AUTOSPC YES PARAM TABS 273.149 PARAM* SIGMA 5.6699-12

How Do We Convert an Existing Heat Transfer Test File from SOL 153 into SOL 400? SOL 153 $ Direct Text Input for Executive Control CEND ANALYSIS = HEAT TITLE = workshop 1 ECHO = NONE TEMPERATURE(INITIAL) = 1 Data SUBCASE 1 SUBTITLE=Default NLPARM = 1 SPC = 1 LOAD = 2 THERMAL(SORT1,PRINT)=ALL FLUX(SORT1,PRINT)=ALL OLOAD(SORT1,PRINT)=ALL SPCFORCES(SORT1,PRINT)=ALL $ Direct Text Input for this Subcase BEGIN BULK

Main Index

CHAPTER 3 85 Advanced Integrated Nonlinear and Contact

SOL 400 $ Direct Text Input for Executive Control CEND ANALYSIS = HSTAT TITLE = workshop 1 ECHO = NONE TEMPERATURE(INITIAL) = 1 SUBCASE 1 $ Subcase name : Default SUBTITLE=Default NLPARM = 1 SPC = 1 LOAD = 2 THERMAL(SORT1,PRINT)=ALL FLUX(SORT1,PRINT)=ALL OLOAD(SORT1,PRINT)=ALL SPCFORCES(SORT1,PRINT)=ALL BEGIN BULK

How Do We Convert SOL 159 into SOL 400? 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 BEGIN BULK TSTEPNL,100,7500,1.0,1,ADAPT,,,U ID MSC-NASTRAN V68 SOL 400 TIME 10 CEND TITLE = EXAMPLE 7B ANALYSIS = HTRAN THERMAL = ALL FLUX = ALL SPCF = ALL OLOAD = ALL IC = 20 TSTEPNL = 100 DLOAD = 200 BEGIN BULK TSTEPNL,100,7500,1.0,1,ADAPT,,,U

The only exception to this conversion in transient thermal analysis is when you have enforced temperature as a function of time, or having convection coefficient as a function of time, or radiation view factor as a function of time. In SOL 400, MD Nastran uses SPCD and SPC1 to impose enforced temperature boundary conditions instead of large stiffness method where u=P/K. Therefore if the test file has Bulk Data entry TEMPBC, then you need to replace it with SPCD and SPC1.

Main Index

86 MD Nastran R3 Release Guide SOL 400 Advanced Heat Transfer

To Convert SOL 159 Models to SOL 400 Models 1. Executive Control Section - change SOL 159 to SOL 400. 2. Case Control Section - replace ANALYSIS=HEAT by ANALYSIS=HTRAN, also add SPC if all temperature boundary conditions are transient (the following Case 3b). 3. Bulk Data Section - replace the “TRAN” type TEMPBC by SPC1 and SPCD. The details are explained below. a. If all temperature boundary conditions are constant, no changes are required. b. If all temperature boundary conditions are transient, replace TEMPBC by SPC1 and SPCD and modify TLOAD1. For example, replace the following entries of SOL 159 model: TLOAD1,40,400,,,4000 TEMPBC,400,TRAN,300.0,99 by SPC = 111 (Case CC) : TLOAD1,40,400,,1,4000 SPCD,400,99,,300.0 SPC1,111,,99 c. If a model has both constant and transient temperature boundary conditions, all boundary conditions must be converted into SPC1 and SPCD. For example, replace the following entries of SOL 159 model: DLOAD,222,1.0,1,0,30,1.0,40 TLOAD1,40,400,,,4000 TEMPBC,400,TRAN,300.0,99 SPC,111,98,,20.0 by DLOAD,222,1.0,1,0,30,1.0,40, 1.0,50 TLOAD1,40,400,,1,4000 SPCD,400,99,,300.0 SPC1,111,,99 TLOAD1,50,500,,1,5000 SPCD,500,98,,20.0 SPC1,111,,98 TABLED1,5000,,,,,,,, ,0.0,1.0,1000.0,1.0,ENDT 2D Transient Thermal Analysis Reference: NAFEM Thermal benchmark problems. 1. Adiabatic at the left end 2. Qvol(temp)= 1.0e7*(1+0.005*T)

Main Index

CHAPTER 3 87 Advanced Integrated Nonlinear and Contact

3. Initially the temperature is at zero degree everywhere 4. The model is 0.01 m by 0.01 m The analytical solution is at: X=0.005 m, time=2 sec, Temp=3.81 C K=52 w/m.C, Cp=460 J/Kg.C, Density=7850 Kg/m3 NASTRAN test deck: vtest8_pc.dat This point corresponds to grid 6 for the model.

Figure 3-1

Main Index

Finite element model

88 MD Nastran R3 Release Guide SOL 400 Advanced Heat Transfer

Figure 3-2

Main Index

Grid 6 at time equal to 2 is 3.80258

CHAPTER 3 89 Advanced Integrated Nonlinear and Contact

Time step = 0.025 sec

Temp (CQUAD4)

Temp(DCT)

Analytical =3.81

3.802579

3.80284

$ANALYTICAL FOR GRID 6 AT X=0.005 AT TIME=2 SEC IS 3.81 SOL 400 $ Direct Text Input for Executive Control CEND ANALYSIS = HTRAN TITLE = MSC.Nastran job created on 20-Mar-03 at 10:11:51 ECHO = NONE SPC = 1 IC = 1 $ Direct Text Input for Global Case Control Data SUBCASE 1 $ Subcase name : tran SUBTITLE=tran TSTEPNL = 1 DLOAD = 2 THERMAL(SORT2,PRINT)=ALL FLUX(SORT2,PRINT)=ALL OLOAD(SORT2,PRINT)=ALL SPCFORCES(SORT2,PRINT)=ALL $ Direct Text Input for this Subcase BEGIN BULK PARAM POST 0 PARAM PRGPST NO TSTEPNL,1,100,.025,10 ,.001 ,,0 $ Direct Text Input for Bulk Data $ Elements and Element Properties for region : plate PSHELL 1 1 1. $ Pset: "plate" will be imported as: "pshell.1" CQUAD4 1 1 1 2 13 12 AND ETC CQUAD4 10 1 10 11 22 21 $ Referenced Material Records $ Material Record : mat4 $ Description of Material : Date: 20-Mar-03 Time: 10:08:36 MAT4,1,52.,460.0,7850.,,,1.0 MATT4,1,,,,,,123 TABLEM2,123 ,0.0,1.0E7,3.0,1.015E7,6.0,1.03E7,10.0,1.05E7, ,20.0,1.10E7,50.0,1.25E7,100.0,1.5E7,200.0,2.0E7 ,ENDT $ Nodes of the Entire Model GRID 1 0. 0. 0. GRID 2 .001 0. 0. AND ETC GRID 22 .01 .01 0. $ Loads for Load Case : tran TLOAD1 4 3 1 DLOAD 2 1. 1. 4 $ Fixed Temperatures of Load Set : right SPC 1 11 1 0. 22 1 0. $ Volumetric Heat Generation of Load Set : qvol

Main Index

90 MD Nastran R3 Release Guide SOL 400 Advanced Heat Transfer

QVOL,3,1.0,,1,THRU,10 $ Referenced Dynamic Load Tables $ Constant Load Table TABLED1 1 0. 1. 1000. 1. ENDT $ Initial Temperatures from Temperature Load Sets TEMP 1 11 0. 22 0. $ Default Initial Temperature TEMPD 1 0. $ Referenced Coordinate Frames ENDDATA 88c8f88b

In transient thermal analysis you can have time adaptive scheme. The advantage of using adaptive scheme is that you can get to the end time with fewer steps. In SOL 400 the adaptive scheme is turn ON by setting the NO field (5) on the TSTEPNL Bulk Data entry to a minus 1. TSTEPNL,5,100,5.0,-1,adapt,,,u

The No field is time step interval for output. For a large transient thermal problem using the adaptive time step can be much more efficient. The adaptive method is the recommend method for SOL 400 transient thermal analysis. The analysis chaining is now available from heat transfer analysis into the structure analysis. Previously in MD Nastran you could run a linear thermal analysis followed by the linear static analysis in a single execution by using PARAM,HEATSTAT,YES. For example: SOL 101 CEND ECHO = sort SUBCASE 1 THERMAL(PRINT) = ALL SPCFORCE(PRINT) = ALL FLUX(PRINT) = ALL SPC = 1 load=101 SUBCASE 2 temp(load)=1 disp=all stress=all spc=8 BEGIN BULK param,heatstat,yes

However, the restriction using the SOL 101 is that the thermal analysis must be linear, that is there is no radiation or thermal conductivity or convection coefficient as a function of temp. Now in SOL 400 the user can run an analysis chaining, with a nonlinear thermal analysis, followed by nonlinear structural analysis.

Main Index

CHAPTER 3 91 Advanced Integrated Nonlinear and Contact

Figure 3-3

Thermal boundary conditions

1. Apply a 30 btu/hr/in2 on one face 2. Radiation to space at 70 F with view factor=1 3. The thermal conductivity is at 0.3 btu/hr/in.F 4. Sigma is equal to 1.1903e-11

Main Index

92 MD Nastran R3 Release Guide SOL 400 Advanced Heat Transfer

Main Index

Figure 3-4

Temperature contour

Figure 3-5

Structure boundary (conditions fixed on one end)

CHAPTER 3 93 Advanced Integrated Nonlinear and Contact

Figure 3-6

Thermal displacement

MD NASTRAN test file: hs_chain1.dat SOL 400 CEND TITLE = MD Nastran job created on 08-Feb-08 at 10:24:41 ECHO = NONE TEMPERATURE(INITIAL) = 1 $ Direct Text Input for Global Case Control Data SUBCASE 1 STEP 1 analysis=hstat SUBTITLE=Default NLPARM = 1 SPC = 1 LOAD = 2 THERMAL(SORT1,PRINT)=ALL FLUX(SORT1,PRINT)=ALL tstru=9 STEP 2 analysis=nlstat temp(load)=9 NLPARM= 1

Main Index

94 MD Nastran R3 Release Guide SOL 400 Advanced Heat Transfer

SPC=2 disp=all stress=all BEGIN BULK param,lgdisp,1 In this SOL 400 analysis chaining we have two steps. The first step is the nonlinear thermal analysis indicated by analysis=hstat, and the second step is the nonlinear static analysis using the final temperature from step 1 as the temperature load for step 2. If one does not specify the TSTRU option in the first step, then the default TEMP(LOAD) =1. If you want to change the TEMP(LOAD) ID, you can use the TSTRU option which allows you to change the ID number for the TEMP(LOAD)=n.

Main Index

CHAPTER 3 95 Advanced Integrated Nonlinear and Contact

BCONTACT=ALLBODY Introduction The Case Control command BCONTACT is used to request 3-D contact analysis in SOLs 101 and 400. The format BCONTACT = n, where n is the ID number of all corresponding BCTABLE (required), BCMOVE (optional), and BCHANGE (optional) Bulk Data entries, is supported in MD Nastran R2. In this release, a new format of the BCONTACT=ALLBODY Case Control command is added to support 3-D Contact. The BCONTACT=ALLBODY functionality was a pre-release capability in the MD Nastran R2.1 release. For MD Nastran R3 this is now a production capability.

Benefits The use of BCONTACT=ALLBODY can save considerable time in preparing the contact input (see the following example).

Input Unlike BCONTACT = n, which selects the contactable bodies on the BCTABLE Bulk Data entry when BCONTACT=ALLBODY is specified in the Case Control Section, all BCBODYs listed in the file are selected as contactable bodies to each other. Also, since there is no BCTABLE referenced, default values are used in the BCTABLE fields. To specify BCMOVE or BCHANGE Bulk Data entries when BCONTACT=ALLBODY, two new Case Control commands, BCMOVE = n and BCHANGE = n, are introduced in this release. These new commands can also be used to overwrite the SID = n from the BCONTACT = n case.

Output There is no new output for BCONTACT=ALLBODY.

Limitation Although potentially convenient, it is strongly recommended to use BCONTACT=ALLBODY carefully. It is appropriate for simple models, or for checking out runs, to use BCONTACT=ALLBODY. Setting BCONTACT=ALLBODY without careful study may produce unacceptable results and poor convergence.

Example The test problem nlc021a.dat can be used as an example to show the advantage of BCONTACT=ALLBODY. This example is a transient analysis in 2-D contact that uses four deformable contact bodies and one rigid contact body. Each of these bodies is contactable, which yields ten possible

Main Index

96 MD Nastran R3 Release Guide BCONTACT=ALLBODY

combinations of contact. With four self-contacts of the deformable bodies, excluding the rigid body, there are a total of fourteen possible combinations. 1. Bodies 6 and 13 contact. 2. Bodies 6 and 14 contact. 3. Bodies 6 and 16 contact. 4. Bodies 6 and 17 contact. 5. Bodies 13 and 14 contact. 6. Bodies 13 and 16 contact. 7. Bodies 13 and 17 contact. 8. Bodies 14 and 16 contact. 9. Bodies 14 and 17 contact. 10. Bodies 16 and 17 contact. 11. Body 13 self-contacts. 12. Body 14 self-contacts. 13. Body 16 self-contacts. 14. Body 17 self-contacts. When BCONTACT=1 is specified, the following BCTABLE Bulk Data entry is required, which must include fourteen slave and master pairs. BCTABLE

1 SLAVE MASTERS SLAVE MASTERS SLAVE MASTERS SLAVE MASTERS SLAVE MASTERS SLAVE MASTERS SLAVE MASTERS SLAVE

Main Index

16 0 FBSH 16 17 0 FBSH 16 17 0 FBSH 17 16 0 FBSH 14 17 0 FBSH 14 14 0 FBSH 14 16 0 FBSH 13 17 0 FBSH

0. 0 1.+20

14 0. 0 0.

0. 0 1.+20

0. 0 0.

0.

0. 0 1.+20

0. 0 0.

0.

0. 0 1.+20

0. 0 0.

0.

0. 0 1.+20

0. 0 0.

0.

0. 0 1.+20

0. 0 0.

0.

0. 0 1.+20

0. 0 0.

0.

0. 0 1.+20

0. 0 0.

0.

0.

0.

0

0.

0

0.

0

0.

0

0.

0

0.

0

0.

0

0.

0

0.

0.

0.

0.

0.

0.

0.

0.

CHAPTER 3 97 Advanced Integrated Nonlinear and Contact

MASTERS 13 SLAVE 14 0 FBSH MASTERS 13 SLAVE 13 0 FBSH MASTERS 13 SLAVE 16 0 FBSH MASTERS 6 SLAVE 17 0 FBSH MASTERS 6 SLAVE 14 0 FBSH MASTERS 6 SLAVE 13 0 FBSH MASTERS 6

0. 0 1.+20

0. 0 0.

0.

0. 0 1.+20

0. 0 0.

0.

0. 0 1.+20

0. 0 0.

0.

0. 0 1.+20

0. 0 0.

0.

0. 0 1.+20

0. 0 0.

0.

0. 0 1.+20

0. 0 0.

0.

0.

0

0.

0

0.

0

0.

0

0.

0

0.

0

0.

0.

0.

0.

0.

0.

Note that this long BCTABLE Bulk Data entry can be eliminated by setting BCONTACT=ALLBODY.

Main Index

98 MD Nastran R3 Release Guide Linear Perturbation and Brake Squeal Analyses in SOL 400

Linear Perturbation and Brake Squeal Analyses in SOL 400 Introduction Linear perturbation analyses, such as Normal Modes, Direct and Modal Complex Eigenvalues, have been implemented in SOL 400. The linear analysis is performed on top of a user-specified linearly or nonlinearly deformed structure configuration. Case Control command, NLIC, is utilized to select a static solution, which is either linear or nonlinear, from the solutions of loading history. The brake squeal analysis which is a combination of general contact with unsymmetrical friction force stiffness matrix and complex eigenvalue extraction is also implemented as a special application of linear perturbation analyses under the framework of the so-called analysis chaining in SOL 400. The system matrices of the linear perturbation analysis include the tangent stiffness matrix, which contains the effects of both linear and nonlinear elements. Damping effect are also included. The tangent stiffness matrix includes both geometrical and material nonlinearities, as well as the follower force stiffness. Contact constraints, either from a general contact or a permanent glued contact, are incorporated in the linear perturbation analyses.

Benefits Bringing the linear perturbation analyses into SOL 400 helps expand its analysis capacities beyond the existing nonlinear static and transient domain. With its flexible control structure of analysis chaining, users are allowed to reference the nonlinear solutions, where the linear perturbation analyses are based upon, at various load increments from different loading steps, without running multiple individual jobs or dealing with the restart. The general contact capability implemented in SOL 400 is available in the ensuing linear perturbation analysis. A major benefit of implementations is the brake squeal analysis, which embraces the full capacity of nonlinear analyses with contact offered by SOL 400.

Input A linear perturbation analysis is introduced by Case Control command, ANALYSIS, with a given value, such as MODES, DCEIG or MCEIG, for a specific analysis discipline. At least one STEP of a nonlinear (or linear) static analysis must precede the STEP of a linear perturbation analysis. Case Control command, NLIC, is used to point to a nonlinear solution, which is previously calculated and saved. For the brake squeal analysis, a new Case Control command, BSQUEAL, as well as a Bulk Data entry of the same name has been introduced. There are two Case Control approaches: One is the same as the general linear perturbation analysis where the brake squeal analysis is performed as a separate STEP

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CHAPTER 3 99 Advanced Integrated Nonlinear and Contact

from the STEP of a nonlinear static analysis. The other is the single-STEP approach in that both a nonlinear and the brake squeal analyses are executed in a single STEP. In a single-STEP approach, the user can choose either to run a complete loading step with the brake squeal analysis at either the pre-load or a given load increment, or alternatively to run only the brake squeal analysis at the specified load increment and exit the nonlinear iteration immediately afterward. Case Control Commands • ANALYSIS=MODES This is for Normal Modes analysis. A Case Control command, METHOD, must be present in the same STEP. • ANALYSIS=DCEIG

This is for Direct Complex Eigenvalue analysis. A Case Control command, CMETHOD, must be present in the same STEP. • ANALYSIS=MCEIG

This is for Modal Complex Eigenvalue analysis. Both Case Control commands, METHOD and CMETHOD, must be present in the same STEP. • BSQUEAL

This command activates the brake squeal analysis. It points to a Bulk Data entry, BSQUEAL, with the same set identification. BSQUEAL is SUBCASE-STEP selectable. In the single-STEP approach where ANALYSIS=NLSTATIC, the approach of the eigenvalues extraction for the brake squeal analysis is determined by how the Case Controls, CMETHOD and METHOD, are present. For instance, if BSQUEAL coexists with both CMETHOD and METHOD, then the modal approach is performed. Otherwise, if only CMETHOD is present, then the direct approach is executed. Bulk Data Entry • BSQUEAL This Bulk Data entry referenced by a Case Control command, BSQUEAL.

Output 1. The output of linear perturbation analyses shares the same data formats and data-blocks as their corresponding linear solution sequences, such as SOL 103, SOL 107 and SOL 110. 2. The solutions, such as stresses and strains, from a linear perturbation analysis are not superimposed on top of the nonlinear static solutions. 3. Data recovery of a linear perturbation analysis is performed in its current SUBCASE-STEP, while the solutions of the nonlinear analysis are output after all iterations are completed, except for the nonlinear PHASE II output.

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100 MD Nastran R3 Release Guide Linear Perturbation and Brake Squeal Analyses in SOL 400

Guidelines and Limitations 1. It is advised that the user put together all steps of linear perturbation analyses and place the group after the step(s) of nonlinear static analysis, for a better organization of the solution sequences. It is not recommended that the steps of nonlinear analyses are intertwined with the steps of linear perturbations. 2. Case Control command, NLIC, must be explicitly specified if the STEP of a linear perturbation analysis does not immediately follow the STEP of a nonlinear static analysis. 3. The linear perturbation analysis must be in the same SUBCASE as the nonlinear static analysis which it references. In other words, NLIC is not allowed to point to a nonlinear solution from a SUBCASE other than the current one. 4. Both super-elements and parts super-elements are not supported in the linear perturbation and brake squeal analyses. 5. Stresses, strains, and forces are not computed for those advanced nonlinear materials and elements (as introduced in the MD Nastran R2 Release Guide under section “SOL 400 Material and Elements”, as well as Nastran nonlinear elements, such as hyperelastic elements). 6. For the brake squeal analysis, there are two approaches. One is the so-called single-STEP approach which combines Case control commands, ANALYSIS=NLSTATIC, BSQUEAL, CMETHOD and/or METHOD in a single STEP. The other is the regular chaining approach with either explicitly or implicitly specified NLIC, along with ANALYSIS=DCEIG/MCEIG and BSQUEAL. In the latter approach, LOADFAC in NLIC overrides OMETH in Bulk Data entry, BSQUEAL. 7. In a brake squeal analysis, the rotating body, such as a brake disk or rotor, may not be completely constrained and acts like a floating body. To achieve a reliable convergent nonlinear static solution, it is helpful to add some insignificant spring element to the brake disk or rotor to constrain the floating movement. Floating bodies in an FE model are sometimes detrimental to the convergence of nonlinear iterations in SOL 400. However if the brake squeal analysis is performed in the pre-load state and BSONLY=YES in Bulk Data entry, BSQUEAL then the floating body is not a concern. 8. AVSTIF from Bulk Data entry, BSQUEAL, and the friction coefficients of contact bodies are primary sources to compute matrices of friction force and normal contact constraint stiffness. Friction-induced heat and thermo-mechanical coupling are not included.

Examples - Examples of Case Control Approaches Example 1: General Case Control Structure of Linear Perturbation Analyses The following is an example of Case Control paradigm used in linear perturbation analyses. The nonlinear static analyses are performed in the first three loading steps. The linear perturbations are then carried out in the following steps, with NLIC referencing the selected load factors from different steps. SUBCASE 1 STEP 1 ANALYSIS=NLST

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CHAPTER 3 101 Advanced Integrated Nonlinear and Contact

…... STEP 2 ANALYSIS=NLST …... STEP 3 ANALYSIS=NLST …... STEP 4 ANALYSIS=MODES NLIC STEP 1, LOADFAC, 0.2 METHOD=1 …... STEP 5 ANALYSIS=DCEIG NLIC STEP 2, LOADFAC, 0.5 CMETHOD=1 ...... Example 2: Case Control Structure of Single-STEP for Brake Squeal Analysis This is an example of the so-called single-STEP approach. The nonlinear static analysis is performed while a brake squeal analysis is requested. In this approach, the user can choose either to continue the nonlinear iterations after the brake squeal analysis is done until the whole nonlinear solution process is completed, or to exit the nonlinear iterations right after the brake squeal analysis is completed. Case Control commands, CMETHOD and METHOD, are placed to determine what eigenvalue extraction approach is used. SUBCASE 1 STEP 1 ANALYSIS=NLST NLPARM=201 BCONTACT=1 LOAD=2 BSQUEAL=101

Direct approach: CMETHOD only

CMETHOD=1 Modal approach: CMETHOD+ METHOD METHOD=1 …... Example 3: Case Control Structure of Brake Squeal Analysis, Separate STEP This example shows that a brake squeal analysis is performed in a separate STEP from a regular nonlinear STEP. Case Control command, BSQUEAL, is the trigger of the brake squeal analysis. LOADFAC of NLIC overrides OMETH from the referenced Bulk Data entry, BSQUEAL. SUBCASE 1 STEP 1 ANALYSIS=NLSTATIC

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102 MD Nastran R3 Release Guide Linear Perturbation and Brake Squeal Analyses in SOL 400

NLPARM=1 BCONTACT=1 ...... STEP 2 ANALYSIS=MCEIG NLIC STEP 1, LOADFAC, 0.2 BSQUEAL=101 CMETHOD=1 METHOD=1 ......

Examples of Linear Perturbation and Brake Squeal Analyses Example 4: Rotating Fan-Blade Model (nlrot103.dat), NLSTATIC+MODES This example is converted from a SOL 106 file, as shown in Figure 3-7. The finite element model consists of CQUAD4 elements. The applied loads include both pressure (PLOAD) and rotational force (RFORCE). Both loads are of follower force loads in nature. The geometrical nonlinearity and the follower force stiffness are taken into consideration in the analysis. The eigensolutions match very well with the ones from SOL 106. Figure 3-8 shows the nonlinear static deformation and linear perturbation mode shapes. The mode shapes are not plotted on the deformed shape. Instead, they are plotted on the pre-deformed structure configuration. Input File ID, MSC NLROT103 $ SOL 400 CEND TITLE =EDB ROTATING BLADE, SOL400, NORMAL MODES SUBCASE 101 STEP 1 SUBTI =Nonlinear Static SPC = 200 LOAD = 300 NLPARM= 400 NLSTR = NONE DISPL = ALL STEP 2 SUBTI =Normal Modes ANALYSIS=MODES SPC = 200 METHOD= 500 DISPL = ALL AUTOSPC= YES RESVEC = NO BEGIN BULK GRID 1 5. -2.427 -1.763 GRID 2 6.25 -2.48835-1.7562 GRID 3 7.5 -2.5497 -1.7494 . . . GRID 126 30. 3.654 1.627 CQUAD4 1 100 1 2 23 22 CQUAD4 2 100 2 3 24 23 . . .

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CHAPTER 3 103 Advanced Integrated Nonlinear and Contact

CQUAD4 100 100 104 105 126 125 PSHELL 100 100 .1 100 MAT1 100 16.+6 .275 2.-4 SPC1 200 123456 1 22 43 64 85 106 LOAD 300 1. 1. 301 1. 302 RFORCE 301 40. 1. 2 PLOAD 302 .01665 2 3 24 23 PLOAD 302 .05435 69 70 91 90 . . . PLOAD 302 .04905 40 41 62 61 $-------2-------3-------4-------5-------6-------7-------8-------9-------0------NLPARM 400 10 FNT PW + + 1.E-6 1.E-6 1.E-6 $-------2-------3-------4-------5-------6-------7-------8-------9-------0------EIGRL 500 3 PARAM COUPMASS+1 PARAM K6ROT 100. PARAM LGDISP 1 ENDDATA

Figure 3-7

FE Model of Rotating Fan Blade

Eigenvalues 0

SUBCASE 101 MODE NO.

Main Index

1 2 3

EXTRACTION ORDER 1 2 3

EIGENVALUE 6.779929E+04 3.178284E+05 5.492646E+05

R E A L E I G E N V A L U E S RADIANS CYCLES 2.603830E+02 5.637627E+02 7.411239E+02

4.144123E+01 8.972562E+01 1.179535E+02

GENERALIZED MASS 1.000000E+00 1.000000E+00 1.000000E+00

STEP 2

GENERALIZED STIFFNESS 6.779929E+04 3.178284E+05 5.492646E+05

104 MD Nastran R3 Release Guide Linear Perturbation and Brake Squeal Analyses in SOL 400

1. Nonlinear Static Deformation

2. First Mode Shape (41.44 Hz)

3. Second Mode Shape (89.73 Hz)

4. Third Mode Shape (117.95 Hz)

Figure 3-8

Nonlinear Static Deformation and Perturbed Mode Shapes

Example 5: Brake Squeal Model (nlbsql01.dat) Figure 3-9 shows a finite element model of a simplified brake assembly. The brake system consists of a

disk, two brake pads and pistons. The pistons are glued to the pads through a general flexible body-tobody contact. The modal brake squeal analysis is performed in the pre-load state and the job is terminated immediately after the brake squeal analysis. Figure 3-10 shows the first unstable mode of brake squealing.

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CHAPTER 3 105 Advanced Integrated Nonlinear and Contact

Disk is in contact with pads

Pads are glued to piston but are in contact with disk

Pistons are glued to pads

Figure 3-9

FE Model of a Simplified Brake Assembly

Input File ID MSC, NLBSQL01 $ SOL 400 CEND ECHO=SORT( EXCEPT GRID, CHEXA ) BCONTACT = 0 SUBCASE 1 SUBTITLE=CASE1 STEP 1 LABEL=Nonlinear Static Step, Loading + Contact NLPARM = 1 BCONTACT = 1 BOUTPUT=ALL BSQUEAL = 988 SPC = 2 LOAD = 2 CMETHOD=1 METHOD =2 $ Modal Approach DISP(PLOT)=ALL AUTOSPC(NOPRINT)=YES RESVEC=NO BEGIN BULK BCPARA 0 NLGLUE 1 PARAM LGDISP 1 NLPARM 1 FNT PV NO $-------2-------3-------4-------5-------6-------7-------8-------9-------0--BCTABLE 1 4 SLAVE 9 0. 0. 1. 0. 0 0.

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106 MD Nastran R3 Release Guide Linear Perturbation and Brake Squeal Analyses in SOL 400

1 2 0 MASTERS 8 SLAVE 10 0. 0. 1. 0. 0 0. 1 2 0 MASTERS 8 SLAVE 11 0. 0. 0. 0. 1 0. 1 2 0 MASTERS 9 SLAVE 12 0. 0. 0. 0. 1 0. 1 2 0 MASTERS 10 EIGC 1 CLAN 20 EIGRL 2 15 $-------2-------3-------4-------5-------6-------7-------8-------9-------0--$ ID OMETH AVSTIF GLUE ICORD BSONLY BSQUEAL 988 0.0 1.e+4 YES 0.0 0.0 1.0 0.0 0.0 0.0 PSOLID 1 1 0 $ Pset: "disk" will be imported as: "psolid.1" CHEXA 1 1 1 2 9 8 1001 1002 1009 1008 CHEXA 2 1 2 3 10 9 1002 1003 1010 1009 CHEXA 3 1 3 4 11 10 1003 1004 1011 1010 . . . $ Elements and Element Properties for region : pad1 PSOLID 2 2 0 $ Pset: "pad1" will be imported as: "psolid.2" CHEXA 1004 2 2004 2005 2012 2011 3004 3005 3012 3011 CHEXA 1005 2 2005 2006 2013 2012 3005 3006 3013 3012 . . . CHEXA 1030 2 2034 2035 2042 2041 3034 3035 3042 3041 $ Elements and Element Properties for region : pad2 PSOLID 3 2 0 $ Pset: "pad2" will be imported as: "psolid.3" CHEXA 1031 3 4000 4001 4005 4004 4024 4025 4029 4028 CHEXA 1032 3 4001 4002 4006 4005 4025 4026 4030 4029 . . . CHEXA 1045 3 4018 4019 4023 4022 4042 4043 4047 4046 $ Elements and Element Properties for region : piston PSOLID 4 2 0 $ Pset: "piston" will be imported as: "psolid.4" CHEXA 1046 4 5007 5008 5002 5005 5012 5009 5010 5011 CHEXA 1047 4 5004 5001 5008 5007 5014 5013 5009 5012

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CHAPTER 3 107 Advanced Integrated Nonlinear and Contact

. . . CHEXA

1053 4 10007 10008 10006 10004 10012 10018 MAT1 1 21000. 8076.92 .3 7.8-6 MAT1 2 2000. 769.231 .3 2.3-6 $ Nodes of the Entire Model GRID 1 40. 0. 0. 1 GRID 2 50. 0. 0. 1 GRID 3 60. 0. 0. 1 . . . GRID 10018 89.08 31.9591 -10. $ Loads for Load Case : case1 SPCADD 2 1 3 4 LOAD 2 1. 1. 1 LOAD 4 1.0-8 1. 1 $ Contraints in Cylindrical Coord. 1 $ On one edge $ SID C G1 G2 ....... SPC1 1 13 1 8 15 22 43 50 57 64 71 78 99 106 113 120 127 134 155 162 169 176 183 190 211 218 225 232 239 246 $ Displacement Constraints of Load Set : pad_fixed SPC1 3 12 3004 3005 3006 3007 3041 3042 $ Displacement Constraints of Load Set : pad_fixed2 SPC1 4 12 4000 THRU 4023 $ Deform Body Contact LBC set: disk BCBODY 8 3D DEFORM 8 0 BSURF 8 1 2 3 4 5 8 9 10 11 12 13 16 17 18 19 20 21 . . . 208 209 210 211 212 213 216 $ Deform Body Contact LBC set: pad1 BCBODY 9 3D DEFORM 9 0 BSURF 9 1004 1005 1006 1010 1011 1017 1018 1022 1023 1024 1028 $ Deform Body Contact LBC set: pad2 BCBODY 10 3D DEFORM 10 0 BSURF 10 1031 1032 1033 1034 1035 1038 1039 1040 1041 1042 1043 $ Deform Body Contact LBC set: piston BCBODY 11 3D DEFORM 11 0 BSURF 11 1046 1047 1048 1049 BCBODY 12 3D DEFORM 12 0 BSURF 12 1050 1051 1052 1053 $ Pressure Loads of Load Set : pressure PLOAD4 1 1046 50. PLOAD4 1 1047 50. PLOAD4 1 1048 50. PLOAD4 1 1049 50.

Main Index

10016

10013

29 85 141 197

36 92 148 204

3039

3040

6 14 22

7 15 23

214

215

1012 1029

1016 1030

1036 1044

1037 1045

5009 5013 5014 5012

5011 5012 5015 5017

108 MD Nastran R3 Release Guide Linear Perturbation and Brake Squeal Analyses in SOL 400

PLOAD4 1 1050 PLOAD4 1 1051 PLOAD4 1 1052 PLOAD4 1 1053 $ Referenced Coordinate CORD2C 1 1. 0. ENDDATA $

ROOT NO.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

EXTRACTION ORDER 1 2 3 4 5 6 8 7 10 9 15 14 13 12 11

Figure 3-10

Main Index

50. 50. 50. 50. Frames 0. 0.

C O M P L E X

50. 50. 50. 50.

50. 50. 50. 50.

50. 50. 50. 50.

0.

0.

0.

E I G E N V A L U E EIGENVALUE (REAL) (IMAG) 0.0 0.0 0.0 5.267539E+01 0.0 5.758587E+01 0.0 8.833070E+01 0.0 1.052037E+02 0.0 1.070820E+02 -1.901260E+00 1.953634E+02 1.901260E+00 1.953634E+02 -1.548788E+00 3.172325E+02 1.548788E+00 3.172325E+02 0.0 3.943055E+02 0.0 4.006665E+02 0.0 4.113044E+02 0.0 4.669658E+02 0.0 4.695969E+02

S U M M A R Y FREQUENCY (CYCLES) 0.0 8.383549E+00 9.165074E+00 1.405827E+01 1.674369E+01 1.704263E+01 3.109305E+01 3.109305E+01 5.048912E+01 5.048912E+01 6.275567E+01 6.376806E+01 6.546112E+01 7.431991E+01 7.473867E+01

First Instable Mode Shape (Frequency=31.1 Hz)

10008 10005 10001 10007 0.

10003 10009 10008 10006 1.

DAMPING COEFFICIENT 0.0 0.0 0.0 0.0 0.0 0.0 1.946383E-02 -1.946383E-02 9.764370E-03 -9.764370E-03 0.0 0.0 0.0 0.0 0.0

CHAPTER 3 109 Advanced Integrated Nonlinear and Contact

SOL 400 Materials and Elements Introduction MD Nastran R3 introduces into SOL 400 extensive enhancements for nonlinear large strain and material behavior. In addition to the materials introduced in MD Nastran R2, the following have been added or enhanced: • Orthotropic material properties for 3-dimensional and plane strain behavior via the MATORT

Bulk Data entry, • Nonlinear gasket material properties for compression behavior via the MATG Bulk Data entry, • Elastoplastic material properties for use in large deformation analysis via the MATEP Bulk Data

entry, • Also, several new materials have been introduced in MD Nastran R3.

Substantial enhancements to element technology in MD Nastran R3 include introduction of several new full and reduced integration continuum and shell elements. The continuum elements include: • Lower and higher order plane stress, • Plane strain, • Axisymmetric elements for two dimensional analysis • Tetrahedral, hexahedral and pentahedral elements for three dimensional analysis.

Other plane stress elements for structural elements include lower order thin and thick shells using full and reduced integration schemes as well as membrane elements. In addition, several truss and beam elements have also been added. The MD Nastran R3 material modeling enhancements include: • A new modeling procedure for large strain incompressible materials using a multiplicative

decomposition of deformation gradient and is activated using the NLMOPTS Bulk Data entry, • Anisotropic plasticity (Hill and Barlat models), • Pressure dependent plasticity (linear and parabolic Mohr-Coulomb), • Viscoplasticity, • Cyclic plasticity and viscoplasticity (Chaboche model), • Nonlinear stress-strain law for isotropic and orthotropic materials using the advanced nonlinear

elements, • Viscoelasticity with or without temperature dependent behaviors (power law, WLF and

Narayanaswamy models), • Creep (Maxwell and Kelvin models), • Elastomers (Mooney, Ogden, Arruda-Boyce and Gent models)

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110 MD Nastran R3 Release Guide SOL 400 Materials and Elements

• Shape memory alloy materials (Aruchhio for mechanical and Asaro-Sayeedvafa for thermo-

mechanical models). To take advantage of these material descriptions the new PSHLN1, PSHLN2, and PSLDN1 Bulk Data entries must be used. Two new procedures for progressive failure analysis of composite materials have been added. Micromechanical module and damage capability have been incorporated and are available through the MATM Bulk Data entry. The MATM option allows the definition of composite properties by giving the properties of the constituent materials. See the separate section for a more detailed description of this option. Secondly, the existing failure criteria in the MATF option have been enhanced to support progressive failure. The available failure criteria include the Puck criterion and variants of the Hashin criterion. Special formulations for tape and fabric type of composites are available. These new procedures are only available together with the PSHLN1, PSHLN2, and PSLDN1 Bulk Data entries. In addition, support for multi-dimensional tables: TABLE3D0, TABL3D1, TABL3D2 has been extended for the advanced nonlinear elements. Initial stress and initial plastic strain can also be input to the analysis for these elements in MD Nastran R3. For the advanced nonlinear elements, the composite shell capabilities in MD Nastran are invoked through use of the PCOMP or PCOMPG Bulk Data entries with PSHELL being extended by PSHLN1 Bulk Data entry. For continuum elements, PLCOMP (for plane strain and axisymmetric elements) and PCOMPLS (for three-dimensional solids) Bulk Data entries must be used. The onset of delamination is simulated using a new class of hexahedral, pentahedral, quadrilateral, and axisymmetric quadrilateral interface elements. This capability is invoked via the CIFPENT, CIFHEX, CIFQUAD, and CIFQDX Bulk Data entries and their associated property entry defined by PCOHE. The elements use cohesive material modeled using the MCOHE Bulk Data entry. Mixed mode delamination is incorporated by converting the normal and shear components of relative displacement into an equivalent relative displacement using the shear-normal weighting factor. Fracture mechanics modeling is now possible using the Virtual Crack Closure Technique via the VCCT Bulk Data entry for evaluating energy release rates. Multiple cracks can be defined and results will be obtained for each crack separately. Each crack consists of a crack tip grid for shells and a crack front for solids. A crack is also allowed to grow. This can occur if the crack is in a glued contact interface. You can enter a crack growth resistance (fracture toughness) for the crack. If the calculated energy release rate is larger than this value the crack will grow. This is done by automatically releasing the glued contact interface segment by segment.

Benefits With these material enhancements, MD Nastran SOL 400 is in a better position to support model products and processes requiring advanced nonlinear analysis in several products and industries e.g. manufacturing processes requiring large deformation plasticity and contact, rubber seals and boots requiring elastomers, stents in bio-medical applications requiring use of shape memory materials, creep and viscoplasticity in analysis of high temperature material behavior for aerospace materials and composite materials design requiring an accurate modeling of failure and delamination.

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CHAPTER 3 111 Advanced Integrated Nonlinear and Contact

Advanced Integrated Nonlinear Analysis Input To take advantage of the new large strain, new material, and fracture mechanics enhancements the following Bulk Data entries are needed: New Element Input 1. CIFPENT, CIFHEX, CIFQUAD, and CIFQDX Bulk Data entries: These are new MD Nastran interface elements (currently valid only in SOL 400) used to simulate the onset or progress of delamination. 2. CQUAD, CQUADX, and CTRIAX Bulk Data entries: These three existing entries have had a (THETA/MCID) field added to their description. This new field is only applicable if the PLPLANE entry has an associated PSHLN2 entry. If the element only has a PLPLANE property, the field is ignored. New Property Input 1. PSHLN1 Bulk Data entry: This entry extends the large strain and new material capabilities to the general shells defined by CQUAD4, CQUADR, CQUAD8, CTRIA3, or CTRIAR elements. This entry MUST have the same property ID as the PSHELL, PCOMP, or PCOMPG associated with the element. If any GRID of a shell element is listed on the new VCCT (Virtual Crack Closure Technique) Bulk Data entry, that shell element MUST have a PSHLN1 entry associated with it. 2. PSHLN2 Bulk Data entry: This entry extends the large strain and new material capabilities to the two-dimensional solid plane strain, plane stress, or axisymmetric elements defined by the CQUAD4, CQUAD8, CTRIA6, CQUAD and CQUADX with either four or eight grids, or CTRIAX with six grids. This entry MUST have the same property ID as the PLPLANE associated with the element. These element MUST lie in the basic X-Y plane. If any GRID of a two-dimensional solid element is listed on the new VCCT Virtual Crack Closure Technique Bulk Data entry, that 2-dimensional solid element must have a PSHLN2 entry associated with it. 3. PSLDN1 Bulk Data entry: This entry extends the large strain and new material capabilities to the three-dimensional solid elements defined by the CHEXA and CTETRA. This entry MUST have the same property ID as the PSOLID associated with the element. If any GRID of a 3-dimensional solid element is listed on the new VCCT (Virtual Crack Closure Technique) Bulk Data entry, that three-dimensional solid element MUST have a PSLDN1 entry associated with it. 4. PLCOMP Bulk Data entry: This entry extends composites to the 2-dimensional solid plane strain, plane stress, or axisymmetric elements defined by CQUAD4, CQUAD8, CQUAD and CQUADX with either four or eight grids. 5. PCOMPLS Bulk Data entry: This entry extends composites to the three-dimensional solid element defined by CHEXA. A solid shell formulation is available with this entry. 6. PCOHE Bulk Data entry: The property interface or the CIFPENT, CIFHEX, CIFQUAD, and CIFQDX elements.

Main Index

112 MD Nastran R3 Release Guide SOL 400 Materials and Elements

7. PSHEARN Bulk Data entry: This entry extends large membrane rotation to the CSHEAR element. Stringer effectiveness is ignored. The Bulk Data entry MDLPRM,SHRTOQ4,1 cannot be used with this entry. 8. PCOMPF Bulk Data entry: This entry allows the use of fast integration for composite shells leading to a computationally efficient solution. This is available for elastic materials, which may use progressive failure, and can include thermal strains. No other material nonlinearity than progressive failure is allowed. 9. PBEMN1 and PBARN1 Bulk Data entry: This entry allows the use of thin elastic as well as open and closed section beams for large deformation nonlinear analysis. 10. PRODN1 Bulk Data entry: This entry allows the use of truss elements for line elements in threedimensional analysis. New Material Input 1. MCOHE Bulk Data entry: This entry specifies material cohesive properties used to simulate the onset or progress of delamination. 2. MATORT and MATG Bulk Data entries: These existing primary material entries have been extended for use with SOL 400. Their associated MATTORT and MATTG entries are also valid for specifying temperature dependent materials. 3. MATEP and MATF Bulk Data entries: These existing associated material entries have been extended for use with SOL 400 for isotropic and anisotropic plasticity, pressure dependent plasticity (linear and parabolic Mohr-Coulomb) as well as cyclic plasticity and viscoplasticity (Chaboche model). The associated MATTEP entry is also valid for specifying temperature dependent materials. 4. MAT3 Bulk Data entry: This existing entry may also be used in conjunction with PSHLN2 and PLCOMP axisymmetric elements. The associated MATT3 entry is also valid for specifying temperature dependent materials. 5. MATS1, MATS3 and MATSORT Bulk Data entries: To model nonlinear stress-strain laws using the advanced nonlinear elements for isotropic and orthotropic materials. 6. MATHE Bulk Data entry: To model elastomers using the generalized Mooney, Ogden as well as Arruda-Boyce and Gent Models. The associated MATTHE entry is also valid for temperature dependent materials. 7. MATVP Bulk Data entry: To allow the use of creep material models using Kelvin and Maxwell models. 8. MATVE Bulk Data entry: To allow the modeling of time dependent behavior of isotropic, elastomeric, foam and glass materials. The associated MATTVE entry is valid for temperature dependent materials represented by the power, WLF (William-Landel-Ferry) and Narayanaswamy models. 9. MATSMA Bulk Data entry: To allow the use of mechanical (Aruchhio) and thermo-mechanical (Asaro-Sayeedvafa) models for analysis of shape memory alloy models. 10. IPSTRAIN and IPSTRESS Bulk Data entry: To allow the use of initial stress and initial plastic strain at the start of analysis from previous analyses.

Main Index

CHAPTER 3 113 Advanced Integrated Nonlinear and Contact

11. MATM Bulk Data entry: To flag the use of the micro-mechanical failure and damage capability for constituent material modeling and progressive failure. MATTM is available for specifying temperature dependent failure data. New Analysis Options Input NLMOPTS Bulk Data entry: This entry controls parameters associated with PSHLN1, PSHLN2, PLCOMP, PCOMPLS, and PCOHE. This allows the use of creep material behavior (using CREEP) as well as new finite strain plasticity procedure using the multiplicative decomposition of deformation gradient (using LRGSTRAIN). If, in the analysis with solid composite elements, a second order shear correction is required (e.g. for compatibility with shells) then it can be triggered through the use of TSHEAR parameter. This transverse shear option is only available for elastic materials and the elements must not be stacked. New Analysis Procedure Input: 1. VCCT Case Control command: By specifying VCCT=n, this command selects the VCCT Bulk Data entry to be used in a given STEP. 2. VCCT Bulk Data entry: This entry specifies the Virtual Crack Closure Technique entry for evaluating energy release rates. Extensions to Table Input The multi-dimensional table options have also been supported in the MD Nastran R3 release. They are TABL3D0, TABL3D1 and TABL3D2. These table options allow you to define a table or formula with up to 4 independent variables and can only be used with Marc elements or materials. These are especially helpful when the material properties are a function of temperature, history variables like plastic strains etc. or time (e.g. rate sensitive materials).

Output The element output is obtained via standard MD Nastran STRESS=n and NLSTRESS=n commands. Both linear formatted nonlinear stress and nonlinear stress/strain output is available. The Virtual Crack Closure Technique output data is automatically placed on file OFVCCT. VCCT is utilized in the run it is automatically output to the .f06 file.

Guidelines and Limitations 1. For the beam and shell elements, the two-dimensional solid elements and three-dimensional solid elements there are two types of property entries: a. The primary property entries are the PROD, PBAR (or PBARL), PBEAM (or PBEAML), PSHELL, PCOMP, PCOMPG, PLPLANE, PSOLID, PLCOMP, PCOMPLS, and PSHEAR. b. An associated property such as a PRODN1, PBARN1, PBEMN1, PSHLN1, PSHLN2, PSLDN1, PCOMPF and PSHEARN. c. The associated property is matched to the primary property by having the same ID.

Main Index

114 MD Nastran R3 Release Guide SOL 400 Materials and Elements

LOAD STEP = 1.00000E+00 V C C T C R A C K R E S U L T S CRACK TIP ------------- ENERGY RELEASE RATE ------------ ESTIMATED CRACK GROWTH DIRECTION CRACK ID GRID ID TOTAL MODE I MODE II MODE III X Y Z 100 1 4.5493E+01 4.5493E+01 7.6309E-16 0.0000E+00 1.0000E+00 1.3297E-16 0.0000E+00 100 2 4.5484E+01 4.5484E+01 1.4533E-15 0.0000E+00 1.0000E+00 1.0262E-16 0.0000E+00 100 3 4.5484E+01 4.5484E+01 4.3923E-17 0.0000E+00 1.0000E+00 1.6459E-16 0.0000E+00 100 4 4.5493E+01 4.5493E+01 1.6856E-15 0.0000E+00 1.0000E+00 9.2419E-17 0.0000E+00

d. The PSHLN1 invokes the enhanced nonlinear capability for shell elements whose PID points to a PSHELL, PCOMP, or PCOMPG. The PSHLN2 invokes the enhanced nonlinear capability for two-dimensional solid elements whose PID points to a PLPLANE. The PSLDN1 invokes the enhanced nonlinear capability for 3-dimensional solid elements whose PID points to a PSOLID. The PBARN1 and PBEMN1 invoke the enhanced nonlinear capability for one-dimensional structural with bending (i.e. beam elements) whose PID points to a PBAR (or PBARL) and PBEAM (or PBEAML) respectively. The PRODN1 invokes the enhanced nonlinear capability for one-dimensional membrane elements whose PID points to a PRODN1. 2. In MD Nastran there are two types of material entries: a. A primary material entry whose ID may appear on an appropriate PSHELL, PLPLANE, PSOLID, PCOMP(G), PSHLN1, PSHLN2, PSLDN1, PLCOMP, PCOMPLS, PSHEAR etc. (e.g. MCOHE, MATG, MATSMA) b. An associated material entry whose ID must appropriately match one of the primary material entry ID’s (e.g. MATEP, MATVP, MATVE) c. The primary material entry MATORT ID may only appear on PSHLN2, PSLDN1, PLCOMP, and PCOMPLS. If its ID appears on say a PSOLID in the MID field it will be ignored and the run will fail with no material defined error. The primary material entry MATG ID may only appear on PSHLN2 and or PSLDN1. d. If the associated materials MATEP or MATF point to a primary material ID for shell elements and there is no associated PSHLN1 pointing to a PSHELL, PCOMP, or PCOMPG the associated material will not be used. If the associated materials MATEP or MATF point to a primary material ID for two-dimensional solid elements that have a PLPLANE as their primary property, and there is no associated PSHLN2 pointing to a PLPLANE, the associated material will not be used. If the associated materials MATEP or MATF point to a primary material ID for three-dimensional solid elements that have a PSOLID as their primary property, and there is no associated PSLDN1 pointing to a PSOLID the associated material will not be used. 3. Using the PSHLN1 entry you can change the material ID associated with the MID1 or MID2 or both on the PSHELL. If these entries are left blank on the PSHLN1 then the MID1 and MID2 values on the PSHELL are used. The flow diagram below shows the PSHLN1’s relationship to the shell elements.

Main Index

CHAPTER 3 115 Advanced Integrated Nonlinear and Contact

4. Using the PSHLN2 entry the user can change the material ID associated with the MID on the PLPLANE. There is no default. The PLPLANE requires a MATHP and the user must override with a MAT1, MAT2, MAT3, MAT8, MATORT, MATHE, or if appropriate a MATG, MCOHE or MATSMA. The flow diagram below shows its relationship to the two-dimensional solid using a PLPLANE entry as its primary property entry. On the PSHLN2 entry the BEHi codes are sensitive to the required primary material used. MAT1 is applicable to all BEHi codes. MAT2 anisotropic and MAT8 orthotropic are applicable to BEHi=PSTRS codes only. MAT3 axisymmetric orthotropic is applicable to BEHi=AXSOLID code only. MATORT orthotropic are applicable to BEHi=PLSTRN code only. MATG is applicable for BEH4=COMPS or AXCOMP with INT4=L codes only. The BEH4=COMPS or AXCOMP with INT4=L should not be used with MAT1, MAT2, MAT3, MAT8, or MATORT as they will suffer hour-glassing. In SOL 400, if a PLPLANE entry has an associated PSNLN2 entry, it can directly refer to an appropriate MAT1, MAT2, etc., material entry and not have a MATHP referral. However, in this case all elements referring to the PLPLANE entry will fail in all other solution sequences.

Main Index

116 MD Nastran R3 Release Guide SOL 400 Materials and Elements

5. The “key” word field entries on the PSHLN1, PSHLN2, PSLDN1, PLCOMP, and PCOMPLS Bulk Data have default integration schemes and do not need to be defined in the property entry again, if you are willing to use these defaults. 6. The MATG gasket material requires a special integration scheme. It is only available for elements using a PSHLN2 or PSLDN1 Bulk Data entry. For the PSHLN2, the “C4” keyword entry with BEH4=COMPS or AXCOMP and INT4=L would be required. For the solid BEH8=SLCOMP, INT8=L would be required.

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CHAPTER 3 117 Advanced Integrated Nonlinear and Contact

7. For composites, a solid shell element formulation is available. The DIRECT field entry must be DIRECT=1 (the default). For the linear and quadratic formulations, no “key” word entry is required. The sample below shows the solid shell element request. 8. Because these new material features often involve large deformation, it is recommended that a full Newton iteration scheme be used. This has been facilitated on the NLPARM Bulk Data entry by the addition to the KMETHOD field the key word “FNT” or “PFNT” and the TSTEPNL Bulk Data entry by the addition to the METHOD field the key word “FNT” or “PFNT”. If the “FNT” option is chosen, then a “V” is added to either one or more of the “U”, “P” or “W” type of convergence criteria. 9. Any shell element that has non structural mass (NSM) that utilizes any PSHELN1 or PSHLN2 entry will lose the associated non structural mass.

Main Index

118 MD Nastran R3 Release Guide Enhancements to Connector Elements

Enhancements to Connector Elements Introduction In MD Nastran R3 the connector elements CBUSH, CWELD and CFAST have been enhanced for usage in a nonlinear SOL 400 analysis. In SOL 400 the elements fully support large displacement and large rotation effects and can now be used in a geometrically-nonlinear analysis where these effects can no longer be ignored. There is no additional modeling effort required for the connector elements when preparing a nonlinear model that includes them, so the input Bulk Data entries CBUSH/PBUSH, CWELD/PWELD and CFAST/PFAST remain unchanged. However, the elements are treated differently internally in a nonlinear SOL 400 analysis than a linear analysis. This results in slightly different ways of presenting the results in the .f06-file and in the op2- or .xdb files.

CBUSH Enhancements in SOL 400 CBUSH is a generalized spring-damper element representing a bushing connection. The element has been enhanced to • Support geometrically-nonlinear analysis involving large displacement and large rotation. • Allow the materially-nonlinear force-deflection curve to support radial and spherical behavior. • Allow the CBUSH to FUSE at various failure criteria.

For CBUSH to support large rotations, appropriate transformations are needed during element stiffness and damping matrices generation as well as during internal force computations. In addition, differential stiffness terms need to be computed. All CBUSH orientation configurations have been enhanced. These include: • Axial CBUSH. • CBUSH defined using an orientation vector ν . • CBUSH defined using a coordinate system CID.

During large rotation, an axial CBUSH will always be oriented from grid GA to grid GB. The user is allowed the following options to control the behavior of a CBUSH defined using a coordinate system or an orientation vector during large rotation: • Allow the CBUSH to rotate with the rotational degrees of freedom of GA (default). • Fix the CBUSH orientation to the initial orientation defined by CID or ν . • Use a mid-increment method to rotate the CBUSH defined by ν

The large rotation options are controlled using the LRGR flag under the modified PBUSHT Bulk Data entry. Enhancements to the materially-nonlinear force-deflection curve to support radial and spherical behavior are controlled by the new flag FDC, under the modified PBUSHT Bulk Data entry. The CBUSH

Main Index

CHAPTER 3 119 Advanced Integrated Nonlinear and Contact

failure criteria introduced in this release include an ultimate load and a maximum relative displacement. These are specified using the FUSE option also under the modified PBUSHT Bulk Data entry.

Inputs The CBUSH element is modeled by the CBUSH and PBUSH Bulk Data entries and the modified PBUSHT Bulk Date entry. The details of these entries are described in the MD Nastran Quick Reference Guide.

Outputs There are no new outputs associated with the CBUSH enhancements.

Example The following example demonstrates the use of CBUSH in a geometrically-nonlinear SOL 400 analysis. In this example, an axial CBUSH is undergoing an axial extension followed by a 90o rigid body rotation. One end of the CBUSH is fixed while the other moves with prescribed displacements to simulate the extension and rotation. The LGDISP flag is turned on. The input file follows: SOL 400 CEND DISP=ALL SPCF=ALL STRESS=ALL STRAIN=ALL NLSTRESS=ALL NLPARM=1 STEP 1 SPC = 1 LOAD = 1 STEP 2 SPC = 1 LOAD = 2 BEGIN BULK PARAM LGDISP PARAM POST NLPARM 1 GRID 1 GRID 2 GRID 3 CBUSH 1 PBUSH 2 SPC1 1 SPC1 1 SPCD 1 SPCD 2 ENDDATA

Main Index

1 0 1

2 K 123456 123456 2 2

0.0 1.0 2.0 1 1.0E5 1 2 1 1

0.0 0.0 0.0 2

0.0 0.0 0.0

1.0 -1.0

2 2

2 2

0.0 2.0

120 MD Nastran R3 Release Guide Enhancements to Connector Elements

The results are as follows:

LOAD STEP = 1.00000E+00 N O N L I N E A R ELEMENT ID. 1

LOAD STEP = 2.00000E+00 N O N L I N E A R ELEMENT ID. 1

F O R C E S

F O R,C E FORCE-X FORCE-Y MOMENT-X MOMENT-Y 1.00000E+05 0.0 0.0 0.0

POINT ID. 1 2 3 LOAD STEP = POINT ID. 1 2 3 LOAD STEP = POINT ID. 1 2 LOAD STEP = POINT ID. 1 2

1.00000E+00 TYPE G G G

0.0 1.000000E+00 0.0

0.0 0.0 0.0

0.0 -1.000000E+00 0.0

TYPE G G

T1 -1.000000E+05 1.000000E+05

2.00000E+00 TYPE G G

0.0 0.0

T2

0.0 0.0 0.0

T2

0.0 2.000000E+00 0.0

F O R C E S

0.0 0.0

F O R C E S T1

O F

I N

T3

B U S H

E L E M E N T S

B U S H

0.0 0.0 0.0

T3

0.0 0.0

T3

0.0 0.0 0.0

0.0 0.0

T3

S T R A I N STRAIN-TX STRAIN-TY STRAIN-TZ STRAIN-RX STRAIN-RY STRAIN-RZ 1.00000E+00 0.0 0.0 0.0 0.0 0.0

E L E M E N T S

( C B U S H )

S T R A I N STRAIN-TX STRAIN-TY STRAIN-TZ STRAIN-RX STRAIN-RY STRAIN-RZ 1.00000E+00 0.0 0.0 0.0 0.0 0.0

R1

0.0 0.0 0.0

R2

0.0 0.0 0.0

R3

V E C T O R 0.0 0.0 0.0

0.0 0.0

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

T2 -1.000000E+05 1.000020E+05

( C B U S H )

V E C T O R

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

T2

O F

I N

S T R E S S STRESS-TX STRESS-TY STRESS-TZ STRESS-RX STRESS-RY STRESS-RZ 1.00000E+05 0.0 0.0 0.0 0.0 0.0

D I S P L A C E M E N T T1

1.00000E+00

S T R E S S E S

D I S P L A C E M E N T T1

2.00000E+00 TYPE G G G

A N D

FORCE-Z MOMENT-Z 0.0 0.0

S T R E S S E S

S T R E S S STRESS-TX STRESS-TY STRESS-TZ STRESS-RX STRESS-RY STRESS-RZ 1.00000E+05 0.0 0.0 0.0 0.0 0.0

FORCE-Z MOMENT-Z 0.0 0.0

F O R C E S

F O R,C E FORCE-X FORCE-Y MOMENT-X MOMENT-Y 1.00000E+05 0.0 0.0 0.0

LOAD STEP =

A N D

0.0 0.0

R1

0.0 0.0 0.0

R2

0.0 0.0 0.0

R3

C O N S T R A I N T R1

0.0 0.0

R2

0.0 0.0

R3

C O N S T R A I N T R1

0.0 0.0

R2

0.0 0.0

R3

The nonlinear forces and stresses section of the output indicate that the element forces due to the axial extension remain constant during the large rotation and are always along the element local x-direction. The SPC forces indicate that the reactions at the grid points due to the prescribed displacements have changed directions from the global x-direction to the global y-direction.

Nonlinear CWELD and CFAST Elements in SOL 400 In a nonlinear SOL 400 analysis each connector element is not assembled as one element, but is internally mapped onto a group of elements, that when assembled together, simulate the behavior of the original connector element. Each assembly consists of one deformable element and a group of rigid body elements. In the case of a CWELD, this deformable element is a CBEAM element, and in the case of a CFAST it is a CBUSH element. The rigid body elements insure that the deformable element gets connected to the plate surfaces on either side of a connection in exactly the same way as the original connector element and all connection types for CWELD (i.e. PARTPAT, ELPAT, ELEMID, GRIDID and ALIGN) and for CFAST (i.e. PROP and ELEM) are supported. All rigid body elements involved in the connections are RBE3 elements. The process of mapping the connector elements requires a number of new elements and grids to be generated internally, that are not present in the original Bulk Data input.

Main Index

CHAPTER 3 121 Advanced Integrated Nonlinear and Contact

The deformable element in a connection inherits the ID of the original connector element, but the RBE3 elements obtain IDs that are automatically assigned by the program. The GA and GB grids of the connector element define the two grids of the deformable CBEAM or CBUSH element and if they are not entered on the CWELD or CFAST entries, their IDs are automatically assigned by the program. The connection types ELPAT and PARTPAT for CWELD and ELEM and PROP for CFAST, define four auxiliary points on each side of a connection. These points are mapped internally to grids that get their IDs automatically assigned by the program. The grid IDs and element IDs assigned by the program have large offsets with respect to the IDs in the model and these offsets may be changed with PARAM,OSWPPT (by default 101,000,000) and PARAM,OSWELM (by default 100,001,001). The material models supported for a CWELD are the ones that are supported for a CBEAM element. For a CFAST the linear stiffness values are entered on the PFAST input. If the CFAST element has a mass, it is mapped on two CONM2 elements connected to the GA and GB grids of the CBUSH element.

Inputs The CWELD and CFAST Bulk Data entries are used to define a CWELD and CFAST element in the same way as for a linear analysis. The properties are defined in the PWELD and PFAST Bulk Data entries. No additional data is needed to prepare these inputs for a nonlinear analysis. MD Nastran recognizes the analysis type and for a nonlinear SOL 400 analysis, it applies the mapping procedure as outlined in the previous section. The MSET-field on the PWELD Bulk Data entry has no effect in a nonlinear SOL 400 analysis. The details of these bulk data entries are described in the MD Nastran Quick Reference Guide.

Outputs The results of a CWELD element are output to the. f06 file in the format of the CBEAM element. The CWELD output is separated from the CBEAM output if there are also CBEAM entries in the bulk data input. The CBEAM output, if present, is always listed first, followed directly by the CWELD output. The CWELD output can be recognized by the presence of the string “C W E L D” in the header lines of the element output. There is no distinction between CWELD, CWELDC and CWELDP elements as there is in the linear case. Similarly the results of a CFAST element are output to the .f06 file in the format of the CBUSH element. The CFAST output is separated from the CBUSH output if there are also CBUSH entries in the bulk data input. The CBUSH output, if present, is always listed first, followed directly by the CFAST output. The CFAST output can be recognized by the presence of the string “C F A S T” in the header lines of the element output. Details about the locations of the projection points, their associated grid IDs and the internally generated RBE3 IDs are printed when the PRTSW-parameter on the SWLDPRM Bulk Data entry is activated. For post-processing the results of connector elements are available as CBEAM or CBUSH results on the .op2- or .xdb-file.

Main Index

122 MD Nastran R3 Release Guide Enhancements to Connector Elements

Supported Output Requests The following element output requests are supported for the CWELD and CFAST elements: NLSTRESS, STRESS/ELSTRESS, FORCE/ELFORCE, STRAIN and ESE. The element summary (ELSUM) reflects the presence of CWELD or CFAST elements, they are not lumped together with the CBEAM or CBUSH elements. The GPFORCE output for the grids involved in a CWELD or CFAST element reflects the output for each separate element that arises from the mapping procedure and not for the assembly of these elements into one connector element, i.e. there is output for the GA- and GB-grids of the deformable element (WELD or BUSH) and the grids of the rigid body elements (RBE3). Details of these output requests are found in the The Case Control Section (Ch. 4) in the MD Nastran Quick Reference Guide.

Limitations When requesting .op2- or .xdb-output to be used for further processing in a separate post-processor, you must include the geometry in these files and open the files in the post-processor reading both the model and the results data. You cannot add the results data to the model data that may already be present in the database of the pre-processor, since the mapping procedure alters the element type of the connector elements and generates additional grids and rigid body elements not present in the original data base. The connector elements are post processed as CBEAM or CBUSH elements and they are present as such in the model and result parts of the .op2- or .xdb-file. The DISP(CONN = …, …) output request for the displacements of grids of selected connector elements is not yet supported.

Example Figure 3-11 shows the connection of two square plates by one CWELD of type ELPAT. The relevant bulk data input for this model is shown. Of special interest for this analysis are the SOL 400 Executive Control statement, the NLPARM Case Control command, the “PARAM, LGDISP,1”, the NLPARM, SWLDPRM, CWELD and PWELD Bulk Data entries. The diameter of the CWELD is 11.28379 mm, resulting in a 10x10 mm auxiliary patch on each side. The two 25x25 mm plates are 5 mm apart, thus the connector element length is 5.0 mm. The material behavior is linear elastic, but the PARAM,LGDISP,1 input allows for large displacement and large rotation effects.

Main Index

CHAPTER 3 123 Advanced Integrated Nonlinear and Contact

pli=QMM `bka qfqib=Z=ja=k^pqo^k=`tbiaIbim^qI^uf^i pr_`^pb=N =pr_qfqibZabc^riq =kim^ojZN =pm`ZQ =il^aZR =afpmi^`bjbkqEploqNIob^iFZ^ii =pm`clo`bpEploqNIob^iFZ^ii =jm`clo`bpEploqNIob^iFZ^ii =kipqobppEploqNFZ^ii =pqobppEploqNIob^iIslkjfpbpI_fifkFZ^ii =pqo^fkEploqNIob^iIslkjfpbpI_fifkFZ^ii =biclo`bEploqNIob^iIslkjfpbpI_fifkFZ^ii =bpbEqeobpeZMKMFZ^ii =dmclo`bZ^ii =biprjE_lqeFZ^ii A A=k^pqo^k=_rih=a^q^ A _bdfk=_rih ptiamojImoqptIN m^o^j====mlpq=====M m^o^j====^rqlpm`=kl m^o^j====idafpm==N m^o^j===moqj^ufj=vbp kim^oj==N=======NM==============^rql====R=======OR======rm======kl clo`b===R=======TS==============MK======KRTTPR==KRTTPR==KRTTPR pm`^aa==Q=======N=======O=======P A A=bibjbkqp=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ A `nr^aQ==O=======N=======N=======NN======NO======S======= `nr^aQ==P=======N=======S=======NO======NP======T======= KKK `nr^aQ==RM======N=======SV======TQ======TR======TM====== `nr^aQ==RN======N=======TM======TR======QO======TN====== A A=dofap=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ A dofaG===N==================================JNKORMMMMbHMN===JNKORMMMMbHMN G==========JOKRMMMMMbHMMM=============== dofaG===O===================================NKORMMMMbHMN===JNKORMMMMbHMN G==========JOKRMMMMMbHMMM=============== KKK dofaG===TR==================================NKORMMMMbHMN====TKRMMMMMbHMM G===========OKRMMMMMbHMMM=============== dofaG===TS==================================MKMMMMMMbHMM====MKMMMMMMbHMM G===========MKMMMMMMbHMMM=============== A A=j^qbof^ip=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ A j^qNG===N===================OKMMMMMMbHMR====================PKMMMMMMbJMN G===========NKMMMMMMbHMM====MKMMMMMMbHMM A A=molmboqfbp=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ A mpebii=========N=======N=====OKM=======N===============N mtbia==========O=======NNNKOUPTV IMKMO `tbia=======NMMM=======O======TS==bim^q=================================H H=============NQ======PV A A=_lrka^ov=`lkafqflkp=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ A pm`G====N===============N==============================N====MKMMMMMMbHMM G======= pm`G====N===============N==============================O====MKMMMMMMbHMM G======= pm`G====O===============N==============================P====MKMMMMMMbHMM G======= KKK A A=pm`a=ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ A pm`aG===R===============N==============================P===JNKMMMMMMbHMM G======= KKK bkaa^q^

Figure 3-11

Main Index

Input data for a model with one CWELD of type ELPAT connecting two square plates.

124 MD Nastran R3 Release Guide Enhancements to Connector Elements

The elements and grids with their IDs are shown in Figure 3-12. The CWELD element ID is 1000, therefore the CBEAM ID in the OP2- or XDB-results file is also 1000. A number of grids are generated internally. The two grids of the CBEAM obtain IDs 101,000,001 and 101,000,002. Per CWELD eight auxiliary grids are generated which obtain IDs 101,000,003 through 101,000,010.

Figure 3-12

FEM model with one CWELD of type ELPAT connecting two square plates.

Results for the connector element are as follows:

... ... CWELD EID= 1000 WITH ELPAT OR PARTPAT AUXILIARY POINTS= (-5.0000E+00,-5.0000E+00,-2.5000E+00) ( 5.0000E+00,-5.0000E+00,-2.5000E+00) ( 5.0000E+00, 5.0000E+00,-2.5000E+00) (-5.0000E+00, 5.0000E+00,-2.5000E+00) (-5.0000E+00,-5.0000E+00, 2.5000E+00) ( 5.0000E+00,-5.0000E+00, 2.5000E+00) ( 5.0000E+00, 5.0000E+00, 2.5000E+00) (-5.0000E+00, 5.0000E+00, 2.5000E+00) AUXILIARY GRIDS GHA= 101000003 101000004 101000005 101000006 AUXILIARY GRIDS GHB= 101000007 101000008 101000009 101000010 RBE3 IDS FOR GHA1-4= 100001004 100001005 100001006 100001007 RBE3 IDS FOR GHB1-4= 100001008 100001009 100001010 100001011 NUMBER OF TIMES GS MOVES= 0 NUMBER OF TIMES DA IS REDUCED= 0 ANGLE BETWEEN TWO SHELL NORMALS= 0.00 GS=( 0.000E+00, 0.000E+00, 0.000E+00) GA=( 0.000E+00, 0.000E+00,-2.500E+00) GB=( 0.000E+00, 0.000E+00, 2.500E+00) T_BE MATRIX: 0.0000E+00 1.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 1.0000E+00 1.0000E+00 0.0000E+00 0.0000E+00

Main Index

CHAPTER 3 125 Advanced Integrated Nonlinear and Contact

d^=fa=====Z=NMNMMMMMN===d_=fa=====Z=NMNMMMMMO RBE3 ID A = 100001002 RBE3 ID B = 100001003 PATCH A: EID= 8 GIDS= 12 18 EID= 18 GIDS= 24 30 EID= 20 GIDS= 26 32 EID= 10 GIDS= 14 20 PATCH B: EID= 33 GIDS= 49 55 EID= 43 GIDS= 61 67 EID= 45 GIDS= 63 69 EID= 35 GIDS= 51 57 ... LOAD STEP = 1.00000E+00 N O N L I N E A R S T R E S S E S ELEMENT GRID ID ID 1000 101000001

101000002

... LOAD STEP = POINT ID. 54 55 ... 75 76 101000001 101000002 101000003 101000004 101000005 101000006 101000007 101000008 101000009 101000010 ... LOAD STEP =

POINT C D E F C D E F

1.00000E+00 TYPE G G

T1 -2.366882E-04 -3.291661E-03

G G G G G G G G G G G G

-7.230500E-03 0.0 -4.453620E-15 3.312258E-15 -3.721987E-03 3.721987E-03 3.721987E-03 -3.721987E-03 -3.721987E-03 3.721987E-03 3.721987E-03 -3.721987E-03

STRESS 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02

56

I N

19 31 33 21

50

68 70 58

W E L D

EQUIVALENT STRESS 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02

13 25 27 15 62 64 52

0

0 0 0 0

0

0 0 0

E L E M E N T S TOTAL STRAIN 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04

0 0 0 0 0 0 0

0

0 0 0 0

0

0 0 0

EFF. CREEP STRAIN 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

V E C T O R R1 -4.363906E-02 -4.370676E-02

R2 2.793858E-02 2.255758E-02

R3 -1.280631E-02 -9.173469E-04

-2.870318E-03 0.0 -4.830421E-15 3.882926E-15 -3.721987E-03 -3.721987E-03 3.721987E-03 3.721987E-03 -3.721987E-03 -3.721987E-03 3.721987E-03 3.721987E-03

7.637381E-02 0.0 -1.973814E-15 -2.339357E-15 3.667419E-02 3.667419E-02 -3.667419E-02 -3.667419E-02 -3.667419E-02 -3.667419E-02 3.667419E-02 3.667419E-02

-6.415410E-02 0.0 1.700749E-15 2.159162E-15 -3.667419E-02 3.667419E-02 3.667419E-02 -3.667419E-02 3.667419E-02 -3.667419E-02 -3.667419E-02 3.667419E-02

3.673183E-02 0.0 1.505883E-17 -5.508353E-17 -1.298351E-16 1.079322E-16 -2.717700E-17 -1.795417E-16 1.043341E-16 -6.137916E-17 -2.464781E-17 1.751367E-16

1.00000E+00

F O R C E S I N W E L D E L E M E N T S ( C W E L D ) STAT DIST/ - BENDING MOMENTS - WEB SHEARS AXIAL TOTAL ELEMENT-ID GRID LENGTH PLANE 1 PLANE 2 PLANE 1 PLANE 2 FORCE TORQUE 1000 101000001 0.000 0.0 -2.019484E-28 0.0 -4.038968E-29 1.290066E+04 0.0 101000002 1.000 0.0 0.0 0.0 -4.038968E-29 1.290066E+04 0.0 ... LOAD STEP = 1.00000E+00 S T R A I N S I N W E L D E L E M E N T S ( C W E L D ) STAT DIST/ ELEMENT-ID GRID LENGTH SXC SXD SXE SXF S-MAX S-MIN 1000 101000001 0.000 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 101000002 1.000 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04 6.450332E-04

Main Index

0 0 0

( C W E L D )

EFF. STRAIN PLASTIC/NLELAST 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

D I S P L A C E M E N T T2 T3 2.518907E-03 2.201321E-01 -1.991543E-03 -1.020590E-02 5.085921E-01 0.0 -1.612583E-03 1.612583E-03 -1.612583E-03 -1.612583E-03 -1.612583E-03 -1.612583E-03 1.612583E-03 1.612583E-03 1.612583E-03 1.612583E-03

0 0 0 0

WARPING TORQUE 0.0 0.0

M.S.-T

M.S.-C

126 MD Nastran R3 Release Guide Enhancements to Connector Elements

LOAD STEP = POINT ID. 12 13 14 15 18 19 20 21 24 25 26 27 30 31 32 33 49 50 51 52 55 56 57 58 61 62 63 64 67 68 69 70 101000001 101000002 101000003 101000004 101000005 101000006 101000007 101000008 101000009 101000010 ... LOAD STEP =

1.00000E+00 TYPE G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G G

F O R C E S

T1 3.521063E-04 -1.718600E-09 -1.636564E-09 3.521063E-04 -1.677591E-09 -3.521096E-04 -3.521096E-04 -1.634595E-09 1.497272E-09 3.521094E-04 3.521095E-04 1.519796E-09 -3.521064E-04 1.497269E-09 1.521348E-09 -3.521064E-04 3.521064E-04 -1.457365E-09 -1.521572E-09 3.521064E-04 -1.464358E-09 -3.521094E-04 -3.521095E-04 -1.521775E-09 1.659815E-09 3.521096E-04 3.521096E-04 1.635683E-09 -3.521063E-04 1.659034E-09 1.634400E-09 -3.521063E-04 1.101021E-09 -1.098538E-09 6.469971E-09 -6.311491E-09 -6.310388E-09 6.314220E-09 6.166376E-09 -6.314767E-09 -6.313828E-09 6.313032E-09

O F

M U L T I P O I N T

T2 3.521062E-04 -1.697555E-09 1.511392E-09 -3.521064E-04 -1.656546E-09 -3.521096E-04 3.521095E-04 1.509423E-09 -1.671058E-09 -3.521096E-04 3.521094E-04 1.485394E-09 3.521063E-04 -1.671055E-09 1.486946E-09 -3.521065E-04 3.521065E-04 -1.495689E-09 1.645789E-09 -3.521063E-04 -1.502682E-09 -3.521095E-04 3.521096E-04 1.645992E-09 -1.486565E-09 -3.521094E-04 3.521096E-04 1.671656E-09 3.521065E-04 -1.485783E-09 1.670374E-09 -3.521063E-04 1.278798E-09 -1.280010E-09 6.435660E-09 6.317369E-09 -6.311536E-09 -6.314174E-09 6.268448E-09 6.312995E-09 -6.315761E-09 -6.311856E-09

T3 8.062816E+02 8.062912E+02 8.062912E+02 8.062816E+02 8.062912E+02 8.063008E+02 8.063008E+02 8.062912E+02 8.062912E+02 8.063008E+02 8.063008E+02 8.062912E+02 8.062816E+02 8.062912E+02 8.062912E+02 8.062816E+02 -8.062816E+02 -8.062912E+02 -8.062912E+02 -8.062816E+02 -8.062912E+02 -8.063008E+02 -8.063008E+02 -8.062912E+02 -8.062912E+02 -8.063008E+02 -8.063008E+02 -8.062912E+02 -8.062816E+02 -8.062912E+02 -8.062912E+02 -8.062816E+02 -1.290066E+04 1.290066E+04 1.113312E-08 1.294347E-08 1.294302E-08 1.294165E-08 -1.343187E-08 -1.294438E-08 -1.294393E-08 -1.294347E-08

C O N S T R A I N T

R1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.306006E-09 -8.807850E-09 -4.506068E-02 -4.506068E-02 4.506068E-02 4.506068E-02 4.506069E-02 4.506068E-02 -4.506068E-02 -4.506068E-02

R2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -4.593276E-09 1.016273E-08 4.506068E-02 -4.506068E-02 -4.506068E-02 4.506068E-02 -4.506068E-02 4.506068E-02 4.506068E-02 -4.506068E-02

1.00000E+00

S T R E S S E S I N W E L D E L E M E N T S STAT DIST/ ELEMENT-ID GRID LENGTH SXC SXD SXE SXF 1000 101000001 0.000 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 101000002 1.000 1.290066E+02 1.290066E+02 1.290066E+02 1.290066E+02 ... LOAD STEP = 1.00000E+00 E L E M E N T S T R A I N E N E R G I E ELEMENT-TYPE = WELD SUBCASE

ELEMENT-ID 1000 TYPE = WELD

Main Index

( C W E L D ) S-MAX

SUBTOTAL

S-MIN

1.290066E+02 1.290066E+02

M.S.-T

1.290066E+02 1.290066E+02

S

* TOTAL ENERGY OF ALL ELEMENTS IN PROBLEM * TOTAL ENERGY OF ALL ELEMENTS IN SET

1

R3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.887649E-09 -1.933290E-09 -3.828222E-10 6.001081E-14 -1.564326E-11 1.954644E-11 7.144588E-10 -7.594164E-12 1.315762E-11 -1.921700E-12

= -1 =

STRAIN-ENERGY 2.080338E+01

PERCENT OF TOTAL 0.1859

2.080338E+01

0.1859

1.118831E+04 1.118831E+04 STRAIN-ENERGY-DENSITY 4.160678E-02

M.S.-C

CHAPTER 3 127 Advanced Integrated Nonlinear and Contact

... LOAD STEP = POINT-ID 1 1 1 2 2 2 ... ... 101000001 101000001 101000001 101000002 101000002 101000002 101000003 101000003 101000003 ...

1.00000E+00 ELEMENT-ID 2 22

1000 100001002 1000 100001003 100001002 100001004

G R I D

F O R C E

B A L A N C E

T1 -6.081972E+03 6.081972E+03 0.0 6.081972E+03 -6.081972E+03 0.0

T2 -6.081972E+03 6.081972E+03 0.0 -6.081972E+03 6.081972E+03 0.0

T3 -3.240928E+03 3.240928E+03 0.0 -3.240928E+03 3.240928E+03 0.0

R1 0.0 -5.258240E+00 -5.258240E+00 0.0 -5.258240E+00 -5.258240E+00

R2 0.0 5.258240E+00 5.258240E+00 0.0 -5.258240E+00 -5.258240E+00

R3 0.0 1.925268E-11 1.925268E-11 0.0 -2.108151E-11 -2.108151E-11

WELD RBE3 *TOTALS* WELD RBE3 *TOTALS* RBE3 RBE3 *TOTALS*

2.002407E-11 1.101021E-09 1.121045E-09 -2.002407E-11 -1.098538E-09 -1.118563E-09 -3.224113E-10 6.792382E-09 6.469971E-09

2.246709E-11 1.278798E-09 1.301265E-09 -2.246709E-11 -1.280010E-09 -1.302477E-09 -2.725434E-10 6.708203E-09 6.435660E-09

1.290066E+04 -1.290066E+04 8.185452E-11 -1.290066E+04 1.290066E+04 -8.185452E-11 3.225165E+03 -3.225165E+03 1.113312E-08

2.019484E-28 2.306006E-09 2.306006E-09 0.0 -8.807850E-09 -8.807850E-09 0.0 -4.506068E-02 -4.506068E-02

0.0 -4.593276E-09 -4.593276E-09 0.0 1.016273E-08 1.016273E-08 0.0 4.506068E-02 4.506068E-02

0.0 1.887649E-09 1.887649E-09 0.0 -1.933290E-09 -1.933290E-09 0.0 -3.828222E-10 -3.828222E-10

* * * END OF JOB * * *

Table 3-1

Main Index

P O I N T

SOURCE F-OF-SPC QUAD4 *TOTALS* F-OF-SPC QUAD4 *TOTALS*

Results for a model with one CWELD of type ELPAT connecting two square plates.

128 MD Nastran R3 Release Guide Adaptive Time Stepping Scheme Enhancements for Quasi-Static Analysis

Adaptive Time Stepping Scheme Enhancements for Quasi-Static Analysis An adaptive time stepping scheme was introduced in SOL 400 (MD Nastran R2) by using the NLAUTO Bulk Data entry. The primary control scheme of the load step is based upon the number of recycles needed to obtain convergence if full Newton Raphson method is used. For modified Newton Raphson method, both the number of recycles and the number of new stiffness formations are taken into account. In the current release (MD Nastran R3), several extensions have been made to improve robustness and user-friendliness. To improve the overall convergence control, the artificial damping and auto-switch features have been added. To analyze the creep material behavior, the adaptive time stepping for creep is introduced. For convenience of use, the Bulk Data entry (NLAUTO) has been replaced by a new Bulk Data entry NLADAPT. With NLADAPT (combined with NLPARM), you can set up the parameters for SOL 400 to control the load step size of each increment.

NLADAPT Bulk Data Entry NLADAPT is newly designed in MD Nastran R3 to replace the original NLAUTO Bulk Data entry used in MD Nastran R2. With the NLADAPT Bulk Data entry, the time stepping control parameters defined by NLAUTO are now defined with the optional word “STEP”. In addition, another optional word “CREEP” is made available for the time step control of creep behavior in the current release. Recycling Criterion The default recycle based criterion works as follows: You specify a desired number of recycles. For most problems, it is sufficient to provide a value in the range of three to five. For problems with severe nonlinearities, or for problems with very small convergence tolerances, it may be necessary to increase this number. This number is used as a target value for the load stepping scheme. If the number of recycles required in the current increment is less than the desired number, the load step for the next increment is increased. The time step increase is based on a factor, S u , that you can also specify. Typical values for S u are in the range of 1.2 to 1.5. While the time step increase is obviously more aggressive with larger scale factors, it should be noted that there may be excessive recycling and cutbacks if sudden nonlinearities are encountered. In order to avoid this, the following logic is used for higher scale factors : If the actual number of recycles in an increment is greater than 60% of the desired number of recycles (i.e., the current increment did not converge easily), the increased scale factor for the next increment is limited to 1.25 for scale factor values between 1.25 and 1.5625, and to 80% of the value for scale factors above 1.5625. Time Step Cutback Scheme The load step is never increased during an increment. If the number of recycles needed to obtain convergence exceeds the desired number, the load step size is scaled back, the recycling cutback number N r is incremented by 1 and the increment is performed again with the new load step. The scaleback factor for the

Main Index

N r th

cutback is taken as

s

Nr

, where the factor s is calculated from the expression

CHAPTER 3 129 Advanced Integrated Nonlinear and Contact

s Z

T JJJJJJsJ Tm

2 ⁄ (N

rm

(N

rm

H 1))

where N r m is the maximum number of recycling related cutbacks for the increment and is calculated from 5

⎛ 10 ⋅ T s⎞ N rm Z log 10 ⎜ JJJJJJJJJJJJJJJJJJJ⎟ ⎝ Tm ⎠ Ts

is the time increment before any recycling related cutbacks occur for the increment and

minimum possible time step for the increment.

Tm

is equal to the value set by the user ( 10

Ó5

Tm

is the

by default)

if there is no quasi-static inertial damping and is equal to 10 Ó3 times the value set by the user ( 10 Ó8 by default) if there is quasi-static inertial damping. The scale-back factor for any cutback is the smaller of ( s Nr , 1 ⁄ S u ). This scheme guarantees that no matter what the starting time step for an increment, the minimum time step is reached in a reasonable number of cutbacks if the increment consistently fails to converge. Quasi-Static Damping Scheme For mechanical static analysis, instability often occurs under the conditions with very strong nonlinearities or very low stress of the whole analyzed model. In order to improve the stability under such circumstances, the artificial damping scheme is made available to SOL 400 in the current MD Nastran R3 release. The optional default damping scheme is identified as scheme number 4 in the corresponding Marc technology (and is the only one implemented in MD Nastran SOL 400). With this feature a damping factor, F d , is introduced, which at the start of the loadcase, is set to 0. The time step for the first increment is set equal to the user defined initial time step. During the assembly of the stiffness matrix K and the right-hand side vector F , the contributions from damping are added to both sides of the equation system as K da mp and F da mp , respectively. With artificial damping option, the adaptive time stepping scheme is still used to control the time step size, however, the adjustment will be made based on the damping energy of the system. For the first increment of the loadcase, the calculation of F d and predicted energy is based on the estimated strain energy and damping energy for the loadcase. For the subsequent increments of the loadcase, F d and the time step size are modified according to the total strain energy and estimated strain energy. Adaptive Time Stepping Control for Creep Analysis Creep is a time-dependant inelastic behavior that can occur at any stress level, either below or above the yield stress of a material. In many cases, creep is also accompanied by plasticity, which occurs above the yield stress of the material. Along with the existing adaptive time stepping scheme, a new option is added to activate the additional time stepping control due to creep behavior of materials. For the current release,

Main Index

130 MD Nastran R3 Release Guide Adaptive Time Stepping Scheme Enhancements for Quasi-Static Analysis

this option only applies to the advanced nonlinear elements, for other elements, the creep stepping control still uses the existing scheme. The NLADAPT Bulk Data entry has added the parameters for the creep time stepping control through optional keyword “CREEP”. The time period of creep time can be specified and a suggested time increment can be defined through NLPARM by fields 2 and 3 of the first line. For a given step t , a solution is obtained and SOL 400 finds the largest values of stress change per stress, Δσ ⁄ σ and creep strain change per elastic strain, values,

Ts

(stress change tolerance) and

Te

Δε

cr

⁄ε

el

. It compares these values to the tolerance

(strain change tolerance), for this period. The value p is

calculated as the larger of ( ( Δ σ ) ⁄ σ ) ⁄ T σ and ( Δ ε c r ⁄ ε e l ) ⁄ T ε . If p < 1 , the solution is continued. Upon the completion of the existing time stepping, the time stepping will chosen for the next step as t ne w Z t ol d ⋅ α , where α is a factor calculated according to the criteria for the creep analysis. The criteria are the tolerances you entered through the optional word “CREEP” of NLADAPT entry. When you enter the tolerances and controls, the following conventions apply: • All stress and strain measures in tolerance checks are second invariants of the deviatoric state

(that is, equivalent von Mises uniaxial values). • You can reset all the tolerances and control upon the completion of one load step (NLADAPT)

sequence. Since the time increment is adjusted to satisfy the tolerances, it is impossible to predetermine the total number of time increments for a given total creep time. Auto-Switch In several types of analyses, maximum reactions or displacements are extremely small (even close to the round-off errors of computers). In such circumstances, not all types of relative convergence criteria may work properly. For example, in a problem with stress-free motion, the convergence check based on relative displacement increments works correctly but not the convergence check based on relative residual or strain energy. In this situation, it is necessary to check the convergence with absolute values of reactions or strain energy; otherwise, the analysis may terminate prematurely. Similarly, this kind of situation may happen for problems with springback and free thermal expansion or constraint thermal expansion. The details for the cases where convergence checking with relative values may encounter difficulties are listed in the table below. The AUTO SWITCH option is designed to switch to the proper convergence check scheme automatically if any of the situations mentioned above occur during the analysis. This optional convergence check is activated by adding character “A” into field (1, 8) of the NLAPRM entry. This AUTO SWITCH option allows automatic switching of the convergence check scheme to check as required on either residuals or displacements if small reactions or displacements are detected, or to use the absolute strain energy checking if necessary. If AUTO SWITCH is turned on, it: 1. Switches on the relative residual checking if the relative displacement criterion is used (which fails when the maximum incremental displacement becomes very small Max._incremental_displacement/Smallest_element size < 1.0e-6)

Main Index

CHAPTER 3 131 Advanced Integrated Nonlinear and Contact

2. Switches on the relative displacement checking if the relative residual force (moment) criterion is used (which fails when the maximum reaction force becomes very small <1.0e-8) 3. To switch on the absolute energy checking if the structure is free of stress and deformation (strain energy density < 1.0e-15). Note that if both residual and incremental displacement criteria are already chosen (like “UP”), AUTO SWITCH feature will not be activated even if character “A” is specified. In this case, SOL 400 will ignore it. Exceptions There are some exceptions to the basic scheme outlined above. If an increment is consistently converging with the current load step and the number of recycles exceeds the desired number, the number of recycles is allowed to go beyond the desired number until convergence is achieved or up to the user specified maximum number. The time step is then decreased for the next increment by 1 ⁄ S u . An increment is determined to be converging if the convergence ratio was decreasing in three previous recycles. Special rules also apply in a contact analysis. During the recycles, the contact status can keep changing (new nodes come in contact, nodes slide to new segments, separate etc.). Whenever the contact status changes during an increment, a new set of contact constraints are incorporated into the equilibrium equations and more recycles are necessary in order to find equilibrium. These extra recycles, due to contact changes, are not counted when the recycle number is checked against the desired number for determining if the load step needs to be decreased within the increment. Thus, only true NewtonRaphson iterations are taken into account. For the load step of the next increment, the accumulated number of recycles during the previous increment is used. This ensures that the time step is not increased when there are many changes in contact during the previous increment.

Results Output In many analyses it is convenient to obtain post file results at specified time intervals. This is naturally obtained with a fixed load stepping scheme but not with an automatic scheme. Traditionally, the post output frequency is given as every nth increment. Using the NLPARM option, you can request post output to be obtained at equally spaced time intervals. In this case, the time step is temporarily modified to exactly reach the time for output. The time step is then restored in the following increment. Defaults The defaults of the NLADAPT option are carefully chosen to be adequate in a wide variety of applications. There are cases, however, when the settings may need to be modified. Assume that the default settings are used, which means that the recycle based control is active with an initial load of one per cent of the total. If the structure is weakly nonlinear, convergence is obtained in just a few recycles and the time steps for successive increments get progressively larger. This can lead to problems if the initially weakly nonlinear structure suddenly exhibits stronger nonlinearities; for instance, occurrence of plasticity or parts coming into contact. Possible remedies to this problem include: 1. Decrease the time step scale factor to a smaller number so the step size does not grow so rapidly.

Main Index

132 MD Nastran R3 Release Guide Adaptive Time Stepping Scheme Enhancements for Quasi-Static Analysis

2. Use the maximum time step to limit large steps. 3. Decrease the desired and maximum number of recycles to decrease the load step if more recycles are needed. Another situation is if the structure is highly nonlinear and convergence is slow. In this case, it may be necessary to increase the desired number and maximum number of recycles. In general, there is a close connection between the convergence tolerances used and the desired number and maximum number of recycles.

Main Index

CHAPTER 3 133 Advanced Integrated Nonlinear and Contact

Contact and Adaptive Time Stepping Enhancements for Transient Dynamic Analysis MD Nastran R3 contains significant enhancements for transient dynamics. This includes enhancements for dynamic contact and dynamic time-stepping scheme.

Enhancements for Dynamic Contact The purpose of the MD Nastran R3 enhancements is to enable a stable solution for dynamic contact / impact problems. High frequency oscillations are excited during dynamic contact and they cause unrealistic solutions unless eliminated/ damped out quickly. The following enhancements have been implemented for dynamic contact: 1. The existing HHT scheme has been extended to a Generalized-Alpha scheme. The generalizedalpha scheme is a two-parameter scheme that allows the spectral radius to vary between 0.0 and 1.0. The governing equations are given by int ext Muˇˇ n H 1 H α H Cuˇ n H 1 H α H F n H 1 H α Z F n H 1 H α m

f

f

f

(3-1)

where α f is identified by NDAMP and can vary between -0.5 and 0.0, α m is identified by NDAMPM and can vary between -0.5 and 1.0. By default, for contact/impact problems, MD Nastran R3 automatically uses NDAMP = 0.0 and NDAMPM = 1.0. This corresponds to a spectral radius of 0.0. For non-contact problems, MD Nastran R3 uses previous HHT defaults: NDAMP = -0.05 and NDAMPM = 0.0. The values of NDAMP and NDAMPM can be explicitly changed by the user by using PARAM,NDAMP,xxx and PARAM,NDAMPM,yyy in the input file. 2. A dynamic penetration cutback scheme has been implemented. The default iterative penetration scheme that is used for statics does not work well for dynamics since high-frequency oscillations are excited by this process. Instead, a time step cutback is triggered when dynamic penetration is detected. The increment is repeated with a smaller time step. This time step Δ t c is defined by the penetration algorithm as a factor of the original time step Δ t o . The scheme is depicted in Figure 3-13:

Main Index

134 MD Nastran R3 Release Guide Contact and Adaptive Time Stepping Enhancements for Transient Dynamic Analysis

Δtc

Δto

Figure 3-13

Cutback scheme implemented for Dynamic Penetration

Multiple penetrations are possible in a single increment. After the penetration cutbacks, time step for the subsequent increment is restored to the pre-penetration time step. Note that the penetration cutback is independent of the bisection algorithm, i.e., MAXBIS, DTBIS do not control the penetration time steps. The penetration cutback is indicated in the .f06 file by *** USER INFORMATION MESSAGE 4550 (nl3con) *** TIME-STEP REDUCTION IS ACTIVATED BY DYNAMIC PENETRATION. 3. Miscellaneous enhancements for dynamic contact include the following: a. Nodal projection (pulling/pushing a node that falls within the distance tolerance onto the surface) is avoided for dynamic contact. This again avoids high frequency oscillations being excited by the nodal projection. The lack of nodal projection may be a result of a small gap seen between the contacting node and the contacted surface at the end of the increment. b. Cutbacks are also initiated when the maximum displacement increments violate internally calculated contact super-box dimensions. This prevents run-away increments where the nodal displacements become unbounded. As a result, a cutback, when there is no apparent penetration, is likely triggered in the program by such a large displacement in the system. 4. The limitations of the dynamic contact enhancements are as follows: a. The Generalized-Alpha scheme with zero spectral radius is a damped operator. The accuracy of the operator is a function of the time steps used. Large time steps can cause frequency ranges of interest also to be damped out. A general recommendation would be to use time steps about 2 to 5% of the dominant period of the system. b. There is no special code to deal with momentum / energy conservation for impact problems. While the elimination of high-frequency content through the mechanisms described previously and satisfaction of the dynamic equilibrium equations given in (1) generally suffices for most contact / impact problems, it may not suffice for systems where large amounts of energy conversion (kinetic energy to strain energy and vice versa) occur during the contact process.

Main Index

CHAPTER 3 135 Advanced Integrated Nonlinear and Contact

A simple example of a ball falling under gravity and bouncing off a rigid surface is shown. All the enhancements described above have been used in calculating the dynamic response of the ball. The model is shown in Figure 3-14 and the displacement response for three successive bounces is shown in Figure 3-15. It is seen that for this elastic problem, there is good conservation of momentum although there is some energy dissipation with small reductions in successive bounce heights.

Figure 3-14

Main Index

Bouncing Ball Model Setup

136 MD Nastran R3 Release Guide Contact and Adaptive Time Stepping Enhancements for Transient Dynamic Analysis

Figure 3-15

Displacement response of Bouncing Ball

Enhancements for Dynamic Time-Stepping The purpose of the MD Nastran R3 enhancements for dynamic time stepping is to address some shortcomings in the MD Nastran R2 time-stepping scheme. 1. The Initial Time Step Adjustment process is extended in MD Nastran R3 to advanced non-linear elements. During this process, if the ADJUST setting (time-step adjustment flag on TSTEPNL) is non-zero and TZEROMAX (specified through integer system cell 373) is non-zero, then after completing a minimum of two converged time steps, the analysis restarts with an appropriate time step size. Note that this time step can be the same as the user-prescribed value or can be smaller. In MD Nastran R2, the TZEROMAX process was not available for advanced non-linear elements identified through PSHLN1, PSHLN2, PSLDN1, PBEMN1. This limitation has been removed in MD Nastran R3. Note that for contact problems, the TZEROMAX process is still not available in MD Nastran R3. 2. If the time step interval, NO, on the TSTEPNL entry is > 1, then the time steps can exceed the initial time step DT specified by the user. The time step bounds for each increment are given by DT DT MIN ⎛ JJJJJJJJJJJJJJJJJJJJJJJ, JJJJJJJJJJJJJJJJJ⎞ ≤ Δt ≤ MIN ( MAXRˇ DT, NOˇ DT ) ⎝ MAXBIS MAXR⎠

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CHAPTER 3 137 Advanced Integrated Nonlinear and Contact

Note that if NO = 1 (default value), then Dt cannot exceed DT (this is similar to the functioning of MD Nastran R2). However, for NO > 1, Dt can exceed DT in MD Nastran R3. The following factors are taken into account by the time stepping algorithm while deciding on the time step for the next increment: a. The time step cannot exceed the values prescribed by the frequency algorithm and by output time step requirements. b. Whenever feasible, the time step will adjust such that it is a perfect sub-multiple (1/2, 1/4, etc.) of the output time step. The time step will also adjust to an optimal value to prevent thrashing (where the frequency and output requirements alternately control the time step). 3. The time steps will adjust such that end-of-step time is reached exactly. This allows multiple steps with tabular loading to function accurately. 4. The default MSTEP value has been set to 10 or 20 depending on the non-linearity of the problem. This default allows better accuracy for nonlinear problems. 5. The frequency based algorithm is used for the time stepping only if ADJUST is not zero. However, the output based algorithm is used for the time stepping even if ADJUST is zero. For instance, if the time step is reduced to an arbitrary number due to a penetration cutback, then the output algorithm will still ensure that the next required output time will be reached exactly.

Main Index

138 MD Nastran R3 Release Guide Progressive Failure Analysis with a Micromechanical Module

Progressive Failure Analysis with a Micromechanical Module Introduction A module to facilitate the micromechanical analysis has been integrated with MD Nastran R3 using an advanced composite technology that can be used for composite materials using shells, solid shells and composite bricks in solution sequences 400 (SOL 400) and shells in solution sequence 700 (SOL 700). It is only available for nonlinear elements, so for shells the PCOMP or PCOMPG must be used (in addition with PSHLN1 for SOL 400) and for solids the PCOMPLS option must be used. The usage of the micromechanical module is possible by the MATM option (See MATM (SOLs 400/700) (p. 2114) in the MD Nastran Quick Reference Guide). The property options PCOMP, PCOMPG or PCOMPLS refer to a material, and a MATM definition can be associated with this material. If any material in a composite definition has an associated MATM, then the micromechanical module will be used for calculating the material stiffness for this composite. The MATM Bulk Data entry may specify the use of properties from other materials also. The micromechanical module calculates the material stiffness for the composite. In addition, it calculates material damage and degrades the material stiffness in case damage occurs.

Definition of a Composite For SOL 400, there are currently five types of composite definitions available: total ply, fiber and matrix, braided, triaxial and honeycomb. These are defined using the parameters of the MATM entry: PLY, MATRIX, BRAID, TRIAX and HONEY. For SOL 700 only the following options are available: PLY, MATRIX and HONEY. Total Ply The orthotropic properties of the ply are given directly. The material moduli are given through the standard MAT8 (shells) or MATORT (solids) options. The PLY keyword to MATM is used, and it identifies which MAT8/MATORT to use and provides the strength values for the ply. Fiber and Matrix The properties for the matrix and fiber materials are given separately. The matrix is isotropic so the moduli are given through MAT1 and the fibers are orthotropic given by MAT8 or MATORT. The fiber material and strength values are given with the PLY keyword and for the matrix the MATRIX keyword is used. The presence of the MATRIX keywords signals to the program to interpret the data under PLY as fiber properties. One also defines the fiber volume fraction and the void volume fraction. The program internally calculates the total ply properties.

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CHAPTER 3 139 Advanced Integrated Nonlinear and Contact

Braided (SOL 400 only) The braided composite is a variant of a fiber and matrix definition. In addition to specifying the fiber and matrix properties, the BRAID keyword of MATM is used for defining the braiding of the fibers. With this option, multiple fiber definitions can be used in the same ply. Triaxial (SOL 400 only) Similar to braided, this option allows further specification of the fibers. The TRIAX keyword is used for defining the fiber packing information. Honeycomb The honeycomb option defines a honeycomb material. The ply properties are defined with the PLY keyword and the cell size of the honeycomb is defined with the HONEY keyword. The stress-strain option and thermal loads are not supported with the honeycomb model and only shell elements are supported. Failure Analysis There are currently 24 failure theories available. They are listed under FTi in the bulk data definition of MATM. The strength values (maximum stresses etc.) are defined with the PLY and MATRIX keywords. When failure occurs, the material stiffnesses are degraded. This can be done in two ways: critical and non-critical failure. Associated with each these two failure types is a degradation factor, both of which default to 0.01. Critical Failure For critical failure, all moduli are decreased to the critical degradation factor times the original modulus. Non-Critical Failure For non-critical failure, the modulus in the fiber direction is not affected. If total ply properties are used, the modulus in the first material direction is not changed. If fiber and matrix properties are given, only the matrix properties are degraded when failure occurs. Crack Density Model (SOL 400 only) A crack density model is available. It allows a gradual degradation of the stiffness upon failure. Only failure in the transverse direction will occur. This model is activated by setting ITYPE=2 (first line of the MATM option). Nonlinear Stress-Strain Curve (SOL 400 only) A simple model for a non-linear stress-strain behavior is available. It is quite similar to the existing NLELAST option of MATS1, MATS3 or MATSORT. A curve giving the effective stress vs. the effective strain is given through the TABL3D0 Bulk Data entry. It can be specified for the PLY or the MATRIX

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140 MD Nastran R3 Release Guide Progressive Failure Analysis with a Micromechanical Module

keyword. If specified on the PLY it refers to the whole ply, and if given on MATRIX it only affects the matrix properties. This option is not supported for the honeycomb model. Temperature Effects (SOL 400 only) There are two effects of temperatures available: temperature dependent material properties and thermal strains. Temperature Dependent Material Properties (SOL 400 only) The material moduli can change with the temperature as in any SOL 400 analysis. The standard options MATT8, MATT1 etc. are used. Temperature dependency of the strength values in MATM is given through the MATTM option. Thermal Strains (SOL 400 only) Thermal strains due to prescribed temperatures are also supported for the micromechanical module. This option is not supported for the honeycomb model.

Output The failure status (1 for failed and 0 for non-failed), crack density and active failure modes are printed to the f06 file. The output can look something like this

A D V A N C E D ELEMENT ID 322

P F A

INTEG. PLY ID POINT ID 4 1 2

R E S U L T S FAILURE STATUS 1 1

F O R

L A Y E R E D

CRACK FAILURE DENSITY MODES 4.295E+00 in-plane 4.290E+00 in-plane

C O M P O S I T E

E L E M E N T S

shear + shear +

Results of failure status and crack density are also available in the DBALL file for post processing in Patran and SimXpert. Licensing The PFA and advanced composites in MD Nastran R3 require separate licensing and can be obtained from your local MSC offices.

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CHAPTER 3 141 Advanced Integrated Nonlinear and Contact

3D Contact: Moment-Carrying Glue and Beam-toBeam, Edge-to-Surface and Edge-to-Edge Introduction General 3D contact capability, along with 2D solid edge to edge contact, was implemented in MD Nastran R2 that supports the Grid-to-Surface type of contact in all translational degree-of-freedoms. In addition, the Permanent Glue and General Glue contact also were introduced at the same time. In MD Nastran R3, the primary enhancements of the 3D contact are (1) Moment-Carrying-Glue contact that includes the rotational degree-of-freedoms in glued-contact as well as the translational degree-offreedoms and (2) General Line contact capability that includes general Beam-to-Beam contact, Edge-toSurface and Edge-to-Edge contact for beam, plate and shell elements. (Note that “Edge” means the perimeter of plate and shell elements.) The new features listed below are discussed in the following sections: 1. Moment Carrying Glue 2. Improved Flexibility in Contact (for Shells only, in this release) 3. In-Plane Shell Edge-to-Edge Glue 4. General Line Contact • Beam-to-Beam Contact • General Shell Edge(-to-Edge and -to-Surface) Contact

5. Optimize Contact Constraints 6. GLUE Control • UNGLUE – release specified grids from being glued. • Breaking Glue

7. Miscellaneous Items • Case Control Command BCONTACT=ALLBODY • Case Control Commands BCMOVE and BCHANGE • Support 3D Contact Restart • MPC with Contact Logic Improvement • Separation Logic Improvement

All 3D contact capabilities introduced in this release are supported in both SOL 400 and SOL 101 contact. At the same time, any type of the Permanent Glue contact is supported in the following solution sequences: SOL 101, 103, 105, 107, 108, 109, 110, 111, 112, 200 and 400.

Main Index

142 MD Nastran R3 Release Guide 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

Benefits 1. Moment Carrying Glue makes the jointing of two dissimilar meshes more realistic and passes the grounding check. Also potential spurious modes should no longer occur. 2. Improved Flexibility in Contact for Shells gives the user more options and controls to the plate and shell in contact. 3. General Line Contact gives users more freedom in modeling. There are no Grid-to-Surface contact limitations when working with beam, plate and shell type of elements. 4. Optimize Contact Constraints can help users determine the contact slave-and-master relation automatically. 5. UNGLUE helps users to exclude Grids from glued-areas to make modeling easier. 6. Breaking Glue offers a new capability to separate the glued-areas under specified conditions. 7. MPC with Contact Logic Improvement remove the conflict between user specified MPCs', including linear Rigid Elements, with the contact constraint equation. 8. BCONTACT=ALLBODY gives the user a choice to abandon the complicated BCTABLE inputs. 9. BCMOVE and BCHANGE Case Control Commands in conjunction with the BCONTACT= ALLBODY allows the user control and change contact definition with BCONTACT=ALLBODY. 10. 3D Contact is supported in chaining analysis.

Moment Carrying Glue In MD Nastran R2, the contact constraint for glued contact with shells only involved the grids translational degrees of freedom. In other words, the Moments were not carried across the contact interface. In MD Nastran R3, full moment carrying glue is supported. It includes all the following types of contact (1) Shell-to-Shell, (2) Shell-to-Solid, (3) Beam-to-Shell, and (4) Beam-to-Solid.

Input Moment Carrying Glue can work with both General Glue and Permanent Glue. By using the existing IGLUE entry on BCTABLE, the user can apply this capability to the model: • IGLUE=3 on BCTABLE: full moment carrying glue with projection of the node

onto the surface • IGLUE=4 on BCTABLE: full moment carrying glue without projection of the node onto the

surface

Limitations Moment carrying glue is NOT supported for the following types of contact: • Beam-to-Beam

Main Index

CHAPTER 3 143 Advanced Integrated Nonlinear and Contact

• Shell Edge-to-Shell Edge (with BEAMB=1 on BCPARA)

Examples Following are examples for the Moment Carrying Glue Contact. Since all of them have been included in the QA Decks library, they are not listed in this guide. The referenced input files can be found in the TPL directory in the MD Nastran R3 installation. Example 1: Beam-to-Solid (nlcmc01.dat) As an example of the Moment Carrying Glue contact in SOL 400, Figure 3-16 shows the undeformed and deformed shape and location.

Figure 3-16

Moment Carrying Glue Contact (Beam-to-Solid)

Here is the basic description of this model • 2 Contact bodies: • Body 1: beam element • Body 2: solid element • Enforced rotation of end point of beam around x-axis

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144 MD Nastran R3 Release Guide 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

• Beam is in moment carrying glued contact with solid • BCTABLE: • IGLUE=3 • BCPARA: • NLGLUE=1 (optional)

Note that if NLGLUE=1 is specified on BCPARA, this job run as Permanent Glue contact. Otherwise, it runs as the General Glue contact. Example 2: Shell-to-Solid (nlcmc02c.dat) As an example of the Moment Carrying Glue contact in SOL 400, Figure 3-17 shows the undeformed and deformed shape.

Figure 3-17

Moment Carrying Glue Contact (Shell-to-Solid)

Here is the basic description of this model • 2 Contact bodies: • Body 3: shell elements • Body 5: solid elements

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CHAPTER 3 145 Advanced Integrated Nonlinear and Contact

• Pressure load on shell elements • Shells are in moment carrying glue contact with solids • BCTABLE: • IGLUE=4 • BCPARA: • NLGLUE=1 (optional)

Note that if NLGLUE=1 is specified on BCPARA, this job run as Permanent Glue contact. Otherwise, it runs as the General Glue contact.

Improved Flexibility in Contact (for Shell only in MD Nastran R3) Currently, different types of elements are not allowed to be mixed in one contact body (defined on BCBODY Bulk Data entry). For example, beam type of elements, plate or shell type of elements and solid type of elements cannot be mixed in one BCBODY. New input flags COPT’s on BCBODY and BCTABLE defining which contact is possible between two contact bodies are introduced for this purpose. We currently only use the COPT's family for Shell elements in contact body. Since the COPT's family is described below in general. Some of the relationships do not apply for the MD Nastran R3 release and are so marked. The basic format of COPT is “COPT = A + 10 * B + 1000 * C” • A: the outside of the solid elements in the body (can be ignored in MD Nastran R3) • = 1: the outside will be in the contact description (DEFAULT) • B (flexible bodies): the outside of the shell elements in the body • = 1: both top and bottom faces will be in the contact description, thickness offset will be

included (DEFAULT) • = 2:only bottom faces will be in the contact description, thickness offset will be included • = 3:only bottom faces will be in the contact description, shell thickness will be ignored • = 4: only top faces will be in the contact description, thickness offset will be included • = 5: only top faces will be in the contact description, shell thickness will be ignored • = 6: both top and bottom faces will be in the contact description, shell thickness will be

ignored Note that if B = 6 for both bodies in a contact combination, then nodes that separate from a body, cannot come in contact again in the current step or in subsequent steps unless a different flag is chosen for one of the bodies. • B (rigid bodies): the rigid surface (can be ignored in MD Nastran R3) • = 1: the rigid surface should be in the contact description (DEFAULT) • C (flexible bodies): the edges of the body

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146 MD Nastran R3 Release Guide 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

• = 1: only the beam/bar edges are included in the contact description (DEFAULT) • = 10: only the free and hard shell edges are included in the contact description • = 11: both the beam/bar edges and the free and hard shell edges are included in the contact

description C. It has no effect if beam-to-beam contact is OFF (BEAMB1 on BCPARA). BCPARA BEAMB will be discussed under Beam-to-Beam Contact. Free shell edge means the opened edge and all the other shell edges are hard shell edges.

Input The new entries of COPT family on BCBODY and BCTABLE are listed here. BCBODY 1

2

3

4

5

6

7

8

9

BCBODY

BID

DIM

BEHAV

BSID

ISTYP

FRIC

IDSPL

CONTROL

DCOS2

DCOS3

NLOAD ANGVEL DCOS1 “ADVANCE”

10

VELRB1 VELRB2 VELRB3

SANGLE COPTB

“RIGID”

CGID

NENT

--- Rigid Body Name ---

“GROW”

GF1

GF2

GF3

“HEAT”

CFILM

TSINK

CHEAT

BNC

EMISS

HBL

“PATCH3D”

NPATCH

TAB-GF1 TAB-GF2 TAB-GF3 TBODY

HCV

HNC

ITYPE

COPTB are the defaults for the contact body, may be overridden by COPTS/COPTM or COPTS1/COPTM1 on BCTABLE: BCTABLE 1

2

3

BCTABLE

ID

IDSLAVE

Main Index

5

6

IDMAST NGROUP COPTS

7

8

9

COPTM

ERROR

FNTOL

FRIC

CINTERF

IGLUE

ISEARCH

ICOORD

JGLUE

TOLID

DQNEAR

DISTID

“FBSH”

FRLIM

BIAS

SLIDE

HARDS COPTS1 COPTM1

“SLAVE” IDSLA1

X

4

“BKGL”

BGST

BGSN

BGM

BGN

“HHHB”

HCT

HCV

HNC

BNC

EMISS

HBL

FK

EXP

METHOD

ADAPT

THICK

THICKOF

PENV

PENCHK

FSF

VSF

BSORT

FACT

TSTART

TEND

MAXPAR

EROSOP

IADJ

SOFT

DEPTH

ISYM

I2D3D

IGNORE

SPR

MRP

VDC

SFS

SFM

SST

MST

SFST

SFMT

AUTO

LCID

FCM

US

PSF

FA

ED

INTTYPE

FRCFRQ SNLOG SBOPT

10

CHAPTER 3 147 Advanced Integrated Nonlinear and Contact

1

2

X X

3

4

5

6

7

8

9

NFLS

SFLS

IGNOFF

FSLIM

PYS

TDIC

CDIST

NFLF

SFLF

NEN

MES

TBLCID

TBLAB

IGAP

FTBID

VC

SMOOTH

FLANGL

PENMAX

THKOPT SHLTHK

10

SLDTHK SLDSTF

X “MASTERS”

DBID

TIDRF

TIDNF

DBDTH

DFSCL

NUMINT

IDMA1

IDMA2

IDMA3

IDMA4

IDMA5

IDMA6

IDMA8

IDMA9

...

IDMA7

COPTS and COPTM are the defaults for the slave and master body combinations in this BCTABLE and may be overridden for a particular body combination by COPTS1 and COPTM1.

Examples In-Plane Shell Edge-to-Edge Glue Only the mid-plane of shell elements are considered in this capability; therefore, shell thickness is ignored. Both top and bottom faces of the shell are included in contact description. Separation is based on the absolute value of the component of the contact force in the direction perpendicular to the touched body.

Input The basic requirements of input are • COPTB=60 on BCBODY, or COPTS=COPTM=60 on BCTABLE • IGLUE > 0 on BCTABLE

Since it is shell with glued contact, the Moment Carrying Glue option IGLUE=3 or 4 on BCTABLE are recommended but not forced.

Limitations In the In-Plane Shell Edge-to-Edge Glue Contact, when Grids separate from a body, cannot come in contact again in the current STEP or in subsequent STEP’s unless a different COPT flag is chosen for one of the bodies.

Examples The following examples are for the In-Plane Shell Edge-to-Edge Glue Contact. Since all of them have been included in the QA Decks library, they are not listed in this guide.

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148 MD Nastran R3 Release Guide 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

Example 3: Four Co-plane Shell Bodies Edge-to-Edge Glue (nlc025a.dat) As an example of the In-plane Shell Edge-to-Edge Glue contact in SOL 400, Figure 3-18 shows the undeformed and deformed shape. These four shells are co-plane in undeformed shape. Their thicknesses are ignored in contact description.

Figure 3-18

Four Shell Bodies Edge-to-Edge Glue

• 4 Contact bodies (all shell elements, edges match) • Pressure load on all shells • Shells are in moment carrying glue contact with each other, shell thickness is ignored • BCTABLE: • COPTS1=COPTM1=60 • IGLUE=3

Please refer to the previous Improved Flexibility in Contact (for Shell only in MD Nastran R3), 145, for the details of COPTS1=COPTM1=60. Example 4: Five Irregular Shell Bodies Edge-to-Edge Glue (nlc026a.dat) As an example of the In-plane Shell Edge-to-Edge Glue contact in SOL 400, Figure 3-19 shows the undeformed and deformed shape. These 5 shells are not co-plane in undeformed shape. Their thickness are ignored in contact description.

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CHAPTER 3 149 Advanced Integrated Nonlinear and Contact

Figure 3-19

Five Irregular Shell Bodies Edge-to-Edge Glue

• 5 Bodies (all shell elements) • Pressure load on some shells • Clamped at bottom (open size) • Shells are in moment carrying glue contact with each other, shell thickness is ignored • BCTABLE: • COPTS1=COPTM1=60 • IGLUE=3 • ISEARCH=0 • ICOORD=3 • BCBODY: • IDSPL= -1 • ISTYP=2

Note that ISEARCH=0 and ISTYP=2 trigger on the Optimize Contact Constraint capability, which is to be introduced below. The entry ICOORD=3 turn on Initial Stress Free and Delay Sliding Off capabilities. At the same time IDSPL=-1 activate the Analytic (SPLINE) Analysis.

Main Index

150 MD Nastran R3 Release Guide 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

Example 5: Five Irregular Shell Bodies Edge-to-Edge Glue plus the 6th Shell Body as a "Footplate" (nlc026c.dat) As an example of the In-plane Shell Edge-to-Edge Glue contact in SOL 400, Figure 3-20 shows the undeformed shape only. The 1st 5 Shell Bodies are the same as Example 4: Five Irregular Shell Bodies Edge-to-Edge Glue (nlc026a.dat), 148. Their thicknesses are ignored in contact description. Contact between the new added footplate structure and the other old Grid-to-Surface contact structure is considered. Its thickness is not ignored.

Figure 3-20

Five Irregular Shell Bodies Edge-to-Edge Glue plus the 6th Shell Body as a “Footplate"

• Clamped at edge of “footplate” • Bodies 1-5 are in moment carrying glue contact with body 6 • Thickness of “footplate” is included • BCTABLE: • COPTB=60 (Bodies 1~5) • COPTB=10 (Body 6) • IGLUE=3 • ISEARCH=0 • ICOORD=3

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CHAPTER 3 151 Advanced Integrated Nonlinear and Contact

• BCBODY: • IDSPL= -1 • ISTYP=2

This model is almost the same as Example 4 except the Footplate, the 6th Body. Note that COPTB=10 for the 6th BCBODY tells that its thickness is not ignored in the contact analysis. In other word, the contact relation between the 6th BODY and others is not the In-plane Shell Edge-to-Edge Glue.

Beam-to-Beam Contact All beam types of elements have to associate cylindrically or conically shaped contact surface first before they can do the general line contact. The radius of the contact surface (beam contact radius) is entered via BCBMRAD Bulk Data entry on a per element basis. Note that the beam contact radii are averaged at the nodes of the beams; therefore, the taper shape is possible to each beam Body. Contact is established between the closest points of the contact surfaces associated with two beam elements. A multi-point constraint is imposed on the closest points of beam elements in contact to suppress relative displacement in the direction of the normal to the contact surfaces. Since beam elements do not have cross-sectional stresses, beam-to-beam contact separation is always based on nodal forces. Only the bilinear Coulomb friction model (FTYPE=6) is supported.

Input When running Beam-to-Beam contact, the following two inputs are required. • BCPARA: BEAMB=1 • BCBMRAD 1

2

3

4

5

6

7

8

9

BCBMRAD

RADIUS

TYPE

ID1

ID2

THRU

ID3

BY

N

ID4

THRU

ID5

ID6

ID7

ID8

ID9

10

Limitations

Field

Contents

RADIUS

Equivalent radius to be used for beam-beam contact problems. (Real, no Default)

TYPE

The attribute of all following ID’s. (Character, Default = “EID”)

IDi

Main Index

EID

Defines all the following entries are the IDs of beam-type elements.

BODY

Defines all the following entries are the IDs of BCBODYs.

ALL

Defines the default RADIUS for all beam-type elements.

ID of a beam-type element, CROD, CBAR, CBEAM and CBEAM3, or a BCBODY with the specified radius. (Integer, no Default)

152 MD Nastran R3 Release Guide 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

1. Only 2-noded beam, bar and rod elements are supported by beam-to-beam contact. CBEAM3 elements are not supported 2. If a beam element is touching another beam element, then the direct neighbor elements of the beam (that is, elements that share a node with the contacting element) cannot come in contact with the same contact body in the same direction. This is to avoid multiple contact constraints being imposed on a node in that direction. 3. Sliding from one beam element to the next element is defined only if the element has a unique neighbor element (i.e. a beam cannot slide over a branch). 4. The check for beam contact conditions is always single sided with automatic optimization of contact constraint equations (ISTYP is ignored) 5. Analytic (SPLINE) option of the contact body is not supported for beam contact bodies (IDSPL is ignored) 6. If the nodes of a beam element touch a rigid body, a solid or a shell element, then the beam contact radius (BCBMRAD) is ignored 7. The searching order for deformable contact bodies (ISEARCH) is supported by beam-to-beam contact, but in general is of little use, since the same constraints will be imposed whether body 1 is touching body 2 or body 2 is touching body 1. However, if contact conditions are ignored due to remark 2., then reversing the search direction by setting ISEARCH=1 and switching slave and master bodies may solve the problem. 8. Stress-free initial contact and delayed slide-off are not supported for beam-to-beam contact (ICOORD is ignored) 9. The glue option that retains initial gaps and overlaps (IGLUE=2), as well the moment carrying glue options (IGLUE=3 or 4), are not supported for beam-to-beam contact. Each case is treated as IGLUE=1. However, these options are supported for the nodes of a beam element that touch a rigid body, a shell or solid element. 10. Since beam elements do not have cross-sectional stresses, beam-to-beam contact separation is always based on nodal forces: • IBSEP is ignored by beam-to-beam contact • FNTOL on BCPARA and BCTABLE is always interpreted as a force • In general, force-based separation must be used with beam-to-beam contact (IBSEP = 0) • If stress-based separation is required, then the separation threshold (FNTOL) for beam-to-

beam contact combinations must be explicitly specified on the BCTABLE and the nodes of the beam elements should not touch other entities 11. Only the bilinear Coulomb friction model (FTYPE=6) is supported

Examples Following are examples for the Beam-to-Beam contact. Since all of them have been included in the QA Decks library, they are not listed in this guide.

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CHAPTER 3 153 Advanced Integrated Nonlinear and Contact

Example 6: Crossed Beams (nlc027a.dat) As an example of the Beam-to-Beam contact in SOL 400, Figure 3-21 shows the undeformed shape only. This example shows that two crossed beam contacts at one point and then separate.

Figure 3-21

Crossed Beams

• Two contact bodies (all CBEAMs) • Body 1 clamped at both ends • Body 2 clamped at one end and loaded by point force in z-direction at the other end • BCPARA: • BEAMB=1 • BCBODY • COPTB=1000 (default) • BCBMRAD,0.05,ALL

Please refer to Improved Flexibility in Contact (for Shell only in MD Nastran R3), 145, for the details of COPB=1000.

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154 MD Nastran R3 Release Guide 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

Example 7: Coiled Beams (nlc027b.dat) Two wires, modeled as cantilever beams, are initially parallel to each other. Figure 3-22 is the deformed shape after twisting them together.

Figure 3-22

Coiled Beams

• Two initially parallel wires • Clamped at one end • Other ends rotated about common center • Two contact bodies (all CBEAMs) • BCPARA: • BEAMB=1 • BCBODY • COPTB=1000(default) • BCBMRAD,0.05,ALL

All crossed lines connect points in contact on the beam axes.

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CHAPTER 3 155 Advanced Integrated Nonlinear and Contact

General Shell Edge(-to-Edge and -to-Surface) Contact To support this capability, the Beam-like contact entities are created automatically on the free and the hard edges of a shell structure. Note that these created entities don’t add any stiffness to the model. Beam-to-beam contact is used internally to detect contact between the beam-like entities and to handle sliding, separation and friction. Contact radii of the beam-like entities are derived from the thickness of the shell elements (R = T/2).

Input Since it is Beam-to-Beam contact internally, the BEAMB must be switched on • BCPARA: BEAMB=1

At the same time, Shell edges must be included in contact description • COPTB=10010 on BCBODY or COPTS=COPTM=10010 on BCTABLE

The above two inputs are the basic requirements for General Shell Edge contact.

Limitations • Since beam-to-beam contact is used internally, all the same limitations of the Beam-to-Beam

contact are also applied to General Shell-Edge contact • Only the bilinear Coulomb friction model (FTYPE=6) is supported • Not available for quadratic shell elements.

Examples Below are examples for the General Shell-Edge contact. Since all of them have been included in the QA Decks library, they are not listed in this guide. Example 8: Shell Free Edge Contact (nlc028a.dat) As an example of the General Shell Edge contact in SOL 400, Figure 3-23 shows the undeformed shape only of two contacting shells along the free edges.

Main Index

156 MD Nastran R3 Release Guide 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

Figure 3-23

Shell Free Edge Contact

• 2 Contact bodies

(all shell elements, edges do not match) • Enforced displacement of the top edge of body 2 • BCPARA: •

BEAMB=1

• BCBODY: •

COPTS1=COPTM1=10010

Please refer to the previous Improved Flexibility in Contact (for Shell only in MD Nastran R3), 145, for the details of COPTS1=COPTM1=10010. Example 9: Thin-Wall Square Boxed Free Edges Contact (nlc028b.dat) As an example of the General Shell Edge contact in SOL 400, Figure 3-24 shows the undeformed shape only of two thick walled open square box structures in contact along the free edges.

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CHAPTER 3 157 Advanced Integrated Nonlinear and Contact

Figure 3-24

Thin-Wall Square Boxed Free Edges Contact

• Two shell bodies contacting each other on the edges • BCPARA: • BEAMB=1 • BCBODY: • COPTS1=COPTM1=10010

Please refer to the previous Improved Flexibility in Contact (for Shell only in MD Nastran R3), 145, for the details of COPTS1=COPTM1=10010.

Optimize Contact Constraints When optimization of contact constraints is activated, the slave and master relation between different BCBODY’s is based on: • Softer-or-harder materials (HARDS=2.0 in default on BCTABLE) • finer-or-coarse meshes

The user can let the program determinate the slave and master relation automatically.

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158 MD Nastran R3 Release Guide 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

Input This capability is activated when: • ISTYP=2 on BCBODY • ISEARCH=0 (Default) on BCTABLE (or no BCTABLE)

Limitations None.

Examples See Example 4: Five Irregular Shell Bodies Edge-to-Edge Glue (nlc026a.dat), 148 and Example 5: Five Irregular Shell Bodies Edge-to-Edge Glue plus the 6th Shell Body as a "Footplate" (nlc026c.dat), 150.

GLUE Control UNGLUE With UNGLUE, the user can select some nodes of the contact body for regular contact instead of glue contact even if the contact table (BCTABLE) says that they should be glued. Those selected nodes will ignore any glue condition and do regular contact instead.

Input The following inputs are required for this capability • UNGLUE (or BCONTACT) Case Control command. Its format is as follows

UNGLUE (SOL 400)

Contact Body Unglue Selection

Selects the grids should use standard contact instead of glued contact in glued bodies. Format: UNGLUE=n • UNGLUE Bulk Data entry I

UNGLUE (SOL 400)

Contact Body

This entry is only necessary if glued contact has been specified and some of the grids should use standard contact instead of glued contact.

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CHAPTER 3 159 Advanced Integrated Nonlinear and Contact

1 UNGLUE

2

3

4

5

6

7

8

ID

BID

ID1

THRU

ID2

BY

N

ID3

THRU

ID4

ID5

ID6

9

10

ID

Identification number referenced by a SUBCASE or STEP Case Control command. See Remark 1. (Integer > 0, no Default)

BID

Identification number of the specified BCBODY (Integer > 0, no Default)

IDi

ID list of Grids (Integer > 0, no Default) • IGLUE(=1, 2, 3 or 4) on BCTABLE

In the same rule as BCMOVE and BCHANGE, the user can still use the ID from BCONTACT Case Control command to select UNGLUE Bulk Data entries but UNGLUE Case Control command always dominates the selection of it.

Limitations UNGLUE is ignored by Permanent Glue.

Breaking Glue When a glued contact node breaks due to the breaking criterion, then it will internally switch to the unglue option.

Input The basic requirements for this capability are listed here. • IGLUE > 0 on BCTABLE • JGLUE = 2 on BCTABLE • 4 new entries (SN, ST, m, n) on BCTABLE under “BKGL” keyword 1

2

3

BCTABLE

ID

IDSLAVE

“SLAVE” IDSLA1 ISEARCH

Main Index

4

5

6

IDMAST NGROUP COPTS ERROR

FNTOL

ICOORD JGLUE

7

8

9

COPTM

FRIC

CINTERF

IGLUE

TOLID

DQNEAR

DISTID COPTS1 COPTM1

“FBSH”

FRLIM

BIAS

SLIDE

HARDS

“BKGL”

BGST

BGSN

BGM

BGN

“HHHB”

HCT

HCV

HNC

BNC

EMISS

HBL

FK

EXP

METHOD

ADAPT

THICK

THICKOF

PENV

10

160 MD Nastran R3 Release Guide 3D Contact: Moment-Carrying Glue and Beam-to-Beam, Edge-to-Surface and Edge-to-Edge

1

2

“MASTERS”

3

4

5

6

7

8

9

FACT

TSTART

TEND

MAXPAR

PENCHK

FSF

VSF

EROSOP

IADJ

SOFT

DEPTH

BSORT

ISYM

I2D3D

IGNORE

SPR

MRP

VDC

10

FRCFRQ SNLOG SBOPT

SFS

SFM

SST

MST

SFST

SFMT

AUTO

LCID

FCM

US

PSF

FA

ED

INTTYPE

NFLS

SFLS

IGNOFF

FSLIM

PYS

TDIC

CDIST

NFLF

SFLF

NEN

MES

TBLCID

TBLAB

IGAP

IDMA1

IDMA2

IDMA3

IDMA4

IDMA5

IDMA6

IDMA7

IDMA8

IDMA9

...

where

“BKGL”

New keyword for BreaKing GLue

BGSN(SN)

Maximum normal stress for Breaking Glue (Real, Default 0.0)

BGST(ST)

Maximum tangential stress for Breaking Glue (Real, Default 0.0)

BGM(m)

The first exponent for Breaking Glue (Real, Default 2.0)

BGN (n)

The second exponent for Breaking Glue (Real, Default 2.0)

The Breaking Criteria is σ n σ m ⎛ JJJJJJNJ⎞ H ⎛ JJJJJTJ⎞ > 1.0 ⎝ SN⎠ ⎝ ST⎠

Limitations Nodes must be glued first during the analysis. Only when they are released due to the breaking criterion will they switch to do regular contact.

Miscellaneous Items • BCONTACT=ALLBODY Case Control Command • In MD Nastran R2, Case Control command BCONTACT=SID is required to all 3D Contact

analysis. • With the new option, BCONTACT=ALLBODY, BCTABLE Bulk Data entries are not

required anymore. All BCBODY’s defined in the file will be searched for contact. All entries on BCTABLE will take the default values. • Case Control Commands BCMOVE and BCHANGE • In MD Nastran R2, BCMOVE and BCHANGE Bulk Data entries shared the same ID with

BCTABLE controlled by BCONTACT Case Control command.

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CHAPTER 3 161 Advanced Integrated Nonlinear and Contact

• With the new Case Control commands BCMOVE and BCHANGE, they can have their own

ID’s at each STEP. • User can still use the ID from BCONTACT Case Control command to select BCMOVE

(and/or BCHANGE) Bulk Data entries but BCMOVE and BCHANGE Case Control commands always dominate their selection. • Input: Refer to MD Nastran Quick Reference Guide • Restart in 3D Contact • In MD Nastran R2, 3D Contact cannot run restart jobs. • In MD Nastran R3, the 3D Contact supports restart capability but only with the model using

traditional Nastran elements (Elements not referred to a PSHLN1, PSHLN2, PSLDN1, and etc. entry). • MPC with Contact Logic Improvement • This improvement will prevent that Grids having M-set degrees of freedom to be constrained

by the contact component. • The M-set Grids of MPC equations will be neglected in the contact search. • Separation Logic Improvement • The separation check will be skipped after 5 consecutive iterations when the members in the

chattering set are not changed • Improved separation message when chattering is detected.

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162 MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

Explicit Nonlinear - SOL 700 Introduction MD Nastran R3 SOL 700 is the third release of powerful Explicit Nonlinear Solution available in MD Nastran and offers an advanced technology to analyze transient dynamic events of short duration with severe geometric and material nonlinearities. MD Nastran SOL 700 allows users to work within one common modeling environment using the same Bulk Data interface. The NVH, linear and nonlinear models can be used for explicit applications such as crash, crush, and drop test, blade out and bird strike simulations. This dramatically reduces the time spent to build different models for implicit and explicit analysis and prevents the users from making mistakes because of unfamiliarity between different programs.

New Capabilities in Explicit Nonlinear - SOL 700 MD Nastran R3 SOL 700 has been dramatically improved to include the following new capabilities in this release: 1. Advanced Fluid Structure Interaction (FSI) – Broadband applications 2. Parallel FSI based on Distributed Memory Parallel Technology 3. Advanced Composites based on micromechanical failure and damage capability 4. SPH Method – Smooth Particle Hydro-Dynamics 5. Sheet Metal Forming with springback capability 6. Integrated, Multi-disciplinary Fan Blade Out (FBO) and Rotor Dynamics simulation 7. Analysis Chaining: • Implicit to Explicit (Prestress) • Explicit to Explicit (Multiple Droptest) • Explicit to Implicit (springback)

8. New element and material models 9. FAA Hybrid II and III Dummies

Advanced Fluid Structure Interaction (FSI) The FSI capability was first introduced in SOL 700 with the MD Nastran R2 release and was limited to airbags and occupant safety simulation. With MD Nastran R3, full capabilities of advanced Dytran FSI technology are implemented in SOL 700 which will allow users to simulate complex, broadband FSI applications such as: • Sloshing • Blasts and Explosives

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CHAPTER 3 163 Advanced Integrated Nonlinear and Contact

• Hydroplaning • Fluid-filled bottle droptest

Fluid Filled Bottles Courtesy - Nampak • Fuel tank sloshing and crush • Fuel pumps • Aircraft crashworthiness on water

Crash with Airbags on Water • Bird Strike with fluid bird

Bird Strike • Weapon Design • Under Water Shock Analysis (UNDEX) • Many more

The analysis of the physical behavior of fluids and gases is best solved using a Eulerian approach. The nature of the behavior of these types of materials is represented in a natural way using a finite volume description based on the Euler equations of motion. Accurate solver(s) are available in MD Nastran R3

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164 MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

SOL 700 that allows you to analyze the behavior of fluids and gases, coupled to structures if necessary and defines the fluxes of mass, momentum and energy, the conserved problem quantities. The objective of fluid-structure interaction using the coupling algorithm is to enable the material modeled in Eulerian and Lagrangian meshes to interact. Initially, the two solvers are entirely separate. Lagrangian elements that lie within an Eulerian mesh do not affect the flow of the Eulerian material and no forces are transferred from the Eulerian material back to the Lagrangian structure. The coupling algorithm computes the interaction between the two sets of elements. It thus enables complex fluid-structure interaction problems to be analyzed. The FSI in MD Nastran R3 SOL 700 is based on the advanced Finite Volume (Eulerian) and Coupling technologies of Dytran while the structural part is co-simulated based on LS-DYNA solver. The following FSI technologies are now available in SOL 700: • Single Material Hydrodynamic • Single Material Hydrodynamics with Strength • Multi-Material Hydrodynamics • Multi-Material Hydrodynamics with Strength

Shaped Charge • General Coupling • Porosity Models • Closed Volume • Fast Coupling • Multiple Eulerian Domains with Multiple Coupling Surfaces • Coupling surface with Failure • Coupling Surfaces with Porous Holes • Flow between Eulerian domains • Deactivation

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CHAPTER 3 165 Advanced Integrated Nonlinear and Contact

Sloshing • Multiple Adaptive Euler • Standard Euler Solver • Roe Solver • Riemann Solver • Special techniques for Fluid-filled containers • Hot filling for plastic bottles • Mesh Box with non-uniform Euler • Graded Mesh • Hydrostatic boundary conditions for UNDEX • Skin Friction

Hydroplaning In addition numerous material models are added that are highlighted in the new material and element sections (see Section 9). For a more detailed discussion of the FSI theories and capabilities, please refer to MD Nastran Explicit Nonlinear (SOL 700) User’s Guide.

Parallel FSI With the release of MD Nastran R3 SOL 700, we are pleased to introduce the long awaited Parallel FSI capability. The Parallel FSI is based on the Distributed Memory Parallel (DMP) technology and will dramatically increase the performance and reduce the simulation time of the CPU intensive FSI applications. The MD Nastran R3 Parallel FSI capability is limited to single material hydro-dynamics and general coupling using the MESH box. Please refer to the MD Nastran Explicit Nonlinear (SOL 700) User’s Guide for a detailed discussion of Parallel FSI capability.

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166 MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

Figure 3-25 This is a sloshing simulation which was run up to 4 CPUs and shows dramatic speed-ups. Cache Coherency with the Euler cubes is the explanation for the super linear scaling as indicated in the picture. The speed-up can also be observed on 2 and 4 CPU runs when the Euler cubes are used (1cpu-cache result). As shown in Figure 3-25, even if the cache coherency is taken out, the scaling is still impressive - 1.62 (2cpu) and 2.41 (4cpu).

Advanced Composites Two major, advanced composite capabilities are added to MD Nastran R3 SOL 700 to support the Progressive Failure Analysis (PFA) and honeycomb material behavior. The first capability is based on prediction of delamination and failure of composite shell structures and the second capability will allow accurate simulation of honeycomb material for both shells and solid structures. The MD Nastran R3 SOL 700 PFA capability will allow users to study the delamination and failure of plies, matrix, fiber and interlaminate plies of composites structures at micro-mechanic levels. New material models and numerous failure criteria are introduced to support the new composite capability. These materials are common and consistent between SOL 400 and SOL 700.

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CHAPTER 3 167 Advanced Integrated Nonlinear and Contact

Please see Progressive Failure Analysis with a Micromechanical Module, 138.

Smooth Particle Hydrodynamics (SPH) Method Smooth Particle Hydrodynamics (SPH) is another important capability that is implemented in MD Nastran R3 SOL 700. The SPH method is known to be an effective technique in certain class of problems where there is a presence of highly deformable material with complex erosion properties. The SPH method is basically a meshless lagrangian technique to model fluid flow problems such as crashworthiness on water or soft soil, high velocity impact, penetration and perforation problems. See the MD Nastran Explicit Nonlinear (SOL 700) User’s Guide for more details.

High Velocity Impact Courtesy - CEI Ensight

Sheet Metal Forming (SMF) with Spring-back Sheet metal forming is a complex application and requires tailored material properties and special contact features such as draw bead models to predict the deep drawing of the sheet metal and the springback effect after the dies are removed. The deep drawing is simulated by SOL 700 explicit solver and then results are transferred to the implicit solver to reduce the computation time for the spring-back effect.

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168 MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

Four new material models are introduced in the MD Nastran R3 SOL 700 which are tailored for SMF: MATD036: This model was developed by Barlat and Lian [1989] for modeling sheets with anisotropic materials under plane stress conditions. This material allows the use of the Lankford parameters for the definition of the anisotropy. MATD037: This model is for simulating sheet forming processes with anisotropic material. Only transverse anisotropy can be considered. Optionally an arbitrary dependency of stress and effective plastic strain can be defined via a load curve. This plasticity model is fully iterative and is available only for shell elements. MATD039: This model is for simulating sheet forming processes with anisotropic material. Only transverse anisotropy can be considered. Optionally, an arbitrary dependency of stress and effective plastic strain can be defined via a table. A Forming Limit Diagram (FLD) can be defined using a table and is used to compute the maximum strain ratio which can be post processed. This plasticity model is fully iterative and is available only for shell elements. MATD190: This model was developed by Barlat and Lian [1989] for modeling sheets with anisotropic materials under plane stress conditions. This material allows the use of the Lankford parameters for the definition of the anisotropy. This particular development is due to Barlat and Lian [1989]. It has been modified to include a failure criterion based on the Forming Limit Diagram. The curve can be input as a table, or calculated based on the n-value and sheet thickness. In addition, four new contact methods are introduced for Metal Forming contact behavior (BCTABLE): METHOD = FORMNS: Forming nodes to surfaces METHOD = FORM1SS: Forming one way surface to surface METHOD = FORM2SS: Forming surface to surface

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CHAPTER 3 169 Advanced Integrated Nonlinear and Contact

METHOD=DRAWBEAD: The draw bead is defined two ways: 1. A consecutive list of slave nodes that lie along the bead using BCGRID 2. A set of property ID’s of beams that lie along the draw bead using BCPROP.

Additional features that are available for draw bead include: • TIDRF TABLEID for draw bead bending force • TIDNF TABLEID for draw bead normal force • DBDTH Draw bead depth • DFSCL Scale factor for TIDRF load curve • NUMINT Number of equally spaced integration points along the draw bead

Springback simulation – Springback simulation is a chained analysis where the results of sheet forming and deep drawing from the explicit run are used as a pre-condition in the implicit solver for springback simulation. The methodology below describes the analysis steps for SMF and follow up springback simulation: • 1st run: drawing simulation with SOL 700 explicit solver • Use the SEQROUT Bulk Data entry to generate a file with nodes, elements and stresses at

the end of the job. This file will be used for a subsequent analysis • File = JobName.dytr.nastin • 2nd run: springback analysis with SOL 700 implicit solver • Use the INCLUDE Bulk Data entry to include prestress file for the structure

(JobName.dytr.nastin) • Use the SPRBCK Bulk Data entry to activate the implicit springback analysis • Use the SEQROUT Bulk Data entry to write a file with nodes, elements and element stresses

at the end of the job, which can also be used for a subsequent analysis The trimming features are not supported in MD Nastran R3 and will be included in future releases.

Integrated Fan Blade Out (FBO) and Rotor Dynamics (RD) simulation The FBO-RD solution in MD Nastran R3 presents an efficient multi-disciplinary, integrated implicitexplicit-implicit analysis process for more accurate simulation of engine fan blade-out condition using

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170 MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

MD Nastran. FBO event is extremely nonlinear due to heavy wide cord fan blades incorporated for new generation of high by-pass ratio jet engines to meet airframe manufacturers’ demand for higher thrust engines with improved performance and optimum weight. Analytical procedures are used by airframe and engine manufacturers to support design of propulsion installation and adjacent wing structures.

Until now the industry standard practice has been primarily focused on the application of the various point solutions to predict pre-stressing of the fan blades, fan blade out analysis and standalone rotor dynamics simulation. However, with MD Nastran R3, the FBO-RD simulation process is automated. The new FBO-RD solution offers an integrated, multi-disciplinary simulation capability in MD Nastran to streamline the FBO event from prestressing of fan blades to blade-out on a fine-meshed finite element model, typically used by engine manufacturers to rotor dynamics simulation using a much coarser mesh as used by airframe companies, all in one common modeling environment. This process can result in much higher levels of accuracy and dramatically reduce cost of analysis and design process.

The engine manufacturers typically use a fine and detailed finite element model of the engine to conduct an explicit FBO simulation. The analysis objective is to generate the loads for the airframe manufacturers to compute the mass unbalance and conduct an implicit rotor dynamics simulation to predict the engine stability. Even though the engine is the same but the simulation models are mostly company-confidential and are not shared among manufacturers. For this reason, the airframe companies construct their own finite element model of the engine for rotor dynamics analysis which usually has a much coarser mesh than the FBO model.

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CHAPTER 3 171 Advanced Integrated Nonlinear and Contact

Typical FBO Loads One of the problems of the current practice has been the FBO loads that are generated by the explicit solver, are not directly shared and rather approximated and normalized before it is sent to airframe manufactures. The problem is exacerbated by the fact the location and exact timing of the FBO loads on the surrounding structure are missing, forcing the airframe companies to approximate the location of applied loads in the coarse mesh model for RD simulation. These loads are usually on the conservative side, resulting in over-design. The MD Nastran R3 will allow the companies “share” the same Nastran database that includes accurate time history of FBO loads, both impact and rub loads, as well as their applied location, as computed by MD Nastran SOL 700 explicit solver. A new entry called “BLDOUT” defines blade out force output information and mapping criteria for a combined SOL 700 – SOL 400 Blade-out analysis (used both in the SOL 700 and subsequent SOL 400 analyses).

Whirl Diagram from Rotor Dynamics Further, it will also allow the airframe manufacturers to read those loads from the database and map them correctly on a coarse mesh model for rotor dynamic simulation performed by MD Nastran R3 SOL 400. The FBO load mapping on the coarse mesh, time steps synchronization between explicit and implicit models, are completely automated in SOL 400. The integrated FBO-RD in MD Nastran R3 offers the first “Industry Standard” solution and will facilitate a common modeling and analysis environment to achieve high fidelity results while dramatically reducing the product design cycle. Please consult MD Nastran R3 SOL 700 User’s Guide for more details.

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172 MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

Analysis Chaining Some of the automated analysis chaining have already been discussed such as FBO-RD simulation which is an implicit-explicit-implicit chaining. There are basically three types of analysis chaining that are available in SOL 700: 1. Implicit to Explicit (Prestressing etc.) 2. Explicit to Explicit (Multiple droptests etc.) 3. Explicit to Implicit (Springback etc.) Implicit to Explicit Chaining (Prestress) The prestressing was available and discussed in MD Nastran R2 and is supported by using the “PRSTRS” entry at the beginning of the run. The results of the prestress will then be written in a file called NASINIT for subsequent runs. Explicit to Explicit (Multiple Droptest etc.) The user will perform a regular impact analysis. By adding a specific output, after the simulation has finished an intermediate file “nastin” is generated. This file holds information of the deformed shape of model together with new thicknesses, stresses and strains of all shells. The nastin file contains GRID, CQUAD4, CTRIA3 (with thinknesses) and ISTSxx describing the stress state of each solid, shell and beam element. This file can be included in a new model, which has a different impact scenario. See the following figure for schematic representation of process flow.

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CHAPTER 3 173 Advanced Integrated Nonlinear and Contact

Explicit to Implicit (Springback etc.) The user first will perform a regular stamping analysis by SOL 700 explicit solver. By adding a specific output request in the model called “SEQROUT”, SOL 700 will generate an intermediate file “nastin” for subsequent springback analysis. This file holds information of the deformed shape of model together with new thicknesses, stresses and strains of all shells. This file can be included in a new model for springback simulation using the SOL 700 implicit solver.

Combined Chaining – Certain applications requires an implicit-explicit-implicit chaining such as sheet metal forming where the sheet metal might be pre-stressed prior to the actual deep drawing operation and the follow up springback effect. Under those scenarios, the user first will perform a regular implicit prestress analysis by using the “PRSTRS” flag to generate the NASINIT file. Next, the results of the NASINIT file are read in the SOL 700 explicit solver while an entry called “SEQROUT” is used to save the results of the stamping analysis. By using different subcases, contacts can be defined to predict the multi-stage interactions of the different parts and bodies. By adding a specific output, after the simulation has finished an intermediate file NASTIN is generated. This file holds information of the deformed shape of model together with new thicknesses, stresses and strains of all shells. This file can be included in a new model, which defines the spring back analysis. If the user has also added the specific entries, the spring back analysis will generate new NASTIN file which holds the same information of the new stabilized shape.

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174 MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

New Materials and Elements With the complete implementation of FSI technology in MD Nastran R3, numerous material models and elements are introduced to simulate the complex behavior of fluids, gases and their interaction with the surrounding structure. These include various Equations of State, Yield, Shear and Failure models in addition to different types of Eulerian elements and properties. In addition new models are added to support SMF capabilities that are highlighted in previous sections. A complete list of these new capabilities is out of the scope of the release notes. Please refer to the MD Nastran Quick Reference Guide for a detailed description. The MD Nastran Explicit Nonlinear (SOL 700) User’s Guide includes the theoretical background of FSI technology and offers numerous examples.

Support for FAA Hybrid II and III Dummy Models MD Nastran R3 SOL 700 supports two new dummies that are tailored for aerospace and defense applications. These are Federal Aviation Administration (FAA) Hybrid II and Hybrid III dummies that are developed in native MD Nastran SOL 700 format and are available from Engineering Technology Associates (ETA).

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CHAPTER 3 175 Advanced Integrated Nonlinear and Contact

New SOL 700 Bulk Data Entries and Parameters Table 3-2 contains new Bulk Data entries for SOL 700 in MD Nastran R3. More details can be found in the MD Nastran Quick Reference Guide.

Table 3-2

New Bulk Data Entries for SOL 700 New for MD Nastran R3 (SOL 700)

Bulk Data Entries

Main Index

Description

ABINFL

Defines an inflator model suited for airbag analyses. The inflator model is defined as part of the GBAG or COUPLE surface.

BARRIER

Defines a barrier for transport in an Eulerian mesh.

BLDOUT

Defines blade out force output information and mapping criteria

CMARKB2

Defines a 2-noded marker beam element by means of connecting two grid points.

CMARKN1

Defines a 1-noded marker element on a grid point.

COUOPT

Defines the interaction factor and a pressure load from the covered side acting on a BSURF.

COUP1FL

Defines the surrounding variables when a segment of a coupling surface fails.

COUPINT

Defines the interaction between two coupling surfaces.

COUPLE

Defines a coupling surface that acts as the interface between an Eulerian (finite volume) and a Lagrangian (finite element) domain.

CSPH

Purpose: Defines a SPH particle.

CYLINDR

Cylindrical shape used in the initial condition definition on the TICEUL entry.

DBREG

Defines a drawbead region.

DETSPH

Defines the ignition point from which a spherical detonation wave travels, causing the reaction of high explosive materials.

176 MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

Table 3-2

New Bulk Data Entries for SOL 700 New for MD Nastran R3 (SOL 700)

Bulk Data Entries

Main Index

Description

EOSIG

Defines the properties of Ignition and Growth equation of state and the reaction rate equation used to model high explosives.

EOSJWL

Defines the properties of a JWL equation of state commonly used to calculate the pressure p of the detonation products of high explosives

EOSMG

Defines the properties of a Mie-Gruneisen equation of state commonly used to calculate the pressure p in high strain rate processes.

EOSTAIT

Defines the properties of an equation of state based on the Tait model in combination with a cavitation model where the pressure p is defined as follows:

FAILJC

Defines the properties of the Johnson-Cook failure model.

FAILMPS

Defines the properties of a failure model where failure occurs when the equivalent plastic strain exceeds the specified value.

FFCONTR

Defines the pressure within a closed volume. Intended for the use in (partially) filled containers, where dynamic fluid effects are negligible, e.g. top loading and hot filling.

FLOWDEF

Definition of default Eulerian flow boundary condition.

FLOW

Defines the properties of a material for the boundaries of an Eulerian mesh.

FLOWSPH

Purpose: Define a flow of particles. This option applies to continuum domains modeled with SPH particles.

FLOWT

Defines the material properties for the in- or outflow of material trough the boundary of an Euler mesh. Inflow velocity and material properties can be chosen time dependent.

GBAGCOU

Defines a switch from full gas dynamics to uniform pressure formulation.

GBAG

Defines the pressure within an enclosed volume.

HEATLOS

Defines the heat-transfer model to be used with GBAG or COUPLE.

HTRCONV

Defines the heat transfer through convection for a COUPLE and/or GBAG surface. Convection is heat transfer from the air bag to the environment through the air bag surface.

HTRRAD

Defines the heat transfer through radiation for a COUPLE and/or GBAG surface. Radiation is heat transfer from the air bag to the environment through the air bag surface.

HYDSTAT

Initializes the Euler element densities in accordance to a hydrostatic pressure profile.

CHAPTER 3 177 Advanced Integrated Nonlinear and Contact

Table 3-2

New Bulk Data Entries for SOL 700 New for MD Nastran R3 (SOL 700)

Bulk Data Entries

Main Index

Description

INFLTR

Defines the inflator characteristics of a COUPLE and/or GBAG subsurface.

INFLCG

Defines the cold gas-inflator characteristics of a COUPLE and/or GBAG subsurface

INFLGAS

Defines a thermically ideal gas to be used with a standard or hybrid inflator.

INFLHB

Defines the hybrid-inflator characteristics of a COUPLE and/or GBAG subsurface.

INFLTNK

Defines the Tanktest-inflator characteristics of a COUPLE and/or GBAG subsurface

INITGAS

Specifies the initial gas composition inside a gasbag or Euler coupling surface.

LEAKAGE

Defines the porosity model to be used with GBAG or COUPLE.

MATDEUL

Defines a complete constitutive model as a combination of an equation of state, a shear model, a yield model, a failure model, a spall model (PMIN), and corotational frame.

MESH

Defines a mesh.

PERMEAB

Defines the permeability of a COUPLE and/or GBAG (sub)surface. Permeability is the velocity of gasflow through a (sub)surface and is defined as a linear or tabular function of the pressure difference over the surface.

PERMGBG

Defines a permeable area of a COUPLE and/or GBAG surface, connected to another GBAG. The velocity of the gas flow through the surface is defined as a linear or tabular function of the pressure difference.

PEULER1

Eulerian element properties. The initial conditions of these elements are defined in geometric regions.

PEULER

Defines the properties of Eulerian elements.

PMARKER

Defines the behavior of the marker element in the FV domain.

PMINC

Defines a spallation model where the minimum pressure is constant.

PORFCPL

Defines an interaction between two coupling surfaces through a hole.

PORFGBG

Defines a hole in a couple and/or GBAG (sub)surface, connected to another GBAG.

PORFLOW

Defines the material properties for the in- or outflow of an Eulerian mesh through a porous area of the couple surface.

PORFLWT

Defines a time dependent flow trough a porous area of the couple surface.

PORHOLE

Defines a hole in a COUPLE and/or GBAG surface.

PORHYDS

Prescribes a hydrostatic pressure profile on a porous BSURF.

178 MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

Table 3-2

New Bulk Data Entries for SOL 700 New for MD Nastran R3 (SOL 700)

Bulk Data Entries

Main Index

Description

PSPH

Purpose: Define properties for SPH particles.

SEQROUT – Sequential Run Output generation

Purpose: At the end of an explicit simulation write out the initial state to a file that can be used for a subsequent explicit SOL 700 run.

SHREL

Defines an elastic shear model with a constant shear modulus.

SHRPOL

Defines an elastic shear model with a polynomial shear modulus.

SPHERE

Spherical shape used in the initial condition definition on the TICEUL entry.

SPRBCK

Activates springback analysis tailored for sheet metal forming.

SURFINI

Defines a surface that is used for initialization of regions of an Eulerian mesh.

TICEL

Defines the initial values of element variables at the beginning of the analysis.

TICEUL

Defines the initial value sets for Eulerian regions. The Eulerian regions are defined by geometric shapes.

TICREG

Defines the initial value sets for Eulerian regions. The Eulerian regions are defined by geometric shapes.

TICVAL

Defines the initial values of an Eulerian geometric region.

YLDHY

Defines a yield model with zero yield stress.

YLDJC

Defines a Johnson-Cook yield model where the yield stress is a function of effective plastic strain, strain rate, and temperature.

YLDMC

Defines a Mohr-Coulomb yield model.

YLDMSS

Defines the yield model for snow material. This entry must be used in combination with MATDEUL, EOSPOL and SHREL.

YLDPOL

Defines a polynomial yield model where the yield stress is a function of effective plastic strain.

YLDRPL

Defines a rate power law yield model where the yield stress is a function of effective plastic strain and strain rate.

YLDSG

Defines the Steinberg-Guinan yield model where the yield stress is a function of effective plastic strain, pressure and temperature.

YLDTM

Defines the Tanimura-Mimura yield model where the yield stress is a function of effective plastic strain, strain rate and temperature.

YLDVM

Defines a bilinear or piecewise-linear yield model with isotropic hardening, using the von Mises yield criterion.

YLDZA

Defines the Zerilli-Armstrong yield model where the yield stress is a function of effective plastic strain, strain rate and temperature.

CHAPTER 3 179 Advanced Integrated Nonlinear and Contact

Table 3-2

New Bulk Data Entries for SOL 700 New for MD Nastran R3 (SOL 700)

Bulk Data Entries

Description

Spotweld Rupture Stress – SPWRS

Purpose: Define a static stress rupture table for shell elements connected to spot weld beam elements using the constrained contact option: METHOD=SPOTWELD. This table will not work with other contact types. Data, which is defined in this table, is used by the stress based spot weld failure model developed by Toyota Motor Corporation. See MATDSWx entries where this option is activated by using MATDSW6 and OPT=RS.

MATD036

Modeling sheets with anisotropic materials under plane stress conditions

MATD037

Simulating sheet forming processes with anisotropic material

MATD039

Simulating sheet forming processes with anisotropic material

MATD078 – Soil and Purpose: This model permits concrete and soil to be efficiently modeled. concrete material

Main Index

MATD145 – Schwer Murray CAP Model

Purpose: The Schwer & Murray Cap Model, a.k.a. Continuous Surface Cap Model, is a three invariant extension of the Geological Cap Model (MATD025) that also includes viscoplasticity for rate effects and damage mechanics to model strain softening. The model is appropriate for geomaterials including soils, concrete, and rocks.

MATD190

This model was developed by Barlat and Lian [1989] for modeling sheets with anisotropic materials under plane stress conditions. The material allows the use of the Lankford parameters for the definition of the anisotropy. It has been modified to include a failure criterion based on the Forming Limit Diagram. The curve can be input as a table, or calculated based on the n-value and sheet thickness.

MATD016 – Pseudo Tensor

Purpose: This model has been used to analyze buried steel reinforced concrete structures subjected to impulsive loadings.

SPHSYM

Purpose: Define a symmetry plane for SPH. This option applies to continuum domains modeled with SPH particles.

SPHDEF

Purpose: Provide controls for computing SPH particles.

EOSGRUN

Purpose: The Gruneisen equation of state.

180 MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

Table 3-2

New Bulk Data Entries for SOL 700 New for MD Nastran R3 (SOL 700)

Bulk Data Entries

Description

MATD053

Purpose: This allows the modeling of low density, closed cell polyurethane foam. It is for simulating impact limiters in automotive applications. The effect of the confined air pressure is included with the air being treated as an ideal gas. The general behavior is isotropic with uncoupled components of the stress tensor.

MATD116

Purpose: This material is for modeling the elastic responses of composite layups that have an arbitrary number of layers through the shell thickness. A pre-integration is used to compute the extensional, bending, and coupling stiffness for use with the Belytschko-Tsay resultant shell formulation. This material model must be used with the user defined integration rule for shells, see *INTEGRATION_SHELL, which allows the elastic constants to change from integration point to integration point. Since the stresses are not computed in the resultant formulation, the stresses output to the binary databases for the resultant elements are zero. Note that this shell does not use laminated shell theory and that storage is allocated for just one integration point (as reported in D3HSP) regardless of the layers defined in the integration rule.

MATD163

Purpose: Crushable foam with optional damping, tension cutoff, and strain rate effects. Unloading is fully elastic. Tension is treated as elastic-perfectlyplastic at the tension cut-off value.

Table 3-3 contains new Bulk Data entries for SOL 700 in MD Nastran R3. More details can be found in

the MD Nastran Quick Reference Guide. Table 3-3

New Parameters For SOL 700 New for MD Nastran R3 (SOL 700)

Parameters

Main Index

Description

AXIALSYM

Enables an efficient and accurate 2d axial symmetry for Eulerian materials. A much larger time step becomes possible by not taking into account the mesh-size in circumferential direction.

BLADEDEL

Option to whether SOL 700 blade out scratch files such as ncforc are deleted or not at the end of the run.

BLADESET

Parameter to set the ID of the UNBALNC entry for SOL 700 blade out computations.

BLDRSTRT

Option to restart SOL 700 blade out analysis after the BINOUT to NCFORCE conversion so that regeneration of the BINOUT, D2PLOT and NCFORCE files is not required.

CHAPTER 3 181 Advanced Integrated Nonlinear and Contact

New for MD Nastran R3 (SOL 700) Parameters

Main Index

Description

BLDTHETA

Parameter to set the value of “THETA” on the UNBALNC entry for SOL 700 blade out computations.

COPOR

Activates contact based porosity.

DELCLUMP

This parameter prevents small clumps in the Euler mesh from determining the time step and prevents the leakage of small masses to isolated regions.

DYNINT

Defines the size of the integer memory in words.

DYNREAL

Defines the size of the float memory in words.

EULBND

Defines boundary treatment for Euler boundaries.

EULBULKL

Defines the default value of the linear bulk viscosity coefficient for Eulerian materials.

EULBULKQ

Defines the default value of the quadratic bulk viscosity coefficient for Eulerian materials.

EULBULKT

Defines the default type of bulk viscosity for Eulerian materials.

EULSTRES

Defines the update logic for stresses when material is transported in Euler elements.

EULTRAN

Sets the definition of the face velocity used in the transport scheme of the Multimaterial solver and the single material strength solver.

FASTCOUP

Defines the fast coupling algorithm.

FBLEND

Eulerian elements with uncovered fractions smaller than FBLEND are blended with adjacent elements to form a clump so that they do not control the time step.

FMULT

Defines the dimension of the multimaterial element array.

GRADMESH

Glues fine meshes to coarse meshes. See the section on Graded meshes in the user manual for further information.

HYDROBOD

Defines a body force for single hydro material in Euler.

ISOL70GO

Option to determine whether SOL 700 blade out analysis continues past its normal stopping point in the GP1 module.

LIMITER

Defines the type and the spatial accuracy of scheme used in the Euler solver based on the ideas of Prof. Philip Roe.

MICRO

Defines the accuracy of the initial conditions in Eulerian elements, when using the geometrical shape definition.

RKSCHEME

Defines the type of time-integration scheme used in the Riemann solution-based Euler solvers.

ROHYDRO

Defines the minimum density for hydrodynamic, single-material Eulerian elements.

ROMULTI

Defines the minimum density for multimaterial Eulerian elements.

182 MD Nastran R3 Release Guide Explicit Nonlinear - SOL 700

New for MD Nastran R3 (SOL 700) Parameters

Main Index

Description

ROSTR

Defines the minimum density for single-material Eulerian elements with shear strength.

VELCUT

Defines the minimum velocity in Eulerian meshes.

VELMAX

Defines the maximum velocity in Eulerian meshes.

CONTACT

Change defaults for computation with contact surfaces.

CHAPTER 3 183 Advanced Integrated Nonlinear and Contact

Arc-Length Methods (Pre-release) Introduction In nonlinear static analysis, when the loading response beyond the critical limit (post buckling status), the conventional Newton-Raphson Method usually cannot be used to analyze the structure. The ArcLength Method(s), which allows the nonlinear solver to find solutions to most of these kinds of unstable problems, is now available in SOL 400. The concept of this method is to modulate the applied loads in order to produce solutions with displacement increments of manageable size for a given load step.

Benefits Although the post-buckling state is not usually allowed in the structure design, the prediction of such response becomes much more interesting to engineers in past decades. In the design process for instance, it may be desirable to trace the response of the snap-through or post-buckling behavior. The Arc-Length Method allow solutions in the unstable regime for such class of problems. The Arc-Length analysis has been merged into the current SOL 400 solution algorithm which takes advantage of the following: • Share the extensive enhancements for the nonlinear large strain and material behavior. • Improved nonlinear iteration algorithms make solution easier and faster to converge. These

includes • ADAPT, AUTO, ITER, SEMI, FNT, and PFNT methods • Bisection Algorithm • Quasi-Newton (BFGS) method • Allow boundary condition change between STEPs.

Method and Theory The theory of the Arc-Length Method is described in the MSC Nastran Handbook for Nonlinear Analysis, Version 67, Section 3.7. Unlike the Newton-Raphson Method, whose load increment is fixed during the iterations, the Arc-Length Method has varied load increment at each iteration. Sometimes we also call it as the Control Increment (C.I.) method whose displacement increment is limited by the constraint equations. Three different types of the constraint equations are available in the Arc-Length Method in SOL 400. They are 1. The Crisfield's Method (TYPE=CRIS), 2. The Modified Riks' Methos (TYPE=MRIK), and 3. The Original Riks' Method (TYPE=RIKS). Please refer to the MSC Nastran Handbook for Nonlinear Analysis, Version 67, Section 3.7 for the details of these equations.

Main Index

184 MD Nastran R3 Release Guide Arc-Length Methods (Pre-release)

It would be difficult to estimate a proper arc-length for multi-degree-of-freedom problems. The initial arc-length is determined by the program that is mainly based on the original number of load increment (NINC on NLPARM Bulk Data entry) and the load increment in the current loadcase (SUBCASE or STEP). It is to be continuously updated at every increment using the information gathered during the preceding converged increment.

Inputs The existing Bulk Data entry NLPCI, which allows the user to define a set of parameters to control the Arc-Length Method(s), is used to trigger on the Arc-Length Method as usual. See the MD Nastran Quick Reference Guide for details. All the input entries are the same as before except that the filed 7, SCALE, is not supported in SOL 400. This value is computed in the code automatically now but does not allow users to change it. The NLPCI Bulk Data entry is selected by the Case Control command NLPARM=ID. There must also be an NLPARM Bulk Data entry with the same ID.

Outputs There are no new outputs associated with this feature other than informational and diagnostic messages. Note that 1. Because of the new format of the “Nonlinear Iteration Module Output” table in SOL 400, the load factor of each iteration can be easily found in the first field now. 2. The field INTOUT, on the NLPARM Bulk Data entry, controls the output in the following ways • =YES, output processed for every computed load increment • =NO, output processed for the last load of the SUBCASE or STEP. • =ALL, output processed for every computed and user-specified load increment.

Limitations Considering that the Arc-Length method only supports the ANALYSIS=NLSTAT in SOL 400, the following limitations exist in MD Nastran R3 1. Restart is not supported 2. Enforce Motion is not supported 3. 3D Contact is not supported 4. CASI solver is not supported 5. Creep Analysis is not supported 6. Heat Transfer is not supported 7. Line Search and NLADAPT are not supported

Main Index

CHAPTER 3 185 Advanced Integrated Nonlinear and Contact

Example - nla011b.dat A spherical shell with an initial imperfection, which was introduced by making the radius of curvature near the apex greater than the shell radius, was analyzed. The shell was subjected to an external uniform pressure, while the periphery was clamped. The problem was assumed to remain axisymmetric geometry and loading throughout the deformation. The material was elasto-plastic with von Mises yield criterion and kinematic hardening. The large displacement effect was also included in the analysis. The detailed input of the model is attached at the end. There were 3 STEPs' in this model. The external pressure was gradually increased from 2000 psi, 3000 psi to 4000 psi at the end of each STEP. The linear buckling load was around 3300 psi; therefore, the first 2 STEPs' only required the Newton-Raphson method (NLPARM Bulk Data entry only without NLCPI) because the stiffness matrix was still positive definite. Since the bucking occurred in the 3rd STEP, the NLPCI Bulk Data entry was added into it by using Crisfield constraint equation. Note that if the Arc-Length Method did not apply to the third STEP, the solution diverged. Figure 3-26 shows the deformed shape and Figure 3-27 the central-load vs. deflection curve.

Figure 3-26

Main Index

Deformed Shape of Imperfect Spherical Shell

186 MD Nastran R3 Release Guide Arc-Length Methods (Pre-release)

3.50E+00 3.00E+00 LOAD FACTOR

2.50E+00 2.00E+00 1.50E+00 1.00E+00 5.00E-01

-8.00E-02

-6.00E-02

0.00E+00 -2.00E-02 0.00E+00

-4.00E-02

DISPLACEMENT OF GD 100

Figure 3-27

Load-Deflection Curve of Imperfect Spherical Shell (Grid 100 is the Central Point)

ID MSC, NLA011B $ SOL 400 $ TIME 5 CEND ECHO=UNSORT SET 1 = 100 DISP = ALL OLOAD=ALL SPC=10 SUBCASE 1 STEP 1 LOAD=20 NLPARM=2 STEP 2 LOAD=30 NLPARM=2 STEP 3 LOAD=40 NLPARM=5 OUTPUT(XYPLOT) CSCALE = 1.5 PLOTTER NAST XTITLE = LOAD FACTOR YTITLE = DISPLACEMENT XYPLOT DISP RESP/100(T3) BEGIN BULK PARAM,POST,-1 $ DEFINE SPHERICAL COORDINATE SYSTEMS CORD2S 100 0. 0.

Main Index

0.

0.

0.

1.

+C2S1

CHAPTER 3 187 Advanced Integrated Nonlinear and Contact

+C2S1 1. 0. CORD2S 200 +C2S2 1. 0. $ DEFINE PLOT ELEMENT GRID 1000 PLOTEL 1000 1000 $ GEOMETRY GRDSET GRID 100 200 GRID 101 200 GRID 102 200 GRID 103 200 GRID 104 200 GRID 105 200 GRID 106 200 GRID 107 200 GRID 108 200 GRID 109 200 GRID 110 200 GRID 111 200 GRID 112 200 GRID 113 200 GRID 114 200 GRID 115 200 GRID 116 200 GRID 117 200 GRID 118 200 GRID 119 100 GRID 120 100 GRID 121 100 GRID 122 100 GRID 123 100 GRID 124 100 GRID 125 100 GRID 126 100 GRID 127 100 GRID 128 100 GRID 129 100 GRID 130 100 GRID 131 100 GRID 132 100 $ CONNECTIVITY CTRIA3 10 2 CQUAD4 11 2 CQUAD4 12 2 CQUAD4 13 2 CQUAD4 14 2 CQUAD4 15 2 CQUAD4 16 2 CQUAD4 17 2 CQUAD4 18 2 CQUAD4 19 2 CQUAD4 20 2 CQUAD4 21 2 CQUAD4 22 2 CQUAD4 23 2 CQUAD4 24 2 CQUAD4 25 2 $ ELEMENT PROPERTIES PSHELL 2 1

Main Index

1. 0. 1.

0.

-.32908 0.

0.

0. 100

0.

0.

123456

1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 1.1506 0.8251 0.8251 0.8251 0.8251 0.8251 0.8251 0.8251 0.8251 0.8251 0.8251 0.8251 0.8251 0.8251 0.8251

0. 0.715 0.715 1.43 1.43 2.145 2.145 2.86 2.86 3.575 3.575 4.29 4.29 5.005 5.005 5.72 5.72 6.435 6.435 10. 10. 11.48 11.48 12.96 12.96 14.44 14.44 15.92 15.92 17.40 17.40 18.8806 18.8806

100 101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 0.0251

101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 131 1

0. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. -5. 5. 102 104 106 108 110 112 114 116 118 120 122 124 126 128 130 132

100 0

102 104 106 108 110 112 114 116 118 120 122 124 126 128 130

345 12456

1.

+C2S2

188 MD Nastran R3 Release Guide Arc-Length Methods (Pre-release)

MAT1 1 10.8+6 0.3 MATS1 1 PLASTIC 1.225+6 1 $ BOUNDARY AND LOADING CONDITIONS SPC1 10 123456 131 132 PLOAD2 20 -2000. 10 THRU PLOAD2 30 -3000. 10 THRU PLOAD2 40 -4000. 10 THRU $ PARAMETERS PARAM LGDISP 1 $ SOLUTION CONTROL NLPARM 2 2 AUTO NLPARM 5 5 AUTO NLPCI 5 ARC $ ENDDATA

Main Index

2

7.8+4

25 25 25

YES

CHAPTER 3 189 Advanced Integrated Nonlinear and Contact

Analysis Chaining Introduction The analysis chaining was released in MD Nastran R2. In that release, the analysis chaining was only supported for nonlinear static analysis and nonlinear transient analysis. In this release, this capability is greatly expanded and is discussed in the following sub-sections. In order for completeness, some of the information may have been previously presented in MD Nastran R2, and repeated here.

Input The combination of SUBCASE, STEP, ANALYSIS and NLIC four Case Control commands provide a mechanism for defining the multiple load steps, running multiple independent load cases, specifying multiple and mixed types of analyses, and altering the natural load sequence in one job. SUBCASE and STEP define load cases for a job. SUBCASE defines multiple load cases, which are independent from each other, i.e., the load history is not passed from one SUBCASE to next. In a SUBCASE, a number of STEPs can be defined. The solution of one STEP is a continuation of the solution of its previous STEP. The user can specify the type of analysis for each SUBCASE and/or STEP by using the Case Control command ANALYSIS. ANALYSIS is discussed in Analysis Type, 189. The Case Control command NLIC will alter the natural load sequence and it has the following formats: NLIC SUBCASE i, STEP j, INCREMENT k How to used this command is explained in the following example.

Analysis Type The analysis type for the analysis chaining is defined by the Case Control command; ANALYSIS = “analysis type” In MD Nastran R3, the following analysis types are available: • STATICS – linear static analysis, • NLSTATICS – nonlinear static analysis, • NLTRAN – nonlinear transient analysis, • MODES – normal modes analysis, • DCEIG – direct complex eigenvalue analysis, • MCEIG – modal complex eigenvalue analysis, • Brake Squeal Analysis – the Case Control command BSQUEAL is used to request the brake

squeal analysis. ANALYSIS = DCEIG or MCEIG can be used. See the following example.

Main Index

190 MD Nastran R3 Release Guide Analysis Chaining

• HSTAT – steady state heat transfer analysis, • HTRAN – transient heat transfer analysis.

The default is ANALYSIS=NLSTATICS. NLSTATICS, NLTRAN, and STATICS are normal linear or nonlinear analysis. MODES, DCEIG, MCEIG, and BSQUEAL are perturbation analysis, which is discussed in Examples of Linear Perturbation and Brake Squeal Analyses, 102. HSTAT and HTRAN are heat transfer analyses, which are discussed in SOL 400 Advanced Heat Transfer, 77.

Examples The following examples illustrate the manner in which the SUBCASE, STEP, ANALYSIS, and NLIC commands are used. • With one SUBCASE and multiple steps, each step defines the total external load and other

characteristics for the step, which will be applied by the completion of the step. The solution of any STEP is a continuation of the solution of its previous STEP. The following is a typical example: SUBCASE 1 $ This line can be omitted STEP 10 ANALYSIS = NLSTAT NLPARM = 100 LOAD = 10 STEP 20 ANALYSIS = NLSTAT NLPARM = 100 LOAD = 20 STEP 30 TSTEPNL = 200 ANALYSIS = NLTRAN DLOAD = 30 In the above example, the solution will be continues from step 10 to step 20 and step 30. • Multiple SUBCASEs may be executed in one job where the types of analysis, loads and

boundary conditions can be changed. All SUBCASE’s are independent from each other, i.e., no load history information is transmitted from one SUBCASE to the next. At the start of each SUBCASE, the displacements, stresses and strains throughout the model are zero if there is no initial condition specified. For example: SUBCASE 1 ANALYSIS = NLSTAT NLPARM = 100 STEP 110 LOAD = 110 STEP 120 LOAD = 120 SUBCASE 2 ANALYSIS = NLTRAN TSTEPNL = 200

Main Index

$ This line can be omitted

CHAPTER 3 191 Advanced Integrated Nonlinear and Contact

STEP 210 DLOAD = 210 STEP 220 DLOAD = 220 In above example, the solutions of SUBCASE 1 and SUBCASE 2 are independent of each other. In case that the solution divergence is detected in a step, SOL 400 will terminate the solution of the current subcase and jump to the next subcase. • A case control command placed below the step level allows that command to vary from on step

to another. If it is placed above the step level, the command becomes the default for all steps in the subcase. Most of the case control commands, which can be placed below the subcase level, can also placed below the step level. For example, all steps in above examples use the same Case Control command NLPARM = 100 in SUBCASE 1 and TSTEPNL = 200 in SUBCASE 2. • NLIC command will alter the load pass. In the following case, the transient step 30 uses the

static analysis of step 10 at load factor 0.5 as its preload. SUBCASE 1 STEP 10 ANALYSIS = NLSTAT LOAD = 10 NLAPRM = 110 STEP 20 ANALYSIS = NLSTAT LOAD = 20 NLPARM = 120 STEP 30 NLIC STEP 10, LOADFAC 0.5 ANALYSIS = NLTRAN DLOAD = 30 TSTEPNL = 130 In order for step 30 to point to load factor 0.5 of step 10, the data at load factor 0.5 must have been saved. This is done by the INTOUT field on the NLPARM Bulk Data entry. • This section gives an example of chaining across the subcase boundary. In the following

example, both the transient analysis of SUBCASE 2 and SUBCASE 3 use the static analysis of SUBCASE 1 at load factor 0.5 as their preload. SUBCASE 1 STEP 10 ANALYSIS = NLSTAT LOAD = 10 SUBCASE 2 STEP 20 NLIC SUBCASE 1, STEP 10, LOADFAC 0.5 ANALYSIS = NLTRAN DLOAD = 20 SUBCASE 3 STEP 20 NLIC SUBCASE 1, STEP 10, LOADFAC 0.5 ANALYSIS = NLTRAN DLOAD = 30

Main Index

192 MD Nastran R3 Release Guide Analysis Chaining

• This section gives an example for the perturbation analysis. In following example, the normal

modes analyses have been performed at load factor of 0.25 and 0.75 of the nonlinear static of STEP 10. SUBCASE 1 STEP 10 ANALYSIS = NLSTAT LOAD = 10 STEP 20 NLIC STEP 10, LOADFAC 0.25 ANALYSIS = MODES METHOD = 20 STEP 30 NLIC STEP 10, LOADFAC 0.75 ANALYSIS = MODES METHOD = 20 • This section gives an example of brake squeal analysis. SUBCASE 3 STEP 1 LABEL = Nonlinear Static Step NLPARM = 3 BCONTACT = 1 SPC = 2 LOAD = 4 STEP 2 LABEL = Modal Brake Squeal with NLIC at 0.5 ANALYSIS = MCEIG BSQUEAL = 989 NLIC STEP 1 LOADFAC 0.5 SPC = 2 CMETHOD = 1 METHOD = 2 AUTOSPC(noprint)= yes RESVEC = NO The second step requests a brake squeal analysis. The BSQUEAL Case Control command requests a brake squeal analysis and it is performed at load factor of 0.5 of the first step. The analysis method can be either DCEIG or MCEIG. For details, please refer to Examples of Linear Perturbation and Brake Squeal Analyses, 102. • This section gives an example of heat to structure chaining.

SUBCASE 1 STEP 1 ANALYSIS = HSTAT NLPARM = 1 SPC = 1 LOAD = 2 THERMAL = ALL FLUX = ALL TSTRU = 200 STEP 2 ANALYSIS=NLSTAT NLPARM = 3

Main Index

CHAPTER 3 193 Advanced Integrated Nonlinear and Contact

SPC = 5 TEMP(load)= 200 LOAD = 13 STEP 3 ANALYSIS=NLSTAT NLPARM = 2 SPC = 5 TEMP(load)= 200 LOAD = 14 In the previous example, the temperature results of steady state heat transfer analysis are used in the structural steps. The temperature ID 200 specified in command TSTRU=200 in STEP 1 is passed to STEP 2 and STEP 3 in command TEMP(LOAD)=200. This means that temperature results of STEP 1 in used in STEP 2 and STEP 3 as temperature load.

Legal Chaining Type In this section, we will discuss which types of analysis chaining are legal for MD Nastran R3. Let us define the symbol “NLSTAT  NLTRAN” means the case control structure giving by the following: STEP 1 ANALYSIS = NLSTAT LOAD = 1 STEP 2 NLIC STEP 1, LOADFAC 0.5 ANALYSIS = NLTRAN DLOAD = 2 In MD Nastran R3, the following types of analysis chaining are legal: NLSTATICS or STATICS  NLTRAN NLSTATICS or STATICS  NLSTATIC or STATICS NLSTATICS or STATICS  MODES, DCEIG, MCEIG, or BSQUEAL HSTAT  NLSTATICS or STATICS The above information can also be presented in the table format as:

STAT

NLST

NLTR

MODE

DCEI

MCEI

BSQU

STAT

Y

Y

Y

Y

Y

Y

Y

NLST

X

X

X

Z

Z

Z

Z

NLTR HSTA HTRA

Main Index

HSTA

HTRA

Y Y

Y

Y Y

194 MD Nastran R3 Release Guide Analysis Chaining

The symbols in previous table have the following meanings: • X – full analysis chaining capabilities are supported as given in input and example sections

previously. • Y – the NLIC Case Control command is not supported, so the chained step is limited to chain to

the end of the previous analysis step • Z - chaining across a subcase boundary is not supported. This means that NLIC can only

reference the steps in the same subcase. • Blank – Chaining not supported in MD Nastran R3.

Limitations For heat transfer analysis, the following limitations exist: • If analysis chaining is used, only a single subcase is allowed in the Case Control packet.

All the above limitations and gaps in the table of allowable chaining will be remedied in future releases.

Main Index

Chapter 4: Implicit Nonlinear

4

Implicit Nonlinear 

Main Index

MD Nastran R3 Nastran Release Guide

Implicit Nonlinear - SOL 600

196 MD Nastran R3 Release Guide Implicit Nonlinear - SOL 600

Implicit Nonlinear - SOL 600 The following is a discussion of the new additions and improvements made for MD Nastran R3.

Support of Large Grid and Element IDs The largest addition to SOL 600 for MD Nastran R3 is the addition of a capability to support very large grid and element IDs. Up to 10-digit IDs may now be used for grids and elements when SOL 600 is used, however to be compatible with other solution sequences, IDs should not normally exceed a value of 99999999. Large IDs may be specified separately for grids, elements, or both items. Large ID capability is not the default for MD Nastran R3 and, if it is needed for a particular model, it must be activated by placing one of the following items shown in bold on the SOL 600,ID (p. 137) in the MD Nastran Quick Reference Guide (most other items are omitted to prevent confusion): SOL 600,SID

MRENUMBR=

MRENUELE=

MRENUGRD=

Please see parameters, MRENUMBR, 771, MRENUELE, 769, and MRENUGRD (p. 770) in the MD Nastran Quick Reference Guide. These key words are only required if the number of digits is greater than seven.

Multiple RFORCE Entries in the Same Subcase SOL 600 now supports multiple RFORCE entries in the same subcase so that different portions of the structure can rotate with different angular velocities, or even in different directions. To accomplish this, the two or more RFORCE entries should have the same SID (see below) and field 4 of the each continuation entry should specify IDRF which points to a SET 3 entry designating which elements apply to that particular RFORCE entry.

RFORCE (addition to the RFORCE entry for SOL 600) Format: 1

2

3

4

5

6

7

8

9

RFORCE

SID

G

CID

A

R1

R2

R3

METHOD

RACC

MB

IDRF

10

IDRF (SOL 600 ID indicating to which portion of the structure this particular RFORCE entry applies. only) It is possible to have multiple RFORCE entries in the same subcase for SOL 600 to represent different portions of the structure with different rotational velocities. IDRF corresponds to a SET3 entry specifying the elements with this acceleration.

Main Index

CHAPTER 4 197 Implicit Nonlinear

BCONTACT Case Control Command Clarification Normally, only one form of this entry may be used in any given analysis. The exception, for SOL 600 only, is that BCONTACT=NONE may now be used for any subcase desired and/or for increment zero and some other form such as BCONTACT=N used for the other subcases. This allows some subcases to have contact and others to have no contact. Analysis restarts must use the same form as the original run BCONTACT=ALLxxx cannot be mixed with BCONTACT=NONE or BCONTACT=N in the same input file. BCTABLE Bulk Data Entry Additions Several new fields have been made in the BCTABLE entry to clarify which shell surfaces may contact for SOLs 101, 400 and 600 and to add new information for SOL 700. For further details please see, Advanced Integrated Nonlinear and Contact (Ch. 3). The new fields are shown in bold: Format: 1 BCTABLE

2

3

4

5

6

ID

IDSLAVE

IDMAST

NGROUP

COPTS

COPTM

“SLAVE”

IDSLA1

ERROR

FNTOL

FRIC

CINTERF

ISEARCH

ICOORD

JGLUE

TOLID

DQNEAR

DISTID

FBSH

FRLIM

BIAS

SLIDE

HARDS

COPTS1

COPTM1

BKGL

BGST

BGSN

BGM

BGN

HHHB

HCT

HCV

HNC

BNC

EMISS

HBL

FK

EXP

METHOD

ADAPT

THICK

THICKOF

PENV

FACT

TSTART

TEND

MAXPAR

PENCHK

FSF

VSF

“MASTERS”

7

8 IGLUE

EROSOP

IADJ

SOFT

DEPTH

BSORT

FRCFRQ

SNLOG

ISYM

I2D3D

IGNORE

SPR

MRP

VDC

SBOPT

SFS

SFM

SST

MST

SFST

SFMT

AUTO

LCID

FCM

US

PSF

FA

ED

INTTYPE

NFLS

SFLS

IGNOFF

FSLIM

PYS

TDIC

CDIST

NFLF

SFLF

NEN

MES

TBLCID

TBLAB

IGAP

FTBID

VC

SMOOTH

FLANGL

PENMAX

THKOPT

SHLTHK

SLDTHK

SLDSTF

DBID

TIDRF

TIDNF

DBDTH

DFSCL

NUMINT

IDMA1

IDMA2

IDMA3

IDMA4

IDMA5

IDMA6

IDMA8

IDMA9

...

For detailed descriptions on the new fields and Remarks 22 and 23 see BCTABLE (SOLs 101/400/600/700) (p. 1090) in the MD Nastran Quick Reference Guide.

Main Index

9

IDMA7

10

198 MD Nastran R3 Release Guide Implicit Nonlinear - SOL 600

Other BCTABLE Clarifications If the user leaves IDSLAVE and IDMAST blank, then NGROUP is normally required and continuation entries are usually expected for NGROUP SLAVE/MASTER combinations. Exceptions are (a) for SOL 700 where self-contact may be designated using a slave IDSLA1 of zero and no MASTER entry and (b) for SOL 600 if no contact is desired in increment zero or a particular subcase, fields 1 and 2 of the primary BCTABLE entry for that subcase is entered, all other fields left blank and no continuation lines are entered. The SOL 600 no contact condition may be achieved in either of two ways - set Case Control BCONTACT=ID and enter a matching BCTABLE with that ID in field 2 and all other fields blank or set BCONTACT=NONE and do not enter BCTABLE for that subcase. New Triangular Plane Stress Element The MRALIAS parameter or the ALIASM option may be used to specify that a 3-node plane stress element is to be used by specifying type 201. New Solid Shell Element A new solid shell element (CSSHL) has been added to SOL 600. The solid shell is normally used for contact problems where contact occurs on both the top and bottom faces. This element may be used with either homogeneous properties or by referencing a PCOMP or PCOMPG. CSSHL (SOL 600) Defines the connection for a Solid Shell with 6 or 8 grid points. Format: 1

CSSHL

2

3

4

5

6

7

8

9

EID

PID

G1

G2

G3

G4

G5

G6

G7

G8

44

11

1

2

3

4

5

6

7

8

51

22

10

Examples: CSSHL

CSSHL

11

12

13

21

22

23 CSSHL

Note:

Main Index

quad quad tria tria

51

22

23

23

11

12

13

13

The second and third examples are equivalent to each other.

21

22

tria tria

CHAPTER 4 199 Implicit Nonlinear

Field

Contents

EID

Element identification number. (1 < Integer < 1E11, Required)

PID

Property identification of a PSHELL, PCOMP, or PCOMPG entry. (Integer > 0, Required). Note that the MID2 entry on the PSHELL or PCOMP is ignored.

Gi

Grid point identification number of connection points. (Integer or blank, for quad shapes all eight values are required, for triangle shapes only G4 and G8 may be left blank in which case G4=G3 and G8=G7.)

See CSSHL (SOL 600) (p. 1367) in the MD Nastran Quick Reference Guide Nastran Quick Reference Guide for additional details. An example is tpl model hextqb-sshl2.dat PSSHL (SOL 600) Defines the properties for Solid Shell (CSSHL) elements. Format: 1 PSSHL

2

3

4

5

PID

MID

IT

SF

11

33

6

7

8

9

10

Example: PSSHL

.8333

Field

Contents

PID

Property identification number. (Integer > 0, Required)

MID

Identification of a MAT1xxx entry. All MAT entries available in SOL 600 can be specified except for hyperelaastic materials. (Integer > 0)

IT

Transition thickness - Enter only if a solid shell is attached to a standard shell (such as CQUAD4), in which case TT is the thickness of the standard shell. (Real, Default = 0.0)

SF

Transverse shear factor - Leave blank if transverse shear is not to be considered. (Real or blank, if entered SF must range between 0.0 and 1.0)

New Penta 15 Solid Element Support for Penta 15 elements with mid-side nodes has been available in previous releases but they were formed using hexa 20 elements with a collapsed side. This formulation is not as accurate as the new true penta 15 formulation. The old collapsed side formulation is no longer used starting with this release and the new formulation is used automatically. There are no changes to the input data required.

Main Index

200 MD Nastran R3 Release Guide Implicit Nonlinear - SOL 600

MARCOUT – t16 Output Results Changes All output quantities supported by Marc are available in the SOL 600 t16 file and may be specified using the MARCOUT Bulk Data entry. Additions for this release are as follows:

E-USER

1st user-defined element post code(s) are generated by user subroutine plotv.f

E-USER1

2nd user-defined element post code(s)

E-USER2

3rd user-defined element post code(s)

E-USER3

4th user-defined element post code(s)

E-USER99

100th user-defined element post code(s) These outputs are only available in the .t16 file, not in .op2, .xdb, .f06, punch. A maximum number of 100 user-defined element post codes may be entered for SOL 600.

N-USER

1st user-defined nodal post code are generated by user subroutine upstnd.f

N-USER1

2nd user-defined nodal post code are generated by user subroutine upstnd.f

N-USER2

3rd user-defined nodal post code are generated by user subroutine upstnd.f

N-USER3

4th user-defined nodal post code are generated by user subroutine upstnd.f

N-USER4

5th user-defined nodal post code are generated by user subroutine upstnd.f

N-USER99 100th user-defined nodal post code are generated by user subroutine upstnd.f, etc. User-defined outputs are only available in the .t16 file, not in .op2, .xdb, .f06, punch. A maximum of 100 user-defined nodal post codes may be entered for SOL 600. Please note that for SOL 600, MD Nastran Case Control commands such as SET ID=, DISP=, STRESS=, STRAIN= only control the output in the .op2, .xdb, punch, .f06 and/or jid.marc.out file(s). The Case Control requests do not affect the. t16 output. Limiting t16 Output to Selected Elements or Grids For large nonlinear models the output can become very large. Sometimes only a certain portion of the structure is of concern. The following new entry may be used in SOL 600 to specify which elements or nodes should be output. The default is all elements and nodes will be output if the entry is not made. This entry may be used in combination with MARCOUT or the default MARCOUTs may be used.

MT16SEL – Limits elements and/or grid results to selected elements or grids for t16 and t19 file results Format

Main Index

1

2

3

4

5

6

7

MT16SEL

TYPE

ID1

THRU

ID2

BY

ID3

8

9

10

CHAPTER 4 201 Implicit Nonlinear

Example: MT16SEL

GRID

1

THRU

100

BY

5

ELEM

100

THRU

500

BY

2

See MT16SEL (SOL 600) (p. 2239) in the MD Nastran Quick Reference Guide for more details. Analytical Contact Threshold Angle Starting with this release it is possible to define analytical contact threshold angles for different subcases. To do so, include the following entry: Defines automatic analytical contact threshold angle for multiple subcases - SOL 600 only. Format: 1

2

3

4

5

6

7

SANGLE

IDC

IDB

Angle

IDC

IDB

Angle

1

4

50.0

1

6

2

4

-1.0

2

6

8

9

10

Example: SANGLE

Field

55.0

Contents

IDC

Identification number of a SUBCASE Case Control command. (Integer, no Default) To enter a value corresponding to Marc’s increment zero, set IDC=0.

IDB

Identification of a contact body (must be the same as a BCBODY ID) (Integer, no Default)

Angle

Threshold automatic analytical contact angle (SANGLE). (Real, Default = 60.0) A value of -1.0 turns off analytical

Please see SANGLE (SOL 600) (p. 2684) in the MD Nastran Quick Reference Guide for more details. An example using SANGLE is TPL model sangle1a.dat. Additions to NLSTRAT The following additions have been made to the NLSTRAT entry to support heat transfer analyses which was introduced in the previous release.

Main Index

PLANKS

Planks second constant (Real, Default=14387.69 microMK) PARAMETERS (4,6)

CLIGHT

Speed of light in a vacuum (Real, Default=2.9979E14 micor M/s) PARAMETERS (4,7)

RAPMAX

Maximum change in the incremental displacement in a Newton-Raphson iteration (Real, Default = 1.0E30) PARAMETERS (4,8)

202 MD Nastran R3 Release Guide Implicit Nonlinear - SOL 600

FISTIF

Initial friction stiffness for model 6 used in first cycle of an increment to define the friction stiffness matrix in cases where a touching node has a zero normal force and the amount of sliding does not exceed the elastic sticking limit (Real, Default = 0.0 in which case the program calculates it) PARAMETERS (5,1)

SNGMIN

Minimum value that indicates a singularity if a direct solver is used (Real, Default = 0.0 in which case the value is set internally by the program) PARAMETERS (5,2)

RTMAX

Maximum change in temperature per iteration in radiation simulations (Real, Default = 10 times the maximum error in temperature estimate or 100.0) PARAMETERS (5,3)

Generalized Alpha Dynamic Integration Method For previous releases, several numerical integration methods were available for dynamic analysis. One additional method, called the Generalized Alpha or Hilber-Hughes Taylor Method has been added. This method is sometimes superior to the others for difficult dynamics problems, particularly those involving contact. The single step Houbolt method is still the default for this release, but the new method may become the default in subsequence releases. To select any of these methods, enter the following bulk data parameter: MHOUBOLT Integer, Default = 0, MD Nastran Implicit Nonlinear (SOL 600) only. If MHOUBOLT=0, SOL 600 transient dynamics will use the single step Houbolt numerical integration method. MHOUBOLT=1, SOL 600 transient dynamics will use the Newmark Beta numerical integration method. MHOUBOLT=2, SOL 600 transient dynamics will use the standard multi-step Houbolt numerical integration method. MHOUBOLT=7, SOL 600 transient dynamics will use the generalized alpha (Hilber-Hughes Taylor) numerical integration method. For additional information, see Advanced Integrated Nonlinear and Contact (Ch. 3).

MATVP Material Property Entry The MATVP entry has completely changed so that both SOL 400 and 600 may use the same entry. Please refer to MATVE (SOLs 400/600) (p. 2165) in the MD Nastran Quick Reference Guide for the new description and be sure to update any existing input files that have an older entry and need to be run with this release. An example is TPL model vcreep.dat.

Main Index

CHAPTER 4 203 Implicit Nonlinear

MATSMA Shape Memory Alloy Material Property Entry A new shape memory allow material property entry is now available for use both in SOL 400 and 600. Please see MATSMA (SOLs 400/600) (p. 2132) in the MD Nastran Quick Reference Guide for a full description of this entry.

Nonlinear Elastic Orthotropic Materials An orthotropic material model that allows the user to enter the nine material parameters as a function of strain and temperature is now available. This is defined through the MATNLE6 and TABLE3Di options.

Composite Integration Methods to Reduce Computer Time SOL 600 allows composite materials to be fully nonlinear. The properties of each layer may have plasticity and/or have properties that vary with temperature. Often analyses are conducted where the material properties are assumed to remain linear and are at a constant temperature. For such cases, computer time can be reduced by significant amounts by taking these factors into account. A new entry, PCOMPF, is available to specify which elements can use the faster integration methods. This entry is shown below and an example is compos1-fast3.dat in the tpl directory. Format: 1

2

3

4

5

6

7

PCOMPF

INT

PID1

THRU

PID2

BY

N

8

9

10

10

Alternate Formats:

Main Index

1

2

3

4

5

6

7

8

9

PCOMPF

INT

PID

PID

PID1

THRU

PID2

PID3

THRU

PID4

PID5

TO

PID6

PID

PID

PID

PID7

THRU

PID8

BY

N

4

5

6

7

8

9

1

2

3

PCOMPF

INT

ALL

10

Field

Contents

PID1

Property identification number. (0 < Integer < 10000000) corresponds to a matching PCOMP or PCOMPG entry.

INT

INT=1, (Default), conventional through the thickness integration of each layer, allows all available material behavior through the thickness.

204 MD Nastran R3 Release Guide Implicit Nonlinear - SOL 600

Field

Contents INT=2, linear elastic material, fast-integrated through the thickness - thermal strains and temperature dependent material properties are not allowed. INT=3, linear elastic material, fast integrated through the thickness, temperature dependent elasticity, and thermal strains are allowed.

Main Index

CHAPTER 4 205 Implicit Nonlinear

New SOL 600 Bulk Data Entries and Parameters Table 4-1 contains new Bulk Data entries for SOL 600 in MD Nastran R3. More details can be found in the MD Nastran Quick Reference Guide.

Table 4-1

New Bulk Data Entries for SOL 600 New for MD Nastran R3 (SOL 600)

Bulk Data Entries

Description

CSSHL

Defines the connection for a solid shell with 6 or 8 grid points.

MATSMA

Material properties for shape memory alloys (SOLs 400 and 600 only)

MATNLE6

Properties for nonlinear orthotropic elastic material

MT16SEL

Limits elements and/or grid results to selected elements or grids for t16 and t19 file results

PSSHL

Defines the properties for solid shell (CSSHL) elements.

SANGLE

Defines automatic analytical contact threshold angle for multiple subcases.

Table 4-2 contains new Parameters for SOL 600 in MD Nastran R3. More details can be found in the MD Nastran Quick Reference Guide.

Table 4-2

New Parameters for SOL 600 New for MD Nastran R3 (SOL 600)

Parameters

Main Index

Description

MARCMATT

(Integer) Determines if Marc input file will be created with materials using the table-driven formats or not (Default = -1 if parameter is not entered)

MARROUTT

Determines whether an inconsistent set of outputs between the Marc t16 file (selected using MARCOUT) and standard Nastran output selected using Case Control requests (and param,post) is allowed or not (Default = -1 if parameter is not entered)

MBENDCAP

Determines how PBEND internal pressure will be treated for SOL 600, (Default = 1 if this parameter is not entered).

MDAREAMD

Option to modify or not modify all DAREA entries which are not associated with any other loads (DAREA entries that supply the actual load)

MFORCOR1

Option to correct forces entered twice (at the same node) in multiple subcases.

MINVASHF

Inverse power “auto sift” value.

MINVCITR

Inverse power method, number of iterations.

MINVCSHF

Inverse power shift frequency in Hz.

206 MD Nastran R3 Release Guide Implicit Nonlinear - SOL 600

Table 4-2

New Parameters for SOL 600 New for MD Nastran R3 (SOL 600)

Parameters

Description

MINVCTOL

Inverse power convergence tolerance.

MINVFMAX

Inverse power max frequency to extract in Hz.

MINVNMOD

Inverse power max number of modes to extract.

MRENUELE

It is best if MRENUELE is specified in the SOL entry. Some models will not have memory allocated properly if this parameter is placed in the bulk data. (Integer) Determines if SOL 600 elements will be renumbered or not (Default = -1 if parameter is not entered and MRENUELE is not entered on the SOL 600 entry)

MRENUGRD

It is best if MRENUGRD is specified in the SOL entry. Some models will not have memory allocated properly if this parameter is placed in the bulk data. (Integer) Determines if SOL 600 grid id’s will be renumbered or not (Default = -1 if parameter is not entered and MRENUGRD is not entered on the SOL 600 entry)

Main Index

MRENUMBR

Determines if both grid and element IDs for SOL 600 will be renumbered or not.

MRPELAST

Determines whether PELAST will be skipped or cause the job to abort for SOL 600, (default = -1 if parameter is not entered). SOL 600 does not support PELAST. PBUSHT along with CBUSH and PBUSH should be used instead.

MRPREFER

Determines to output SOL 600 stresses on the t16 file in the standard Marc coordinate system for the element or the “preferred” (layer) coordinate system when the model contains composite elements.

MSPEEDCB

Determines whether CBEAM increased speed options are to be applied. This option may be necessary for models with a large number of beams whose element ID’s are large.

MTABLD1M

Option to modify or not to modify all TABLED1 entries which do not start with the first point of (0.0, 0.0)

MTABLD1T

Specifies the second time value of all TABLED1 entries that do not start with the first point being (0.0, 0.0) if PARAM,MTABLD1M=1.

MULRFORC

Option to activate multiple RFORCE entries for different portions of the model in the same subcase.

Chapter 5: NVH and Acoustics

5

Main Index

MD Nastran R3 Release Guide

NVH and Acoustics 

NVH Enhancements



Enhancements to the Frequency Response Function (FRF) and FRF Based Assembly (FBA) Feature



Enhancements to ADAMSMNF Case Control Command

208 MD Nastran R3 Release Guide NVH Enhancements

NVH Enhancements ACMS with Acoustic External Superelement Creation The ACMS feature (see the DOMAINSOLVER ACMS (PARTOPT=DOF) Executive Control statement in the MD Nastran Quick Reference Guide) is now fully integrated with the creation of an external acoustic superelement which contains both the fluid cavity and the fluid-structural boundary. External superelement creation is requested with the EXTSEOUT Case Control command. For an acoustic external superelement, the component modes and their associated reduced stiffness, mass, etc. matrices are computed separately for the fluid and structure. If QSETi and SPOINT Bulk Data entries are used to define the generalized coordinates then there must be a sufficient number to accommodate both the fluid and structure modes. If there are insufficient generalized coordinates then the program will truncate both the fluid and structural modes proportionally. It is for this reason that PARAM,AUTOQSET,YES is strongly recommended to avoid potential modal truncation. Fluid points may also be specified on the boundary of the superelement using the ASETi entry. However, free-fixed or free-free fluid or structure boundaries are not permitted with ACMS.

Multiple RANDOM Looping Prior to this release, only one set of RANDPS Bulk Data entries could be selected per run. In other words, the RANDOM Case Control command could only reference a single RANDPS set identification number (SID). In this version multiple SIDs may be specified on the SET command if its identification number is in turn referenced on a RANDOM command. For example; SET 1000 = 101 103 107 110 RANDOM = 1000 where 101, 103, 107, and 110 refer to multiple RANDPS SIDs. It should be noted for this type of usage the SET id must be unique with respect to all RANDPS SIDs; e.g., 1000 is not an SID on any RANDPS entry.

Sparse OUTPUT4 Format for External Superelement Creation The sparse OUTPUT4 format option is now used for EXTSEOUT (MATRIXOP4=unit) Case Control command. This will result in significant disk space reduction of the resulting op4 file.

Binary op2 and op4 Compatibility Robustness Starting in version V2004 r3, binary op2 and op4 files could be read across dissimilar platforms. However, several errors were encountered since V2004 r3 and are now corrected in MD Nastran R3.

Main Index

CHAPTER 5 209 NVH and Acoustics

Merged Superelement Results PARAM, FULLSEDR, YES may be specified in a superelement analysis to merge several types of results (displacements, stresses, etc.) across all superelements into a single non-superelement results format. FULLSEDR is intended for superelement models which contain unique IDs across all element and grid points. FULLSEDR benefits third party post-processing programs which have difficulty digesting superelement results in the op2 or .pch files.

Main Index

210 MD Nastran R3 Release Guide Enhancements to the Frequency Response Function (FRF) and FRF Based Assembly (FBA) Feature

Enhancements to the Frequency Response Function (FRF) and FRF Based Assembly (FBA) Feature Introduction The FRF / FBA (Frequency Response Function / FRF Based Assembly) capability was first introduced in MD Nastran R2. This capability facilitates the computation of the FRFs of individual components and also the subsequent computation of the FRFs of an assembly of such components from their individual FRFs. The capability available in MD Nastran R2 had several limitations that were pointed out in the MD Nastran R2 Release Guide. These limitations have been eliminated in MD Nastran R3. The enhancements made in MD Nastran R3 are discussed in the following sections. These changes also involved enhancements to the FRF Case Control command and the addition of seven new Bulk Data entries (FBADLAY, FBALOAD, FBAPHAS, FRFCONN, FRFFLEX, FRFRELS and FRFSPC1) related to FRF/FBA usage. The descriptions of the expanded FRF Case Control command and the new Bulk Data entries are given in the MD Nastran R3 Quick Reference Guide.

Names for FRF Components The name of an FRF component is now as much a characteristic as its identification number (ID). The FRF Case Control command has been enhanced so that the COMPNAME keyword (which was optional earlier) is now required if the COMPID keyword is specified or vice versa.

Interchangeable COMPID/COMPNAME Fields in All Bulk Data Entries Meant for FBA Use All Bulk Data entries meant for use in the FBA process are designed so that the FRF components can be identified either by their component IDs or by their component names. These items can be used interchangeably. This feature offers great convenience and flexibility to users.

User Load Specification in the FBA Process It is now possible to specify user loads in the FBA process. In order to facilitate this, three new Bulk Data entries FBALOAD, FBADLAY and FBAPHAS have been introduced. These entries define loads by referencing points in the FRF components that comprise the FRF assembly.

Responses to Unit Loads and User Specified Loads It is now possible to get responses not only to unit loads, but also to user specified loads in both FRF generation runs and in the FBA process. This is meaningful if the user specifies a dynamic load in a FRF

Main Index

CHAPTER 5 211 NVH and Acoustics

or FBA job via a DLOAD Case Control command. To facilitate this, the XITOUT keyword in the FRF Case Control command has been expanded. Details are given below. FRF Case Control XITOUT Keyword Possible values are UNIT, UNITALL, USER and USERTOTL. Their meanings are given below: XITOUT = UNIT • Generates output for all user specified unit loads (either explicitly via FRFXIT/FRFXIT1 Bulk Data entries or implicitly via the DLOAD Case Control command) XITOUT = UNITALL • Generates output not only for all user specified unit loads (either explicitly via

FRFXIT/FRFXIT1 Bulk Data entries or implicitly via the DLOAD Case Control command), but also for unit loads applied automatically by the program at all connection points in the set specified by the FRF Case Control CONNPTS keyword XITOUT = USER • Meaningful only if there is a DLOAD Case Control command • If the specified dynamic load involves loads on N DOFs in the model, the program

automatically generates output for (N+1) load cases. The first N of these load cases represent loads on each of the N DOFs separately and individually and the (N+1)th load case represents the total applied load. XITOUT = USERTOTL • Meaningful only if there is a DLOAD Case Control command • Generates output only for the total applied load, corresponding to the (N+1)th load case

mentioned previously. If N = 1 in the above discussion, then XITOUT = USER and XITOUT = USERTOTL will both generate output only for the total applied load. The prior scenario is in contrast to standard SOL 108 / SOL 111 jobs wherein the output is generated only for the total applied load (just like XITOUT = USERTOTL). The output generated by the XITOUT = USER option described is perfectly well suited for TPA (Transfer Path Analysis) studies since it allows for the examination of the effects on the response of the system due to loads on individual DOFs as well as due to the total applied load. XITOUT Keyword Defaults • XITOUT = UNIT is the default if there is no DLOAD Case Control command. • XITOUT = USER is the default if there is a DLOAD Case Control command.

If the user specifies XITOUT = USER or XITOUT = USERTOTL, but there is no DLOAD Case Control command, the program issues a warning message and assumes XITOUT = UNIT.

Main Index

212 MD Nastran R3 Release Guide Enhancements to the Frequency Response Function (FRF) and FRF Based Assembly (FBA) Feature

Connection of Scalar Points and Explicit Connection of Coincident Grid Points It is now possible to connect scalar points of FRF components and also to specify the explicit connection of coincident grid points. The latter feature is particularly helpful to handle cases wherein an FRF component may have two or more coincident grid points among its connection points. A new Bulk Data entry called FRFCONN has been introduced for this purpose. This entry is analogous to the SECONCT entry employed in superelement analysis.

Flexible Connection of Degrees-of-Freedom The connections in the FBA process are no longer restricted to rigid connections. The enhancements allow for flexible connections between DOFs of coincident grid points or those of scalar points. Elastic (K), damping (B) and non-uniform structural damping (Ge) properties may be specified for these connections for use in the FBA process. These properties may be specified either as constant values (that are independent of the forcing frequency) or as frequency dependent values. A new Bulk Data entry called FRFFLEX has been introduced for this purpose.

Release of Connection Degrees-of-Freedom It is now possible to release specific DOFs of connection grid points in the FBA process. A new Bulk Data entry called FRFRELS has been introduced for this purpose.

Grounding of Connection Degrees-of-Freedom It is now possible to specify single-point constraints for DOFs of connection points in the FBA process. A new Bulk Data entry called FRFSPC1 has been introduced for this purpose. This entry is selected by the SPC Case Control command. Handling of Coincident Connection Grid Points of FRF Components in the FBA Process As part of the enhancements, the program now examines each FRF component in the FBA process for the existence of coincident connection grid points. If such points exist, the program performs the following tasks: • Outputs a list of such points for each FRF component in the FBA process. • Examines each coincident connection grid point to ensure that it is referenced either on an

FRFCONN Bulk Data entry or all six (6) of its DOFs are released by being referenced on an FRFRELS Bulk Data entry. If this condition is met, the program continues the execution. Otherwise, the program terminates the execution with a User Fatal Message (UFM). The above design ensures that coincident connection grid points will NOT be automatically combined with other such points, leading possibly to invalid, unwanted or inadvertent connections. Instead, the design ensures that such points will be combined only via explicit user directives.

Main Index

CHAPTER 5 213 NVH and Acoustics

Handling of Displacement (or Local) Coordinate Systems at Connection Grid Points of FRF Components in the FBA Process When the program connects two or more grid points of the FRF components in the FBA process, it examines the displacement (or local) coordinate systems of each of those connection points to ensure that they all represent the same coordinate system transformations with respect to the basic coordinate system. If this condition is not met, the program terminates the job with a User Fatal Message (UFM). The previous requirement is necessary to ensure proper results from the FBA process.

FRFs for PLOTEL Grid Points The program logic has been enhanced so that, if COMPID/COMPNAME is specified in the FRF Case Control command, then FRFs are automatically computed for all grid points referenced on PLOTEL Bulk Data entries regardless of any other user requests. With this enhancement, the specific points for which FRFs are computed in a FRF generation run comprise the following: • All points specified via DISP, VELO and ACCE requests • All grid points referenced on PLOTEL Bulk Data entries • All points associated with elements for which STRESS/FORCE requests are specified • All points where unit loads are applied (either explicitly via FRFXIT/FRFXIT1 Bulk Data

entries or implicitly via the DLOAD Case Control command) • All points comprising the set referenced by the CONNPTS keyword in the FRF Case Control

command

Summary of the Enhancements The enhancements made in MD Nastran R3 for the FRF/FBA capability represent significant improvements over what was available in MD Nastran R2. These improvements make the feature an excellent tool for practical situations and a viable alternative to traditional superelement analysis for NVH studies. In particular, the results generated for user specified loads are very well suited for subsequent processing by visualization tools.

Main Index

214 MD Nastran R3 Release Guide Enhancements to ADAMSMNF Case Control Command

Enhancements to ADAMSMNF Case Control Command The general goal of this enhancement is to provide MD Nastran database access for ADAMS/FLEX MNF, i.e., Modal Neutral File-type, data storage and/or processing. This will allow you to persist multiple flexible bodies in the same database instead of generating multiple “MNF” files. Moreover, tests show that you will experience up to 30 times faster data access speeds if the MNF data is stored in a MD Nastran database compared to the same data stored in an MNF file. This enhancement is implemented in the ADAMSMNF Case Control command using a new option keyword as shown below: ADAMSMNF FLEXBODY=YES EXPORT=MNF/DB/BOTH It should be noted that at this time MD Nastran databases may not be shared among binary incompatible machines. That is, if you generate a database on a 32-bit Big Endian platform, e.g., HPUX, SUN, and would like to read the data on a 32-bit Little Endian platform, e.g., WINDOWS, LINUX, then you must convert the database using the “DBUNLOAD/DBLOAD” procedure.

Main Index

Chapter 6: Numerical Methods and High Performance Computing

MD Nastran R3 Release Guide

=

6

Main Index

Numerical Methods and High Performance Computing 

Linear and Nonlinear Contact Analysis



High Performance Iterative Solver Now Available for Nonlinear Transient Analysis



Matrix Based Iterative Solver Now Available for Nonlinear Static Analysis



Factor Matrix Caching for Lanczos and Nonlinear Transient Analysis with NLAUTO



New TAUCS Indefinite Solver Improves Lanczos Performance



Shared Memory Parallel (SMP) Scalability Improvements for Static Analysis



New MAXRATIO Information Output



New SPARSESOLVER MDTSTATS Information Output

216 MD Nastran R3 Release Guide Linear and Nonlinear Contact Analysis

Linear and Nonlinear Contact Analysis Introduction Linear and nonlinear contact analysis is available in MD Nastran SOL 101 and SOL 400. The CASI element based iterative solver was integrated into contact analysis for the MD Nastran R2.1 release. This enhancement enabled efficient computation for the solution of equations [ A ] { x } Z { b } for contact with solid models. Contact between two or more solid bodies, over a varying contact area, involves significant computational cost. The original implementation of contact in MD Nastran utilized previously existing functional and computational tools. For MD Nastran R3, new computational tools and procedures have been implemented, resulting in improved performance.

Benefits Users should observe improved computational efficiency and performance for both linear and nonlinear contact analysis, especially for solid models using the CASI element based iterative solver.

Inputs To select the CASI iterative solver, specify the SMETHOD command in the Case Control Section. SMETHOD = ELEMENT To modify parameters for the CASI solver, specify the ID of an ITER Bulk Data entry: SMETHOD = 10 For example, to specify a convergence tolerance of 1.0e-4 for the CASI solver: ITER, 10 PRECOND=CASI, ITSEPS=1.0E-4 The user interface for the CASI iterative solver for contact analysis is the same as it is for linear static analysis in SOL 101. Refer to the Case Control command SMETHOD, 457 and the Bulk Data entry ITER, 1772 in the MD Nastran Quick Reference Guide for more information.

Guidelines and Limitations Significant reduction is observed in disk I/O and scratch disk capacity requirements. This results in reduced elapsed analysis times for systems with minimal memory and/or relatively slow scratch disk drive performance.

Main Index

CHAPTER 6 217 Numerical Methods and High Performance Computing

Demonstration Example Examples are taken from actual models from industry. The models are proprietary, so they may not be displayed. However, the basic model characteristics are shown along with the performance comparison. Example 1 Analysis type:

Linear contact

Number of grid points:

817,556

Number of solid elements:

525,741

Number of iterations:

3

Compute platform used:

IBM AIX POWER5

Linear contact example 3500 Elapsed Sec

3000

CPU Sec 2500 2000 1500 1000 500 0 MD R2.1

Main Index

MD R3

Disk I/O (GB)

Scratch Disk Required (GB)

MD Nastran R2

268.1

31.9

MD Nastran R3

140.2

17.1

218 MD Nastran R3 Release Guide Linear and Nonlinear Contact Analysis

Example 2 Analysis type:

Nonlinear contact

Number of grid points:

146,979

Number of solid elements:

97,928

Number of iterations:

60

Compute platform used:

IBM AIX POWER5

Nonlinear contact example 10000 9000

Elapsed Sec

8000

CPU Sec

7000 6000 5000 4000 3000 2000 1000 0 MD R2.1

Main Index

MD R3

Disk I/O (GB)

Scratch Disk Required (GB)

MD Nastran R2

1008.9

64.6

MD Nastran R3

754.5

5.75

CHAPTER 6 219 Numerical Methods and High Performance Computing

High Performance Iterative Solver Now Available for Nonlinear Transient Analysis Introduction Nonlinear analysis is available in MD Nastran SOLs 400 and 101. At each nonlinear iteration, a solution of the equations [ A ] { x } Z { b } is performed using sparse direct factorization and forward-backward substitution (FBS). For large models composed primarily of solid finite elements, the bulk of the solution time is spent computing { x } . For MD Nastran R2.1 structural static analysis, iterative solutions are available to compute { x } for models that will benefit from an iterative solution, such as solid models. For MD Nastran R3, the CASI element-based iterative solver is now available for use in non-linear transient structural analysis.

Benefits Users may experience significant performance increases by selecting an iterative solver for nonlinear analysis of large solid models. Depending on the number of nonlinear iterations in the overall analysis, the anticipated speedup is from two to five times.

Inputs To select an iterative solver, specify the SMETHOD command in the Case Control Section. The following SMETHOD command selects the CASI element-based iterative solver: SMETHOD = ELEMENT (To select a matrix-based iterative solver, specify SMETHOD = MATRIX.) The ELEMENT solver generally results in the best performance. To modify the specific parameter settings for one of the preceding iterative solvers, the SMETHOD command can specify the ID of an ITER Bulk Data entry. The user interface for the iterative solver is the same as it is for linear static analysis in SOL 101. Refer to the Case Control command SMETHOD, 457 and the Bulk Data entry ITER, 1772 in the MD Nastran Quick Reference Guide, for more information.

Outputs There are no new engineering outputs associated with this feature other than informational and diagnostic messages. In addition, a “PCS” output text file contains additional diagnostic output.

Guidelines and Limitations The element-based iterative solution option is primarily intended for use in nonlinear contact analysis of large solid models exceeding one million DOFs. There may be no performance gain if one substitutes

Main Index

220 MD Nastran R3 Release Guide High Performance Iterative Solver Now Available for Nonlinear Transient Analysis

the CASI solver for direct solution (DECOMP/FBS) in situations where many FBS operations are performed using the factor matrix from a single decomposition. This situation arises for simple linear transient analysis. The CASI solver is not designed to handle indefinite coefficient matrices. If a solution fails, the NLSOLV module automatically switches to the direct sparse solver method to continue the solution process. Differential stiffness effects and follower stiffness can produce an indefinite and possibly unsymmetrical coefficient matrix. Due to the unsymmetrical nature of the follower stiffness matrix, use caution when follower stiffness is present and the SMETHOD is ELEMENT or selects the CASI solver. By default, the presence of any of the MOMENTi, FORCEi, PLOADi, and RFORCE Bulk Data entries causes automatic generation of follower stiffness. If CASI is specified and follower-stiffness is present, it is automatically symmetricized. In cases where this is not acceptable, PARAM,FOLLOWK,NO must be specified in the Bulk Data Section. However, this will alter the analysis results by not including follower stiffness. Currently, follower stiffness resulting from RFORCE, PLOADX and GRAV loadings cannot be handled by the CASI solver interface. Therefore, the presence of these Bulk Data entries will generate User Fatal Message 9192 unless PARAM,FOLLOWK,NO is also specified.

Main Index

CHAPTER 6 221 Numerical Methods and High Performance Computing

Matrix Based Iterative Solver Now Available for Nonlinear Static Analysis Introduction For symmetric linear systems, the matrix-based iterative solver was introduced in MD Nastran R2.1 for nonlinear structural static analysis for (SOL 101 and SOL 400). In MD Nastran R3, the matrix-based iterative solver is also available for unsymmetric systems in nonlinear static and transient structural analysis. Certain applications in nonlinear static analysis (SOL 400) result in unsymmetric systems to be solved inside the nonlinear solution module. These examples include: • Heat transfer analysis with advection (one-directional fluid flow) or radiation • Follower-force stiffness • Friction force stiffness • Damping matrices • Transfer functions

For solid modeling applications, the default unsymmetric direct factorization and solve provide numerical stability. However, the performance characteristics of this solver are sub-optimal. Typically, for solid models, an iterative solver proves to be significantly faster than a direct solver.

Benefits For MD Nastran R3, the Nastran matrix-based unsymmetric iterative solver is available in the nonlinear solution module in SOL 400. This solver can provide up to two times speedup compared to the equivalent direct unsymmetric solver. In order to maintain desired performance, unsymmetric nonlinear systems are often “symmetricized”. This can have the desired effect on performance, while sacrificing some degree of numerical and engineering integrity. The availability of the Nastran matrix-based iterative solver substantially lowers the performance penalty for solving a true unsymmetric system for large solid models.

Method and Theory The Jacobi (default) and Cholesky preconditioning methods with and without scaling are available. BIC preconditioning (the default preconditioning method for symmetric systems) is not available for unsymmetric systems. If BIC is chosen by the user, the program automatically switches to Jacobi preconditioning without scaling. Similarly, the element-based CASI iterative solver is not available for unsymmetric systems, and the program will switch automatically to Jacobi preconditioning without scaling if it is chosen.

Main Index

222 MD Nastran R3 Release Guide Matrix Based Iterative Solver Now Available for Nonlinear Static Analysis

Inputs There is no change to the iterative solver interface. The matrix-based iterative solver is specified by the Case Control command SMETHOD = matrix or SMETHOD = k where k is the ID of an ITER Bulk Data entry. For more information please refer to the Case Control command SMETHOD, 457 and the Bulk Data entry ITER, 1772 in the MD Nastran Quick Reference Guide. The program will decide automatically whether the symmetric or unsymmetric path is taken.

Outputs Diagnostic output is available according to the options on the ITER Bulk Data entry.

Guidelines and Limitations The Nastran matrix-based iterative solver is best suited for large solid models that yield unsymmetric nonlinear solutions.

Demonstration Examples Below are three examples using heat transfer analysis, demonstrating the significant benefits of the matrix-based iterative solver for this type of problem. Both examples were run with the default preconditioner, Jacobi without scaling. Both examples require solutions of unsymmetric linear systems in SOL 400. Example 1: Analysis type:

Heat transfer with radiation

Number of grid points:

71,750

Number of solid elements:

65,360

Number of iterations:

3

Compute platform used:

IBM AIX POWER5

When run with SMETHOD=matrix in MD Nastran R2, this job fails in the iterative solver because only the direct method works for unsymmetric systems in SOL 400. In MD Nastran R3, the command SMETHOD=matrix will result in significant performance improvements.

Main Index

CHAPTER 6 223 Numerical Methods and High Performance Computing

Heat transfer exam ple 1600 1400 1200

Elapsed Sec

1000

CPU Sec

800 600 400 200 0 MD R2.1

MD R3

Example 2: Analysis type:

Heat transfer

Number of grid points:

84,943

Number of solid elements:

473,233

Number of iterations:

7

Compute platform used:

IBM AIX POWER5

When run with SMETHOD=matrix in MD Nastran R2, this job fails in the iterative solver because only the direct method works for unsymmetric systems in NLSOLV. In MD Nastran R3, the command SMETHOD=matrix will result in significant performance improvements.

Main Index

224 MD Nastran R3 Release Guide Matrix Based Iterative Solver Now Available for Nonlinear Static Analysis

Heat transfer exam ple 1400 1200 Elapsed Sec 1000

CPU Sec

800 600 400 200 0 MD R2.1

MD R3

Example 3: Analysis type:

Heat transfer with radiation

Number of grid points:

335,282

Number of solid elements:

198,376

Number of iterations:

8

Compute platform used:

IBM AIX POWER5

Heat transfer example 14000 12000 Elapsed Sec

10000

CPU Sec

8000 6000 4000 2000 0 MD R2.1

Main Index

MD R3

CHAPTER 6 225 Numerical Methods and High Performance Computing

Factor Matrix Caching for Lanczos and Nonlinear Transient Analysis with NLAUTO Introduction In solution sequences where many linear systems are solved using the same coefficient matrix, the FBS time can be significant when the factor matrix is stored out of core. Examples include dynamic solution sequences which use the Lanczos method and nonlinear transient response. In MD Nastran R3, new logic has been introduced to cache as much of the factor as possible in memory.

Benefits The reduced I/O can cut the elapsed time for FBS by five to 30 percent, depending on the size of the factor matrix, the number of right-hand sides, and the amount of memory available.

Method and Theory The underlying method has not changed; only the memory usage. Previously, only the minimum amount of factor data needed to perform the FBS was read from the factor data block each time and FBS was required. Now, as much of the factor as possible is cached in memory between FBS calls, reducing the I/O required.

Inputs For Lanczos, no input is required, except when running on Linux IA64. This option has not been beneficial on Linux IA64, but it can be turned-on setting SYSTEM cell 146 to -1. For nonlinear transient analysis, the factor caching logic must be activated by setting SYSTEM(146) to -1. For comparison purposes, the factor-caching logic can be deactivated by setting SYSTEM(146)=+1.

Outputs A new System Information Message 4157 will appear in the. f04 file:

MEMORY REQUIREMENTS FOR IN-CORE FACTOR OPTION: AVAILABLE MEMORY: NUMBER OF TOTAL FRONTS: NUMBER OF FRONTS WHICH FIT IN CORE: EST MEMORY FOR ENTIRE FACTOR TO IN CORE:

229909 42935 14225 586268

KWORDS KWORDS

In addition, when SYSTEM cell 166 to 2, additional time stamps “FBSI BGN” and “FBSI END” appear in the .f04 file.

Main Index

226 MD Nastran R3 Release Guide Factor Matrix Caching for Lanczos and Nonlinear Transient Analysis with NLAUTO

Guidelines and Limitations It is difficult to estimate the amount of memory to specify for a given model so that most of the factor can be cached. The “estimate” program can give a starting point. A rule of thumb would be to give 3 times the amount of memory recommended in the “estimate” output, but no more than 75% of the physical memory available on the machine.

Demonstration Examples Example 1: The following example is a nonlinear transient analysis model, with approximately 4000 dof which performs approximately 34,000 FBS operations. The analysis was run on a workstation with two dualcore 64-bit Pentium Xeon processors running at 3GHz, 8GB of physical memory and a 4-way striped SCSI disk array. The job was submitted with mem=4gb. Specifying system(146)=-1 reduces total I/O by 11% and results in a 10% overall performance improvement in elapsed time.

Nonlinear Transient Performance 60000

Seconds or MB

50000

40000 Default

30000

Factor Cached

20000

10000

0 Elapsed Time [sec]

Main Index

I/O [MB]

CHAPTER 6 227 Numerical Methods and High Performance Computing

Example 2: The following example is a powertrain model with 160,000 grids and 940,000 degrees of freedom. Twenty mode shapes are required using Lanczos. A total of 14 FBS operations are performed. The job is run on workstation with two dual-core 64-bit Pentium Xeon processors running at 3GHz, 8GB of physical memory. The job is submitted with mem=6gb. By caching the factor, the total FBS time is reduced by 30%, resulting in a 13% reduction in the overall READ time.

Lanczos Performance Improvement 350

CPU seconds

300 250 200

Factor out of core Factor Cached

150 100 50 0 FBS time [seconds]

Main Index

READ time [seconds]

228 MD Nastran R3 Release Guide New TAUCS Indefinite Solver Improves Lanczos Performance

New TAUCS Indefinite Solver Improves Lanczos Performance Introduction A new symmetric indefinite factorization method from the TAUCS software project www.tau.ac.il/~stoledo/taucs/ has been integrated into MD Nastran R3. It is available in the DCMP, DECOMP, SOLVE, RMG2, SDR2, and READ modules, with the main focus on the READ module. The new solver keeps all data in memory.

Benefits The new method can significantly improve the factorization and FBS time, particularly in the Lanczos procedure, for problems which fit in memory. In this release, the method is only recommended on the Linux x86_64 platforms (Intel EM64T and AMD Opteron).

Method and Theory The new method is based on a hybrid left-looking /supernodal multifrontal technique, with emphasis on data locality.

Inputs The new method can be selected by setting SYSTEM cell 166 to 16384.

Outputs The following information is printed in the .f04 file.

Elimination tree depth is 7043 Symbolic Analysis of LDL^T: 1.53e+08 nonzeros, 9.48e+10 flops, 1.40e+09 bytes in L Relaxed Analysis of LDL^T: 1.80e+08 nonzeros, 1.14e+11 flops, 1.72e+09 bytes in L Symbolic Analysis = 3.415 seconds (3.411 cpu) 12:07:41 1:05 15753.0 24.0 61.1 6.5 TAUD END 12:07:47 1:11 16890.0 1137.0 66.7 5.5 TAUD BGN Using blocked update in dense factorization. Supernodal Left-Looking LDL^T = 49.121 seconds (48.390 cpu) Post Analysis of LDL^T: 1.80e+08 nonzeros, 1.14e+11 flops, 1.72e+09 bytes in L

Guidelines and Limitations In this release, this method has only been tuned for the Linux x86_64 platform (Intel EM64T/AMD Opteron) and is only recommended for that platform. This method must keep all data in memory, so it is recommended that it be submitted with 75% of the physical memory available.

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CHAPTER 6 229 Numerical Methods and High Performance Computing

Demonstration Examples A normal modes computation has been performed using the default factorization method (SPDC) and the new TAUCS method on the following models. The jobs are run on a workstation with two dual-core 64-bit Pentium Xeon processors running at 3GHz, 8GB of physical memory. Each job was submitted with mem=6gb.

Model

Grids

DOF

Modes

Factorizations

FBS’s

Powertrain

160,000

940,000

20

2

14

Rotor

197,000

592,000

8

2

8

Viga

139,000

413,000

5

2

5

Van

103,000

584,000

73

2

43

Lanczos Performance

READ time [cpu seconds]

1400 1200 1000 800

SPDC TAUCS

600 400 200 0 Rotor

viga

Powertrain Model

Main Index

van

230 MD Nastran R3 Release Guide Shared Memory Parallel (SMP) Scalability Improvements for Static Analysis

Shared Memory Parallel (SMP) Scalability Improvements for Static Analysis Introduction In solution sequences where a linear system must be solved with a large number of right-hand sides, several passes over the factor matrix may be needed to compute all of the solution vectors. This performance enhancements keeps as much of the factor matrix as possible in memory to reduce the I/O, improve overall performance, particularly SMP performance.

Benefits The performance of any large FBS with many right-hand sides will be improved by as much as 30%. For example, superelement models with static (Guyan) reduction, statics models with many load cases, and heat transfer models with radiation will benefit from this enhancement.

Method and Theory The underlying method has not changed; only the memory usage. Previously, only the minimum amount of factor data need to perform the FBS was read from the factor data block during each FBS pass. Now, as much of the factor as possible is cached in memory between FBS passes, reducing the I/O required.

Inputs The feature is automatically activated on all platforms except Linux IA64 when enough memory is available to store at least 32 right-hand side vectors, and when the factor and right-hand side have the same data type (both real or both complex). The minimum number of right-hand sides required to activate the feature can be overridden with the value of SYSTEM cell 70.

Outputs A system information message is printed in the .f04 file if any part of the factor is cached:

*** SYSTEM INFORMATION MESSAGE 4157 (PREFAC1) A PORTION OF THE SPARSE FACTOR HAS BEEN CACHED IN MEMORY FOR THE FBS. 34435 FRONTAL MATRICES OUT OF A TOTAL OF 37881 ARE STORED IN MEMORY. MEMORY AVAILABLE: 412 M WORDS ESTIMATED ADDITIONAL MEMORY NEEDED TO STORE THE ENTIRE FACTOR: 281 M WORDS

Guidance and Limitations 1. This feature is not available on the Linux IA64 platform.

Main Index

CHAPTER 6 231 Numerical Methods and High Performance Computing

2. This feature requires additional memory. The recommended amount is three times the amount specified by the “estimate” program plus enough to hold 32 right-hand side vectors.

Demonstration Examples The following example is a linear statics model of a car body with 42,000 grid points, 246,000 degrees of freedom, and 8,300 load cases. The job was run on an IBM pSeries workstation with 8 1.9GHz power5 processors, and 8GB of physical memory.

Linear Static Performance 1000

Elapsed Time [Seconds]

900 800 700 600 R2

500

R3(Factor Cached)

400 300 200 100 0 Serial

Main Index

SMP=2

SMP=4

232 MD Nastran R3 Release Guide New MAXRATIO Information Output

New MAXRATIO Information Output Introduction A new interface is now available for analysts to better control the generation of matrix diagonal term ratio statistics produced by the sparse symmetric matrix decomposition process in the DCMP module. The matrix diagonal term ratio statistics are sometimes useful in determining the quality of the matrix decomposition process. In general, for linear static analysis, high or negative ratios indicate a loss of accuracy and could be indicative of a modeling error. The MAXRATIO functionality was a pre-release capability in the MD Nastran R2.1 release. For MD Nastran R3 this is now a production capability.

Benefits The new interface provides analysts with more control over the process than the existing method of supplying a value for the MAXRATIO DMAP parameter. In addition, a new output data option is available in the form of a simple bar chart that provides a more comprehensive view of the ratio data.

Method and Theory No new theory is involved. The method simply involves the computation of a ratio defined as the original matrix diagonal term divided by the decomposed matrix diagonal term. These ratios are placed in a table together with the external identifier associated with the row/column of the term. This table is then processed according to the options requested by the user.

Inputs The matrix diagonal term ratio output options are controlled by keywords specified on the SPARSESOLVER Executive Control statement. See New SPARSESOLVER MDTSTATS Information Output, 236 for a complete description of this statement.

Outputs The matrix diagonal term ratios can be presented in two different views. The first view is the table view, in which each ratio is listed together with the external identifier of the row/column of the matrix, as well as the original input matrix diagonal term. This format is virtually identical to that produced by the previous version when any ratio exceeds the value of the MAXRATIO input parameter. The second view of the ratios is statistical in nature. It is similar to a bar chart. A series of bar segments are generated. There are two options for specifying the segment widths of the bars. The default option uses powers of 10 as the widths (e.g., 10.0 to 100.0, and 100.0 to 1000.0). The second option allows the user to specify how many segments are desired. The program will compute the segment width using the maximum and minimum ratios. For each bar in the chart, the total number of terms in the range is tabulated together with a visual indication of the percentage number of terms in that particular bar.

Main Index

CHAPTER 6 233 Numerical Methods and High Performance Computing

Note that when negative matrix diagonal term ratios are detected, they will always be output if the TABLE option is specified. These new views of the ratios do not replace any existing diagnostics generated by the DCMP module if a problem is detected. Under these conditions, output from the table view may duplicate previous output generated by DCMP module error processing.

Guidelines and Limitations The matrix diagonal term ratio statistics are sometimes useful in determining the quality of the matrix decomposition process. In general, high ratios indicate a loss of accuracy. The feature can be used by taking all of the program defaults for the various control variables. These defaults produce both the table and bar outputs. The table is limited to 25 ratios that exceed 1.0E+05. The bar chart uses powers of ten for segment widths. This can be done by adding SPARSESOLVER DCMP (MDTRATIO) to the Executive Control Section of the input data file. The use of this new feature is currently limited to sparse symmetric matrix operations in the DCMP module. If there are scalar-type points present in the problem, the degrees of freedom associated with these points will be grouped into the results for the translational degrees of freedom output.

Demonstration Example A simple example is presented that demonstrates the use of some of the new features available for output of the matrix diagonal term ratios. The SPARSESOLVER Executive Control statement is used to specify the desired features. The example is for demonstration purposes only, and is not representative any particular modeling situation. The model data consists of a simple plate structure subject to an end load.

Example Input Data $ $ Example problem to demonstrate matrix diagonal term ratios $ id test,case sol 101 SPARSESOLVER DCMP (MDTRATIO) cend spc=100 load=1000 disp=all begin bulk grdset,,,,,,,6 cquad4,101,101,1,2,52,51 cquad4,102,101,2,3,53,52 cquad4,103,101,3,4,54,53 cquad4,104,101,4,5,55,54

Main Index

234 MD Nastran R3 Release Guide New MAXRATIO Information Output

cquad4,105,101,5,6,56,55 cquad4,106,101,6,7,57,56 cquad4,107,101,7,8,58,57 cquad4,108,101,8,9,59,58 cquad4,109,101,9,10,60,59 cquadr,1101,101,1,2,52,51 cquadr,1102,101,2,3,53,52 cquadr,1103,101,3,4,54,53 cquadr,1104,101,4,5,55,54 cquadr,1105,101,5,6,56,55 cquadr,1106,101,6,7,57,56 cquadr,1107,101,7,8,58,57 cquadr,1108,101,8,9,59,58 cquadr,1109,101,9,10,60,59 grid, 1,, 0.0,0.0,0.0 grid, 2,, 1.0,0.0,0.0 grid, 3,, 2.0,0.0,0.0 grid, 4,, 3.0,0.0,0.0 grid, 5,, 4.0,0.0,0.0 grid, 6,, 5.0,0.0,0.0 grid, 7,, 6.0,0.0,0.0 grid, 8,, 7.0,0.0,0.0 grid, 9,, 8.0,0.0,0.0 grid,10,, 9.0,0.0,0.0 grid,51,, 0.0,1.0,0.0 grid,52,, 2.4,1.0,0.0 grid,53,, 3.5,1.0,0.0 grid,54,, 4.6,1.0,0.0 grid,55,, 5.7,1.0,0.0 grid,56,, 6.8,1.0,0.0 grid,57,, 7.9,1.0,0.0 grid,58,, 9.0,1.0,0.0 grid,59,,10.1,1.0,0.0 grid,60,,11.2,1.0,0.0 $ ctria3,201,101,101,102,151 ctria3,202,101,102,152,151 ctria3,203,101,102,103,152 ctria3,204,101,103,153,152 ctria3,205,101,103,104,153 ctria3,206,101,104,154,153 ctria3,207,101,104,105,154 ctria3,208,101,105,155,154 ctriar,1201,101,101,102,151 ctriar,1202,101,102,152,151 ctriar,1203,101,102,103,152 ctriar,1204,101,103,153,152 ctriar,1205,101,103,104,153 ctriar,1206,101,104,154,153 ctriar,1207,101,104,105,154 ctriar,1208,101,105,155,154 grid,101,, 0.0,0.0,0.0 grid,102,, 1.0,0.0,0.0 grid,103,, 2.0,0.0,0.0 grid,104,, 3.0,0.0,0.0 grid,105,, 4.0,0.0,0.0 grid,151,, 0.0,1.0,0.0 grid,152,, 3.4,1.0,0.0 grid,153,, 4.5,1.0,0.0 grid,154,, 5.6,1.0,0.0

Main Index

CHAPTER 6 235 Numerical Methods and High Performance Computing

grid,155,, 6.7,1.0,0.0 $ pshell,101,1,0.05,1 mat1,1,10.+6,,0.33 spc1,100,123,1,101 spc1,100,3,5,55,105,155 spc1,100,1,55,155 spc1,100,2,1,101 force,1000,10,,1000.0,1.0,0.0,0.0 force,1000,60,,1000.0,1.0,0.0,0.0 force,1000,105,,1000.0,1.0,0.0,0.0 force,1000,155,,1000.0,1.0,0.0,0.0 enddata

Example Output The output generated by the example is shown as follows. Notice that there are two separate sections of output: one for translational degrees of freedom, and one for rotational degrees of freedom. Within each section, both a bar chart and table of matrix diagonal term ratios are output.

TRANSLATIONAL DOF DIAGONAL TERM RATIO STATISTICS CHART FOLLOWS FOR THE DECOMPOSITION OF MATRIX KLL ------------------------------------------------|--------------------------------------------------------------------------DIAGONAL TERM RATIO RANGE #TERMS % TOT |MAXIMUM RATIO = 6.90963E+02 MINIMUM RATIO = 1.00000E+00 ------------------------------------------------|--------------------------------------------------------------------------1.0000E+00 TO 1.0000E+01 62 79.49 |**************************************************************************> 1.0000E+01 TO 1.0000E+02 12 15.38 |*************** 1.0000E+02 TO 1.0000E+03 4 5.13 |***** 0 0

MATRIX/FACTOR DIAGONAL TERMS RATIO SUMMARY TABLE FOR TRANSLATIONAL DOF SORTED ON DIAGONAL RATIO GRID POINT ID DEGREE OF FREEDOM MATRIX/FACTOR DIAGONAL RATIO MATRIX DIAGONAL (TOP 1 RATIOS>MAXRAT= 6.90963E+02) 58 T3 6.90963E+02 5.65535E+04 ROTATIONAL DOF DIAGONAL TERM RATIO STATISTICS CHART FOLLOWS FOR THE DECOMPOSITION OF MATRIX KLL ------------------------------------------------|--------------------------------------------------------------------------DIAGONAL TERM RATIO RANGE #TERMS % TOT |MAXIMUM RATIO = 3.35974E+02 MINIMUM RATIO = 1.00000E+00 ------------------------------------------------|--------------------------------------------------------------------------1.0000E+00 TO 1.0000E+01 38 63.33 |*************************************************************** 1.0000E+01 TO 1.0000E+02 18 30.00 |****************************** 1.0000E+02 TO 1.0000E+03 4 6.67 |*******

0 0

Main Index

MATRIX/FACTOR DIAGONAL TERMS RATIO SUMMARY TABLE FOR ROTATIONAL DOF SORTED ON DIAGONAL RATIO GRID POINT ID DEGREE OF FREEDOM MATRIX/FACTOR DIAGONAL RATIO MATRIX DIAGONAL (TOP 1 RATIOS>MAXRAT= 3.35974E+02) 58 R2 3.35974E+02 2.14135E+04

236 MD Nastran R3 Release Guide New SPARSESOLVER MDTSTATS Information Output

New SPARSESOLVER MDTSTATS Information Output Introduction A new interface is now available to control the generation of matrix diagonal term statistics for the input matrix to the sparse symmetric matrix decomposition process in the DCMP module. The matrix diagonal term statistics can be useful in determining the quality of the model in regions that produce unusually large or small terms. In general, for linear static analysis, model degrees of freedom with small stiffnesses could indicate areas where loads will produce large displacements. This feature complements the MDTRATIO option that controls MAXRATIO output described previously. The SPARSESOLVER MDTSTATS functionality was a pre-release capability in the MD Nastran R2.1 release. For MD Nastran R3 this is now a production capability.

Benefits The new interface provides another means of identifying potential modeling errors other than monitoring the MAXRATIO statistics. One of the new output data options is a simple bar chart that provides a more comprehensive view of the diagonal term data.

Method and Theory No new theory is involved. The method involves adding the original matrix diagonal term to the ratio table where the computation of the ratio is defined to be the original matrix diagonal term divided by the decomposed matrix diagonal term. These terms are placed together in a table with the external identifier associated with the row/column of the term. This table is then processed according to the options requested by the user.

Inputs The matrix diagonal term statistical output options are controlled by keywords specified on the SPARSESOLVER Executive Control statement. See the MD Nastran Quick Reference Guide for a complete description of this statement.

Outputs The matrix diagonal term statistics can be presented in two different views. The first is the table view in which each diagonal term is listed together with the external identifier of the row/column of the matrix, as well as with the Aii/Lii diagonal term ratio. This format is almost identical to that produced now when any ratio exceeds the value of the MAXRATIO input parameter. The second view of the diagonal terms is statistical in nature, similar to a bar chart. A series of bar segments is generated. There are two options for specifying the segment widths of the bars. The default option uses powers of 10 as the widths (e.g., 10.0 to 100.0, and 100.0 to 1000.0). The second option allows the user to specify how many segments are desired. The program will compute the segment width using the maximum and minimum diagonal

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CHAPTER 6 237 Numerical Methods and High Performance Computing

terms. For each bar in the chart, the total number of terms in the range is tabulated together with a visual indication of the percentage number of terms in that particular bar. These new views of the diagonal terms do not replace any existing diagnostics generated by the DCMP module if a problem is detected. Under these conditions, output from the table view may duplicate previous output generated by DCMP module error processing.

Guidelines and Limitations The matrix diagonal term statistics are sometimes useful in determining areas of the model that may pose problems during the decomposition process, or afterwards during the solution of equations that produce displacements. In general, unusually large or small values could indicate a modeling problem. The feature can be used by taking all of the program defaults for the various control variables. These defaults produce both the table and bar outputs. The table is limited to the 25 largest terms that exceed 1.0E+10, and the 25 smallest terms less than 1.0. The bar chart uses powers of ten for segment widths. This can be done by adding SPARSESOLVER DCMP ( MDTSTATS ) to the Executive Control Section of the input data file. The use of this new feature is currently limited to sparse symmetric matrix operations in the DCMP module. If there are scalar-type points present in the problem, the degrees of freedom associated with these points will be grouped into the results for the translational degrees of freedom output.

Demonstration Example A simple example is presented that demonstrates the use of some of the new features available for output of the matrix diagonal term statistics. The SPARSESOLVER Executive Control statement is used to specify the desired features. The example problem is used for demonstration purposes only, and is not representative of any particular model. The model data consists of a simple plate structure subject to an end load. The model properties have been designed to indicate a potential problem in the bending properties at grid points 4 and/or 54.

Example Input Data $ $ Example problem to demonstrate matrix diagonal term statistics $ id test,case sol 101 $ Note: SPARSOLVER DCMP options must be enclosed in () $ Note also that MDTSTATS options must also be enclosed in their own () SPARSESOLVER DCMP ( MDTSTATS = ( CHART, TABLET, NMAXVALT=10, MAXVALT=1.0e+08,

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238 MD Nastran R3 Release Guide New SPARSESOLVER MDTSTATS Information Output

NMINVALT=20, MINVALT=1.0, TABLER, NMINVALR=30, MINVALR=100.0 ) ) cend spc=100 load=1000 disp=all begin bulk grdset,,,,,,,6 cquad4,101,101,1,2,52,51 cquad4,102,101,2,3,53,52 cquad4,103,102,3,4,54,53 cquad4,104,102,4,5,55,54 cquad4,105,101,5,6,56,55 cquad4,106,101,6,7,57,56 cquad4,107,101,7,8,58,57 cquad4,108,101,8,9,59,58 cquad4,109,101,9,10,60,59 cquadr,1101,101,1,2,52,51 cquadr,1102,101,2,3,53,52 cquadr,1103,102,3,4,54,53 cquadr,1104,102,4,5,55,54 cquadr,1105,101,5,6,56,55 cquadr,1106,101,6,7,57,56 cquadr,1107,101,7,8,58,57 cquadr,1108,101,8,9,59,58 cquadr,1109,101,9,10,60,59 grid, 1,, 0.0,0.0,0.0 grid, 2,, 1.0,0.0,0.0 grid, 3,, 2.0,0.0,0.0 grid, 4,, 3.0,0.0,0.0 grid, 5,, 4.0,0.0,0.0 grid, 6,, 5.0,0.0,0.0 grid, 7,, 6.0,0.0,0.0 grid, 8,, 7.0,0.0,0.0 grid, 9,, 8.0,0.0,0.0 grid,10,, 9.0,0.0,0.0 grid,51,, 0.0,1.0,0.0 grid,52,, 2.4,1.0,0.0 grid,53,, 3.5,1.0,0.0 grid,54,, 4.6,1.0,0.0 grid,55,, 5.7,1.0,0.0 grid,56,, 6.8,1.0,0.0 grid,57,, 7.9,1.0,0.0 grid,58,, 9.0,1.0,0.0 grid,59,,10.1,1.0,0.0 grid,60,,11.2,1.0,0.0 $ ctria3,201,101,101,102,151 ctria3,202,101,102,152,151 ctria3,203,101,102,103,152 ctria3,204,101,103,153,152 ctria3,205,101,103,104,153 ctria3,206,101,104,154,153 ctria3,207,101,104,105,154

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CHAPTER 6 239 Numerical Methods and High Performance Computing

ctria3,208,101,105,155,154 ctriar,1201,101,101,102,151 ctriar,1202,101,102,152,151 ctriar,1203,101,102,103,152 ctriar,1204,101,103,153,152 ctriar,1205,101,103,104,153 ctriar,1206,101,104,154,153 ctriar,1207,101,104,105,154 ctriar,1208,101,105,155,154 grid,101,, 0.0,0.0,0.0 grid,102,, 1.0,0.0,0.0 grid,103,, 2.0,0.0,0.0 grid,104,, 3.0,0.0,0.0 grid,105,, 4.0,0.0,0.0 grid,151,, 0.0,1.0,0.0 grid,152,, 3.4,1.0,0.0 grid,153,, 4.5,1.0,0.0 grid,154,, 5.6,1.0,0.0 grid,155,, 6.7,1.0,0.0 $ pshell,101,1,0.05,1 pshell,102,1,0.05,2 mat1,1,10.+6,,0.33 mat1,2,10.+1,,0.33 spc1,100,123,1,101 spc1,100,3,5,55,105,155 spc1,100,1,55,155 spc1,100,2,1,101 force,1000,10,,1000.0,1.0,0.0,0.0 force,1000,60,,1000.0,1.0,0.0,0.0 force,1000,105,,1000.0,1.0,0.0,0.0 force,1000,155,,1000.0,1.0,0.0,0.0 enddata

Example Output The output generated by the example is shown as follows. There are two separate sections of output: one for translational degrees of freedom and one for rotational. Within each section, both a bar chart and table of matrix diagonal terms are output.

=============================================================================================================================== TRANSLATIONAL DOF Aii DIAGONAL TERMS STATISTICS CHART FOLLOWS FOR MATRIX KLL Matrix Trace(Aii) = 1.27351E+08 ------------------------------------------------|--------------------------------------------------------------------------| MAXIMUM VALUE = 5.94121E+06 MINIMUM VALUE = 4.07806E-01 MATRIX DIAGONAL TERM RANGE #TERMS % TOT | GRID ID = 104, DOF = T2 GRID ID = 54, DOF = T3 ------------------------------------------------|--------------------------------------------------------------------------1.0000E-01 TO 1.0000E+00 2 2.56 |*** 1.0000E+03 TO 1.0000E+04 2 2.56 |*** 1.0000E+04 TO 1.0000E+05 18 23.08 |*********************** 1.0000E+05 TO 1.0000E+06 6 7.69 |******** 1.0000E+06 TO 1.0000E+07 50 64.10 |**************************************************************** ===============================================================================================================================

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240 MD Nastran R3 Release Guide New SPARSESOLVER MDTSTATS Information Output

0

MATRIX/FACTOR DIAGONAL TERMS SUMMARY TABLE FOR TRANSLATIONAL DOF SORTED ON Aii DIAGONAL GRID POINT ID DEGREE OF FREEDOM Aii TERM Lii TERM Aii/Lii RATIO (TOP 1 VALUES > 5.94121E+06) 104 T2 5.94121E+06 3.57301E+06 1.66280E+00

0

MATRIX/FACTOR DIAGONAL TERMS SUMMARY TABLE FOR TRANSLATIONAL DOF SORTED ON Aii DIAGONAL GRID POINT ID DEGREE OF FREEDOM Aii TERM Lii TERM Aii/Lii RATIO (TOP 2 VALUES < 1.00000E+00) 54 T3 4.07806E-01 4.07806E-01 1.00000E+00 4 T3 4.70350E-01 2.84250E-01 1.65471E+00

=============================================================================================================================== ROTATIONAL DOF Aii DIAGONAL TERMS STATISTICS CHART FOLLOWS FOR MATRIX KLL Matrix Trace(Aii) = 4.52211E+05 ------------------------------------------------|--------------------------------------------------------------------------| MAXIMUM VALUE = 2.34493E+04 MINIMUM VALUE = 4.71107E-02 MATRIX DIAGONAL TERM RANGE #TERMS % TOT | GRID ID = 9, DOF = R2 GRID ID = 54, DOF = R1 ------------------------------------------------|--------------------------------------------------------------------------1.0000E-02 TO 1.0000E-01 2 3.33 |*** 1.0000E-01 TO 1.0000E+00 2 3.33 |*** 1.0000E+02 TO 1.0000E+03 3 5.00 |***** 1.0000E+03 TO 1.0000E+04 36 60.00 |************************************************************ 1.0000E+04 TO 1.0000E+05 17 28.33 |**************************** =============================================================================================================================== 0

MATRIX/FACTOR DIAGONAL TERMS SUMMARY TABLE FOR ROTATIONAL DOF SORTED ON Aii DIAGONAL GRID POINT ID DEGREE OF FREEDOM Aii TERM Lii TERM Aii/Lii RATIO (TOP 1 VALUES > 2.34493E+04) 9 R2 2.34493E+04 4.87230E+03 4.81277E+00

0

MATRIX/FACTOR DIAGONAL TERMS SUMMARY TABLE FOR ROTATIONAL DOF SORTED ON Aii DIAGONAL GRID POINT ID DEGREE OF FREEDOM Aii TERM Lii TERM Aii/Lii RATIO (TOP 4 VALUES < 1.00000E+02) 54 R1 4.71107E-02 3.08701E-02 1.52610E+00 4 R1 4.71334E-02 9.03202E-03 5.21847E+00 54 R2 1.48139E-01 8.62427E-02 1.71770E+00 4 R2 1.48232E-01 7.96377E-02 1.86133E+00

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Chapter 7: Upward Compatibility MD Nastran R3 Release Guide

=

7

Main Index

Upward Compatibility 

TEMPERATURE Case Control Command



Improvements in Fluid Eigenvalue Analysis



FLUID GRID Points and Partitioning



Distributed Memory Parallel (DMP) Diagnostic Messages



System Information Message (SIM) 6916

242 MD Nastran R3 Release Guide Upward Compatibility

TEMPERATURE Case Control Command According to Remark 8 under the Case Control command TEMPERATURE (Ch. 4) in the MD Nastran Quick Reference Guide, TEMPERATURE(INITIAL) and TEMPERATURE(MATERIAL) cannot be specified in the same run and User Fatal Message 633 will be issued. User Fatal Message 633 is also issued if TEMPERATURE(BOTH) is specified with TEMPERATURE(INIT) and TEMPERATURE(MATERIAL). However, in MD Nastran R2 and prior, this rule was not enforced when just TEMPERATURE was specified with TEMPERATURE(INITIAL) or TEMPERATURE(MATERIAL); and, depending on their relative locations in the Case Control Section, one of them would be ignored and results will be wrong. For example, the following input file (modified from TPL problem tempload): sol 101 cend temp(init) = 10 subcase 1 temp = 20 load = 100 spc = 10 disp = all begin bulk force,100,3,0,100.0,1.0,0.0,0.0 grid, 1,, 0.0,0.0,0.0 grid, 2,,10.0,0.0,0.0 grid, 3,,20.0,0.0,0.0 cbar,1,10,1,2,0.0,0.0,1.0 pbar,10,100,1.0,1.0,1.0,1.0 mat1,100,1.+4,,0.3,,1.-3 rbar,2,2,3,,,,,2.0-4 temp,10,1,51.0 temp,10,2,52.0 temp,10,3,53.0 temp,20,1,61.0 temp,20,2,62.0 temp,20,3,63.0 spc1,10,123456,1 enddata produces the following results in versions MD Nastran R2 and prior: Case Control

T1 Displacement at Grid 2

Comment

TEMP(INIT) and TEMP(LOAD)

0.200

Correct answer

TEMP(LOAD)

0.715

Correct answer

TEMP(INIT) and TEMP

0.715

Wrong answer because TEMP(INIT) is ignored

In MD Nastran R3, this rule is now enforced with TEMPERATURE and UFM 633 will be issued. To avoid User Fatal Message 633 in MD Nastran R3, simply replace TEMPERATURE with

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CHAPTER 7 243 Upward Compatibility

TEMPERATURE (LOAD). In MD Nastran R4 or later, the BOTH keyword may be removed from the documentation and the program as an option of the TEMPERATURE command.

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244 MD Nastran R3 Release Guide Upward Compatibility

Improvements in Fluid Eigenvalue Analysis 1. The elemental mass matrix formulation for the 4-noded CTETRA fluid element has been modified to prevent spurious modes. Changes may be observed in the fluid’s natural frequencies especially at the higher frequencies. Use NASTRAN SYSTEM(446)=1 to obtain the previous version’s formulation. 2. Householder method is automatically selected for the fluid’s system modes if the acoustic cavity is defined in a superelement and there exist fluid boundary points. The Householder method is more reliable method when there are fluid points on the boundary of an acoustic superelement. The switch to Householder occurs if the number of estimated fluid modes is less than or equal to the value of user PARAMeter FLUIDNE (Default=500).

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CHAPTER 7 245 Upward Compatibility

FLUID GRID Points and Partitioning The GP4 module processes displacement set definition Bulk Data entries (e.g. ASET/ASET1). During this process, it performs various integrity tests on the data supplied by users. One of these tests verifies that the degree-of-freedom (DOF) components exist for the points specified. The allowable components depend upon the point type. For instance, a GRID point has six degrees of freedom and one may specify any (or all) of the components one through six. An SPOINT on the other hand has only a single DOF and one may specify only a blank or zero as the component. One must also remember that for some types of analysis, a GRID point may have a reduced number of components available. For example, in acoustics, one can define GRID points attached to fluid that have only a single component DOF. If the DOF integrity test fails, Nastran issues message 2049 that informs the user of the problem. The severity of the message depends upon whether one uses the standard input format (e.g. ASET) or the alternative format (ASET1) for the Bulk Data entry. When one uses the standard format, one defines each point and DOF component code explicitly and it must exist. Otherwise, GP4 issues a FATAL 2049 message indicating that the point is missing. When one uses the alternate entry format, GP4 is prepared for the possibility that one or more points may not exist in THRU ranges defined on the entry. For this case, a missing point/DOF produces a WARNING 2049 message. Consider the following Bulk Data entries:

1. GRID,1130,,0.0,0.0,0.0,-1

$ this is a FLUID GRID point (OCID=-1)

2. ASET,1130,1

$ standard format

3. ASET,1130,123456

$ standard format

4. ASET1,1,1130

$ alternate format

5. ASET1,123456,1130

$ alternate format

Since point 1130 is a fluid GRID point, it has only a single DOF associated with it. This DOF is referenced with DOF component 1. Standard format entry #2 and alternate format entry #4 both use the proper DOF component code and GP4 places the entries in the a-set without generating any messages. Standard format entry #3 and alternate format entry #5 on the other hand, contain DOF components that do not exist for the specified point. Previous versions handle the processing of entries #3 and #5 as follows: • For entry #3 (ASET), GP4 issues a FATAL message 2049 indicating that it could not find the

point and the job stops. • For entry #5 (ASET1), GP4 issues a WARNING message 2049 indicating that it could not find

the point and the job continues, BUT, the point is NOT placed in the a-set as requested.

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246 MD Nastran R3 Release Guide Upward Compatibility

MD Nastran R3 contains a modification to this process for FLUID GRID points and SPOINTs as follows: • For entry #3 (ASET), GP4 issues a WARNING message 2049 indicating that certain DOFs are

not available at the point, places the one DOF available at the point in the a-set and continues the job. • For entry #5 (ASET1), GP4 issues a WARNING message 2049 indicating that certain DOFs are

not available at the point, places the one DOF available at the point in the a-set and continues the job Note the difference between MD Nastran R3 and previous versions in this area applies only to FLUID GRID and SPOINT entries found on displacement set membership (partitioning) definition Bulk Data entry (ASET, ASET1, OMIT, OMIT1, etc.). Existing bulk data files containing “illegal” specifications for DOF component codes for FLUID GRIDs and SPOINTs on the partitioning bulk data entries that ran successfully on previous versions will continue to run, but may produce different results when run with MD Nastran R3 if a DOF becomes a part of the a-set.

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CHAPTER 7 247 Upward Compatibility

Distributed Memory Parallel (DMP) Diagnostic Messages Several DMP diagnostic messages used to indicate one or more of the following keywords MDMODES, GDMODES, FDMODES, MDACMS, GDSTAT, MDSTAT, FDFREQ in the .f06 and f04 files. They have been replaced by their proper DOMAINSOLVER description, for example, MDMODES was replaced by “DOMAINSOLVER MODES (PARTOPT=DOF)”.

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248 MD Nastran R3 Release Guide Upward Compatibility

System Information Message (SIM) 6916 SIM 6916 which looks similar to the example below is no longer printed in the .f06 file unless you set system(294) to a value greater than zero. *** SYSTEM INFORMATION MESSAGE 6916 (DFMSYM) DECOMP ORDERING METHOD CHOSEN: BEND, ORDERING METHOD USED: BEND

Main Index

Chapter 8: Optimization

8

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MD Nastran R3 Release Guide

Optimization 

Enhancements in DRESP3



Topometry Optimization



Topography (Bead or Stamp) Optimization



Permanent Glued Contact Modeling in SOL 200



Randomization of an Input Data File



Random Elimination of Element Types



Enhancements in SOL 200 Optimization



Optimization of Nonlinear Structural Responses (Pre-release)

250 MD Nastran R3 Release Guide Enhancements in DRESP3

Enhancements in DRESP3 Introduction DRESP3 is a feature of SOL 200 in MD Nastran that allows the user to invoke external software to calculate design responses that are not available as standard DRESP1 quantities or that cannot be synthesized using the DRESP2 capability. The DRESP3 is a special purpose capability that requires some work on the user’s part to function effectively, but it has its adherents who appreciate its ability to include design responses that are not available from Nastran. Use of this capability has identified three enhancements for this capability that have been implemented for MD Nastran R3: 1. Provision for a capability to provide analytic gradients for the response 2. The ability to produce multiple response outputs from a single DRESP3 call. 3. Reordering of finite difference sensitivities when the DRESP3 has only DRESP1 flags and there are more DRESP1 responses in the DRESP3 than there are independent design variables in the model.

Benefits Analytical gradients provide a performance benefit as well as more robust results than can be expected from a finite difference approach to obtaining gradients. The multiple response requirement arises from a typical scenario where a number of design criteria for a particular component share a common set of inputs. For example, a panel may have criteria on stress, buckling and fatigue that share parameters for geometry, properties and internal responses. By evaluating all of these criteria in a single call, duplicate calculations are avoided and the number of calls to the server are reduced. The third enhancement above is for the very special application where there are perhaps thousands of DRESP1 entries and a few hundred design variables. In this case, it makes sense to do the finite difference gradient calculation by perturbing all the DRESP1 quantities for a particular design variable and then calling the DRESP3 evaluator. In this way, the number of call to the evaluator is reduced from 2*NRESP1 to 2*NDVI. When NRESP1 >> NDVI, this can provide a major performance improvement to the extent it enables performing design tasks that were previously out of reach.

User Inputs The format of the DRESP3 Bulk Data entry is unchanged. The user is required to modify the two server subroutines that serve to supply Nastran with the information required to evaluate the DRESP3 responses. These two subroutines are R3SGRT and R3SVALD and have the same names as has been used in previous releases of this capability. They now have additional inputs and outputs as shown here by examples. The R3SGRT now not only checks that the DRESP3 Bulk Data entry is supported by the server, but also identifies the number of responses that are produced from the server and whether analytic or finite

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CHAPTER 8 251 Optimization

difference gradient techniques will be used during the sensitivity and optimization evaluations. Listing 8-1 shows an R3SGRT subroutine that utilizes the new features in solving the DRESP3 example contained in External Response to Include Alternative Buckling Response (p. 504) in the MD Nastran Design Sensitivity and Optimization User’s Guide. Listing 8-1

R3SGRT Subroutine

SUBROUTINE R3SGRT(GRPID,TYPNAM,NRESP, GRDTYP, ERROR) C ---------------------------------------------------------------------C C PURPOSE: VERIFY THE EXTERNAL RESPONSE TYPE C C GRPID INPUT INTEGER - GROUP ID C TYPNAM INPUT CHARACTER*8 - NAME OF EXTERNAL RESPONSE TYPE C NRESP OUTPT INTEGER - NUMBER OF RESPONSES FOR THIS DRESP3 C GRDTYP OUTPT INTEGER - INTEGER ARRAY OF LENGTH NRESP C INDICATING HOW GRADIENT ARE TO BE C COMPUTED C = 2 THE USER WILL SUPPLY ANALYTIC C GRADIENTS C = -2 FINITE DIFFERENCE TECHNIQUES ARE USED C ERROR INPUT/OUTPUT INTEGER -ERROR CODE FOR THE CALL. C C METHOD C MATCH THE USER INPUT: TYPNAM WITH THE LIST OF AVAILABLE C EXTERNAL RESPONSE TYPES. IF NO MATCH IS FOUND, SET ERROR CODE. C SPECIFY THE NUMBER OF RESPONSES AND THE GRADIENT TECHNIQUE TO C BE USED FOR EACH C C CALLED BY C R3CGRT C C NOTE: C THE WRITER OF THIS ROUTINE IS RESPONSIBLE TO SPECIFY C NTYPES AND R3TYPE. C ---------------------------------------------------------------------C C VARIABLES PASSED IN C INTEGER GRPID, ERROR, NRESP INTEGER GRDTYP(*) CHARACTER*8 TYPNAM C C LOCAL VARIABLES C INTEGER NTYPES, BADTYP PARAMETER(NTYPES=6) CHARACTER*8 R3TYPE(NTYPES) C DATA BADTYP/7554/ DATA R3TYPE/'USEVAR1 ','USEVAR10','USEALL', . 'USEMIXVS','FREQMOD ','EULJOH '/ ERROR = 0 DO 100 ITYPE = 1, NTYPES IF (TYPNAM .EQ. R3TYPE(ITYPE)) THEN NRESP = 2 GRDTYP(1) = 2

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252 MD Nastran R3 Release Guide Enhancements in DRESP3

100 200

GRDTYP(2) = 2 GOTO 200 END IF CONTINUE ERROR = BADTYP CONTINUE RETURN END

This is an update of Listing 7-33 in the and items in bold are highlighted for the following discussion. There are two additional arguments for the subroutine: • NRESP – indicates how many responses are to be calculated for this response type • GRDTYP – indicates how gradients are to be supplied to an optimization or sensitivity analysis.

GRDTYP is a vector of length NRESP. Setting GRDTYP(iresp)=2 specifies that analytic gradients will be provided while =-2 indicates that finite difference techniques will be required to compute gradient information. In the Listing 8-1, the user has specified that there are two responses and that analytical gradients will be supplied for each. The corresponding R3SVALD subroutine is an update of Listing 7-34 in the MSC.Nastran Design Sensitivity and Optimization User’s Guide: Listing 8-2

R3SVALD Subroutine

SUBROUTINE R3SVALD(GRPID,TYPNAM, . NITEMS,ARGLIS, . NSIZE, ARGVAL, . NWRDA8,ARGCHR, . FORG,NRESP,NARG, . DR3VAL,SENVAL, . ERROR) C ---------------------------------------------------------------------C C PURPOSE: COMPUTE THE EXTERNAL RESPONSE C C GRPID INPUT INTEGER - GROUP ID C TYPNAM INPUT CHARACTER*8 - NAME OF EXTERNAL RESPONSE TYPE C NITEMS INPUT INTEGER - DIMENSION OF ARRAY ARGLIS C NSIZE INPUT INTEGER - DIMENSION OF ARRAY ARGVAL C NWRDA8 INPUT INTEGER - DIMENSION OF CHARACTER ARRAY ARGCHR C ARGLIS INPUT INTEGER - ARRAY OF NO. OF ITEMS FOR EACH C ARGUMENT TYPE C ARGVAL INPUT DOUBLE - ARRAY OF ARGUMENT VALUES (EXCEPT C CHARACTERS) C ARGCHR INPUT CHARACTER*8 - ARRAY OF CHARACTER VALUES C NRESP INPUT INTEGER - NUMBER OF RESPONSES C FORG INPUT INTEGER - TYPE OF CALL C = 0 FUNCTION EVALUATION C = 1 SENSITIVITY EVALUATION C NARG INPUT INTEGER - NUMBER OF ARGUMENTS NEEDING GRADIENTS C DR3VAL OUTPUT DOUBLE - VALUE OF THE EXTERNAL RESPONSES C SENVAL OUTPUT DOUBLE - MATRIX OF THE SENSITIVITY OF THE IRTH C RESPONSE TO THE IARGTH ARGUMENT C C

Main Index

ERROR

INPUT/OUTPUT INTEGER -ERROR CODE FOR THE CALL.

CHAPTER 8 253 Optimization

C METHOD C A)SET UP VARIOUS PARAMETERS FROM THE ARGUMENT LIST C B)IF FORG = 0 EVALUATE THE EXTERNAL RESPONSE BASED ON THE C GIVEN TYPNAM C C)ELSE IF FORG = 1 EVALUATE THE SENSITIVITIES OF THE EXTERNAL C RESPONSES TO THE ARGUMENTS THAT CAN VARY FOR C THE GIVEN TYPNAM C D)RETURN BADTYP ERROR IF TYPNAM IS NOT MATCHED HERE. C C NSIZE - THE NUMBER OF ARGUMENTS OR VALUES IN A DRESP3 ENTRY C C NSIZE=NV+NC+NR+NNC+NDVP1+NDVP2+NDVC1+NDVC2+NDVM1+NDVM2+NRR2 C WHERE: C NV = NUMBER OF DESVARS NR = NUMBER OF DTABLES C NR = NUMBER OF DRESP1S NNC = NUMBER OF DNODE PAIRS C NDVP1 = NUMBER OF DVPREL1S NDVP2 = NUMBER DVPREL2S C NDVC1 = NUMBER OF DVCREL1S NDVC2 = NUMBER DVCREL2S C NDVM1 = NUMBER OF DVMREL1S NDVM2 = NUMBER DVMREL2S C NRR2 = NUMBER OF DRESP2S C NARG = NSIZE - NC C C CALLED BY C VARIOUS C ---------------------------------------------------------------------C C VARIABLES PASSED IN C CHARACTER*8 TYPNAM, ARGCHR(NWRDA8) INTEGER FORG , NRESP INTEGER GRPID, NITEMS, NSIZE, ARGLIS(NITEMS), ERROR, NWRDA8 DOUBLE PRECISION ARGVAL(NSIZE), DR3VAL(*), SENVAL(NRESP,*) C C C LOCAL VARIABLES C INTEGER BADTYP, IDBG DOUBLE PRECISION PI, FAC, FACT, SLNDER DOUBLE PRECISION R,L,E,SIGMA,SIGMAC, RGYRA C DATA BADTYP /7554/, BADFG /7555/ C PI = 3.14159 PI2 = PI * PI C C THE USER-SUPPLIED EQUATION TO DEFINE THE EXTERNAL RESPONSES C SIGMA = DRESP1, R=DESVAR, L, E AND SIGMAC = DTABLE CONSTANTS C C EULER : EULER= -SIGMA * (L/ RGYRA ) **2 / (PI**2 * E) C RGYRA = R / 2.0 C C JOHNSON: JOHNSON = -SIGMA / (SIGMAC * FACTOR ) C FACTOR = 1. - SIGMAC * (L/RGYRA)**2 /(4 * PI**2 * E) ERROR = 0 C C SET UP PARAMETERS FOR VARIOUS ARGUMENT ITEMS C IF (TYPNAM .EQ. 'EULJOH ') THEN C FUNCTION EVALUATION R = ARGVAL(1) L = ARGVAL(2)

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254 MD Nastran R3 Release Guide Enhancements in DRESP3

C C C C

20 10 C C C C C C 25

E = ARGVAL(3) SIGMAC = ARGVAL(4) SIGMA = ARGVAL(5) RGYRA = R / 2.0 SLNDER = L / RGYRA FACT = PI * SQRT(2.0D0 * E / SIGMAC) FAC = 1.0D0 - SIGMAC * (SLNDER) ** 2 /(4.0D0 * PI2 * E ) IF ( FORG .EQ. 0 ) THEN FUNCTION EVALUATION JOHNSON CRITERION DR3VAL(1) = -SIGMA / (SIGMAC * FAC) EULER CRITERION DR3VAL(2) = -SIGMA * SLNDER**2 / (PI2 * E *10.0D0) ELSE IF ( FORG .EQ. 1 ) THEN GRADIENT EVALUATION DO 10 IRESP = 1, NRESP DO 20 IARG = 1, NARG SENVAL(IRESP,IARG) = 0.0D0 CONTINUE CONTINUE NOTE THAT ARGVAL(2,3 AND 4) ARE CONSTANT AND THEREFORE HAVE ZERO SENSITIVITY DSLDR = -SLNDER / R DFACR = -SIGMAC * SLNDER * DSLDR / (2.0D0 *PI2 * E) SENSITIVITY OF THE FIRST RESPONSE TO THE FIRST ARGUMENT SENVAL(1,1 ) = DFACR * SIGMA / ( SIGMAC * FAC ** 2) SENSITIVITY OF THE SECOND RESPONSE TO THE FIRST ARGUMENT SENVAL(2,1) = -2.0D0*SIGMA * SLNDER * DSLDR / 1 (PI2 * E * 10.0D0) SENSITIVITY OF THE FIRST RESPONSE TO THE SECOND ARGUMENT SENVAL(1,2) = - 1.0D0 / (SIGMAC * FAC) SENSITIVITY OF THE SECOND RESPONSE TO THE SECOND ARGUMENT SENVAL(2,2) = -SLNDER**2 / (PI2 * E* 10.0D0) DO 25 IDBG =1,2 CONTINUE ELSE ERROR = BADFG ENDIF ELSE ERROR = BADTYP END IF RETURN END

There are three new arguments and one modified argument in the calling statement: • FORG – input integer - flag to indicate whether this call is to perform function evaluations or

gradient evaluations. 0-function, 1-gradient • NRESP – input integer - indicates how many responses are to be calculated for this response

type • NARG – input integer -number of arguments requiring gradients • DR3VAL – output real – vector of responses • SENVAL, - output real – matrix of sensitivities

Main Index

CHAPTER 8 255 Optimization

DR3VAL is the modified argument in that it previously was a scalar and now is a vector. A comparison with the listing in the User’s Guide shows that now two responses are being returned (one for the Euler criteria and one for the Johnson criteria) rather than a single argument which was the most critical of the two criteria. NARG is used to supply the number of columns in the SENVAL matrix and it is important to note that any constant terms (i.e, those input using DTABLE) are not included in the count of NARG even though they are in the ARGVAL vector. SENVAL has NRESP rows and NARG columns. DR3VAL is output when FORG=0 while SENVAL is output when FORG=1. Additional discussion of these arguments is provided in Guidelines and Limitations, 255.

Output .f06 output associated with the DRESP3 has been altered in one subtle respect: a response number field has been added to the print as a count of which of the multiple responses is associated with the print. As an example, the

---- RETAINED DRESP3 RESPONSES -------------------------------------------------------------------------------------------------------------------------INTERNAL DRESP3 RESP RESPONSE GROUP TYPE LOWER UPPER ID ID NO LABEL NAME NAME BOUND VALUE BOUND -----------------------------------------------------------------------------------------------------------------------1 32 1 JOHNSON TESTGRP EULJOH N/A 1.4018E+00 1.0000E+00 1 32 2 JOHNSON TESTGRP EULJOH N/A 1.3761E+00 1.0000E+00 2 32 1 JOHNSON TESTGRP EULJOH N/A 1.4018E+00 1.0000E+00 2 32 2 JOHNSON TESTGRP EULJOH N/A 1.3761E+00 1.0000E+00 3 32 1 JOHNSON TESTGRP EULJOH N/A 1.4018E+00 1.0000E+00 3 32 2 JOHNSON TESTGRP EULJOH N/A 1.3761E+00 1.0000E+00 4 32 1 JOHNSON TESTGRP EULJOH N/A 1.4018E+00 1.0000E+00 4 32 2 JOHNSON TESTGRP EULJOH N/A 1.3761E+00 1.0000E+00 5 32 1 JOHNSON TESTGRP EULJOH N/A 1.4018E+00 1.0000E+00 5 32 2 JOHNSON TESTGRP EULJOH N/A 1.3761E+00 1.0000E+00

It is seen that a single DRESP3 entry has generated 10 responses. These are 2 responses in each five elements that have the buckling criteria imposed on them. It is up to the user to decipher that RESP NO. 1 is the Johnson buckling criterion while RESP NO. 2 is the Euler criterion.

Guidelines and Limitations Modifying Existing Server Subroutines The enhanced capability does not require any changes in the input files that have been developed to utilize the DRESP3, but it does require changes in the R3SGRT and R3SVALD server subroutines. To retain the current capability for an existing DRESP3, the changes required in the R3SGRT subroutine are to: 1. Add arguments NRESP and GRDTYP 2. Type NRESP and GRDTYP as integers. 3. Once the appropriate TYPNAM has been selected, add NRESP = 1 and GRDTYP(1) = -2

Main Index

256 MD Nastran R3 Release Guide Enhancements in DRESP3

For the R3SVALD subroutine, the changes are to: 1. Add arguments FORG, NRESP, NARG, and SENVAL 2. Type FORG, NRESP and NARG as integers and DR3VAL(*) and SENVAL(NRESP,*) as double precision 3. Replace the current DR3VAL = statements with DR3VAL(1) =. 4. Since FORG=1 is not supported, it is not necessary to specify any SENVAL output. Other Guidelines In R3SGRT, GRDTYP needs to be defined for all NRESP responses and the values must be either 2 or 2. It is an error if any other value is used. As mentioned previously, NARG is an input to R3SVALD and this value is determined from all the DRESP3 arguments minus the constants and the string inputs. If a particular response is not a function of one of the arguments, it is necessary to explicitly set the corresponding SENVAL output to zero. It is a good practice to initialize the entire SENVAL array to 0.0. It is important to realize that the gradients that are provided are for the responses with respect to the DRESP3 arguments and not (necessarily) the design variables. This takes the burden of performing the chain rule calculations from the user and uses existing Nastran operations to compute terms such as: dr 3 δr 3 JJJJJJJJ Z JJJJJJJJ H dx δx

δr 3 δr i

J JJJJJJJ ∑ JJJJJJJ δr δx i

Instead, the R3SVALD subroutine provides the are performed within Nastran.

δ r3 ⁄ δ x

and

δ r3 ⁄ δ ri

terms and the remaining operations

Limitation There is a current limitation that all GRDTYP’s for a particular TYPE must be the same, either -2 or 2. The GRDTYP’s do not need to all be the same for all the DRESP3’s in an input file. That is, one can specify analytic gradients for one TYPE and finite difference gradients for another type. Validation and Verification Checking that the gradients are correct is an important and challenging process. Tips for facilitating this include: 1. Setting DSAPRT(END=SENS) = n will stop the run after printing the sensitivities of the responses in set n. 2. Setting DSAPRT(START=1) = n will provide sensitivities for the response in set n on the first design cycle. 3. One can use two different versions of a DRESP3 to have the program check on itself. One would use finite difference gradients while the second would use analytic gradients. The results should agree except for numerical rounding due to the finite difference calculation.

Main Index

CHAPTER 8 257 Optimization

Examples Three test cases are discussed here. The first of these is ds13grad and is a variation of the dsoug13 example in External Response to Include Alternative Buckling Response (Ch. 7) in the MD Nastran Design Sensitivity and Optimization User’s Guide. The R3SGRT and R3SVALD subroutines listed above are used in this example. The second example is dresp3aa is a test example to demonstrate all the types of arguments that can be included in a DRESP3. The DRESP3 input in this example is: Listing 8-3

ds13grad

$ F101 = X1 DRESP3 101 EXTERNR3TESTGRP USEVAR1 DESVAR 1 DTABLE CONST DRESP1 808 DNODE 2 1 DVPREL1 1 DVCREL1 3 DVMREL1 5 DVPREL2 2 DVCREL2 4 DVMREL2 6 DRESP2 909 $ F102 = R2 DRESP3 102 EXTERNR3TESTGRP USEVAR10 DESVAR 1 DTABLE CONST DRESP1 808 DNODE 2 1 DVPREL1 1 DVCREL1 3 DVMREL1 5 DVPREL2 2 DVCREL2 4 DVMREL2 6 DRESP2 909 $ F103 = F(X1,CONST,R1,G,DVP1,DVC1,DVM1,DVP2,DVC2,DVM2,R2) $234567 DRESP3 103 EXTERNR3TESTGRP USEALL DESVAR 1 DTABLE CONST DRESP1 808 DNODE 2 1 DVPREL1 1 DVCREL1 3 DVMREL1 5 DVPREL2 2 DVCREL2 4 DVMREL2 6 DRESP2 909 $ F104 = F(X,g,P1,C1,M1,p2,R2) DRESP3 104 EXTERNR3TESTGRP USEMIXVS DESVAR 1 DTABLE CONST DRESP1 808 DNODE 2 1

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258 MD Nastran R3 Release Guide Enhancements in DRESP3

DVPREL1 1 DVCREL1 3 DVMREL1 5 DVPREL2 2 DVCREL2 4 DVMREL2 6 DRESP2 909 USRDATA thisisa teststring foraddingxxx $ F105 = F(X,R1) DRESP3 105 EXTERNR3TESTGRP FREQMOD DESVAR 1 DRESP1 505

The relevant part of the R3SGRT subroutine that goes with this input file is: Listing 8-4

dresp3aa

nresp = 1 IF (TYPNAM .EQ. 'FREQMOD' ) then grdtyp(1) = 2 Else if (typnam .eq. 'USEVAR1' ) then grdtyp(1) = -2 ELSE IF (TYPNAM .EQ. 'USEVAR10') THEN grdtyp(1) = 2 ELSE IF (TYPNAM .EQ. 'USEALL') THEN grdtyp(1) = -2 ELSE IF (TYPNAM .EQ. 'USEMIXVS') THEN grdtyp(1) = 2 else ERROR = BADTYP endif

There is a single response for each DRESP3 and analytic gradients are to be provided for TYPNAM=’FREQMOD’,USEVAR10’ and ‘USEMIXVS’ The relevant part of the R3SVALD subroutine is: Listing 8-5 c

20 10

dresp3sig

if ( forg .eq. 1 ) then gradient evaluation do 10 iresp = 1, nresp do 20 iarg = 1, narg senval(iresp,iarg) = 0.0d0 continue continue Endif IF (TYPNAM .NE. 'FREQMOD') THEN x = argval(1) const = argval(2) r1 = argval(3) g = argval(4) p1 = argval(5) c1 = argval(6) m1 = argval(7) p2 = argval(8) c2 = argval(9) m2 = argval(10)

Main Index

CHAPTER 8 259 Optimization

r2 = argval(11) END IF IF (TYPNAM .EQ. 'USEVAR1') THEN dr3val(1) = x+r1+r2 ELSE IF (TYPNAM .EQ. 'USEVAR10') THEN if ( forg .eq. 0 ) then dr3val(1) = r2 else senval(1,9) = 1.0d0 endif ELSE IF (TYPNAM .EQ. 'USEALL') THEN dr3val(1) = x+const+r1+g+p1+c1+m1+p2+c2+m2+r2 ELSE IF (TYPNAM .EQ. 'USEMIXVS') THEN if ( forg .eq. 0 ) then dr3val(1) = x+g+p1+c1+m1+p2+r2 else senval(1,1) = 1.0d0 senval(1,3) = 1.0d0 senval(1,4) = 1.0d0 senval(1,5) = 1.0d0 senval(1,6) = 1.0d0 senval(1,9) = 1.0d0 endif ELSE IF (TYPNAM .EQ. 'FREQMOD') THEN x = argval(1) r1 = argval(2) if ( forg .eq. 0 ) then dr3val(1) = x*r1 else senval(1,1) = r1 senval(1,2) = x endif ELSE ERROR = BADTYP END IF

It is expedient to zero out all the gradient values, whether they are needed or not. For the TYPNAM’s that don’t support analytic gradients, it is only necessary to provide the response value in DR3VAL(1). For the TYPNAM’s that do support analytic gradients, an if test on FORG is provided. For FORG=0, a function evaluation is made while a gradient evaluation is made for FORG=1. Note that for TYPNAM= ‘USEVAR10’, the input file shows 11 inputs, 1 for each of the available “Flags” while the actual response shown in R3SVALD only uses the DRESP2 argument, the eleventh ARGVAL. Furthermore, the gradient calculation has a single non-zero result: senval(1,9) = 1.0d0, indicating that the sensitivity of the first response to the ninth argument that can vary is 1.0. The constant term in the ARGVAL list and the undesigned DNODE do not count as one of the NARG sensitivity arguments, hence the discrepancy between eleven and nine. A final example is entitled dresp3sig and demonstrates the feature that reorders the sensitivity calculations when NRESP1>>NDVI. In this case, there are 181 DRESP1’s and 10 DESVAR’s so the criteria is satisfied. The job has two DRESP3’s that have the same arguments but one has TYPNAM=RSS and the other has TYPNAM=RSSA. The RSS response has its gradients calculated using finite difference techniques while the RSSA uses analytical gradients. Since these are the same response, the test case serves to demonstrate that the same sensitivity information is generated using analytic or finite difference gradient techniques. The problem is too small to make any assessment of the performance gains that have resulted from the third enhancement mentioned in the Introduction, 250.

Main Index

260 MD Nastran R3 Release Guide Topometry Optimization

Topometry Optimization Introduction Topometry optimization is an element-by-element sizing optimization. Unlike conventional sizing optimization where all elements referencing a property entry are grouped as one design variable, each designable element has an independent design variable in topometry optimization. Since element-byelement optimization has many design variables, it may find a better design than conventional sizing optimization. In previous versions of Nastran, the user can use the design variable Bulk Data entry DESVAR and the relation of model property and design variables Bulk Data entry DVxREL1 to support element-by-element sizing optimization. However, with this approach the user must generate a unique property data entry for each element and perhaps prepare thousands of DESVAR and DVPREL1 entries. With the topometry optimization capability released in MD Nastran R3, the user can utilize a new Bulk Data entry, TOMVAR, to select designable regions (model property or material property identification number), design parameters (such as thickness of PSHELLs, or Young’s Modulus of materials), input initial values, lower and upper bounds to perform element-by-element sizing optimization. The MD Nastran program internally generates DESVAR and DVPREL1 (and/or DVMREL1) for each designed element. The implementation provides a very simple user interface to do element-by-element sizing design optimization. In addition, topometry optimization supports the fully stressed design algorithm in MD Nastran. FSD is very efficient for certain problems with many stress constraints. Topometry optimization released in MD Nastran R3 can be applied to all elements that can be resized through Bulk Data entries DVPREL1 and DVMREL1. Those element types include not only volumebased elements like CQUAD4 but also non-volume elements like CWELD, CBUSH, and CFAST. Topology optimization is another element-by-element optimization technology. However, topology optimization and topometry optimization are fundamentally different. Topology optimization is a “0” or “1” discrete element-by-element optimization methodology. Topology optimization can be used to decide which element should be retained and which element should be discarded from the design space. One the other hand, topometry optimization aims to get a continuous variation of the designed properties. Although topometry optimization is not recommended for topology optimization tasks, it is observed topometry optimization can be used to get “similar topological results” for some cases. It is particularly useful for non-structural elements like CELAS, CFAST, and CBUSH that MD Nastran topology optimization does not support. In a single optimization problem, it is allowable to resize (or shape, topology) certain properties while topometry optimizing other properties.

Benefits • Topometry optimization is easy-to-use. One TOMVAR Bulk Data entry replaces many

thousands of DESVAR and DVxREL1 entries for large element-by-element design optimization problems. • Topometry optimization is good to identify critical design regions.

Main Index

CHAPTER 8 261 Optimization

• Topometry optimization is good to locate where to add/or remove material to improve structural

performance. • Topometry optimization is good for finding the optimal location of spot welds. In particular,

topometry optimization is very useful for some properties that MD Nastran topology does not support; for example, PDAMP, PELAS, PMASS, PBUSH, PVISC, PGAP, PACBAR, and PFAST.

Input The TOMVAR Bulk Data entry is used to select a topometry designable region and designed property name. The initial, lower, and upper bound of the designed property value are also specified on the topometry entry. The program automatically generates one design variable DV i for each element referencing a property PID. The relationship between design variables DV i and the element property P i given by P i Z DVi

i Z 1, NE

XLB ≤ DV i ≤ XUB where P i is the analysis model property value for the ith element. NE is the total number of elements referencing to the property PID. The user must input an initial value (such as the analysis model input property value). The default of lower bound (XLB) on DV i is 0.5 ⋅ DV i , and default of upper bound on DV i (XUB) is 1.5 ⋅ DV i . The topometry Bulk Data entry is: Format: N TOMVAR

2

3

4

5

6

7

8

9

10

ID

TYPE

PID

PNAME /FID

XINIT

XLB

XUB

DELXV

Example: Design all element's thickness referencing PSHELL ID = 5 with initial design = 10.0 ( t 0 element thickness), lower bound 0.5 ⋅ t 0 and upper bound 1.5 ⋅ t 0 . TOMVAR

10

PSHELL

5

T

Z 10.0

input

10.0

Example: Design all element's Young Modulus referred by PSHELL ID = 100 with initial design XINIT = 3.E+5, XLB=1.0, and XUB= 1.0E+6.

Main Index

262 MD Nastran R3 Release Guide Topometry Optimization

TOMVAR

10

PSHELL

100

E

3.E+5

1.0

1.E+6

Field

Contents

ID

Unique topometry design region identification number. (Integer > 0)

TYPE

Property entry type. Used with PID to identify the elements to be designed. (Character: “PBAR”, “PSHELL”, “PSOLID”, etc. see Remark 2.)

PID

Property entry identifier (Integer > 0). This PID must be unique for PIDs referenced by other TOPVAR, DVPREL1, DVPREL2, DVMREL1, and DVMREL2 entries. (Integer > 0). See Remark 2.

PNAME/FID

Property name or property material name, such as “T”, “A”, “E”, and “GE”, or field position of the property entry or word position in the element property table of the analysis model. Property names that begin with an integer such as 12I/T**3 may only be referenced by field position. (Character or Integer > 0. see Remark 2.)

XINIT

Initial value. (Real or blank, no default). Typically, XINIT is defined to match the mass target constraint (so the initial design does not have violated constraints) or the analysis model input property value.

XLB

Lower bound. (Real or blank; Default = blank). The default is XLB=0.5*XINIT.

XUB

Upper bound. (Real or blank; Default = blank). The default is XLB=1.5*XINIT.

DELXV

Fractional change allowed for the design variable during approximate optimization. (Real > 0.0; Default = 0.5. See Remark 3.).

Remarks: 1. Multiple TOMVAR’s are allowed in a single file. 2. Property name and FID > 0 can be used for element property values just like a Bulk Data entry DVPREL1. Only property name can be used for material property values like DVMREL1. If a property name is shared by both property and material (such as “A” for PROD and MAT1), this name is taken as a material name. The user must provide a FID for property name (FID=4 for PROD). PCOMP, PCOMPG, PBEAML, PBARL, PBMSECT, PBRSECT are not supported. If material property name is selected, PSHELL (with multiple MID inputs) must reference a unique material ID. 3. Combined topometry, topography, topology, sizing, and shape optimization is supported in a single file. However, topometry and topology cannot reference the same property ID. It is possible to topometry certain elements while sizing others. It is allowed to simultaneously design the same elements with topometry and desvar (sizing and/or shape) variables but topometry and sizing cannot reference the same property name. 4. The design response DRESP1=FRMASS (fractional mass) can be used for topometry optimization. The initial FRMASS is defined as1.0 at the initial design specified on a TOPVAR entry. For non-volume elements like CELAS, a artificial mass = 1.0 is assumed for each element.

Main Index

CHAPTER 8 263 Optimization

Output A regular SOL 200 summary table is produced. In addition, a Patran element result file jobname.des contains the optimal design values for each element. This Patran element result file can be imported to Patran a third party post-processor to display topometry optimization results. Two parameters DESCPH and DESPCH1 are used to specify in SOL 200 when the optimized topometry results are written to the jobname.des.

DESPCH

DESPCH specifies when the topometry optimized design values are written to the element result history file jobname.des. The Default = 0 writes the last design cycle only. DESPCH < 0 never. DEPSCH1 > 0 at every design cycle that is a multiple of DESPCH and the last design cycle.

DESPCH1

DESPCH1 > 0, write all topometry designed and non-designed element values to the element result history file jobname.des. 1.0 is assigned to the non-designed element value. DESPCH1 < 0, write all topometry designed element values to the element result history file jobname.des.

Guidelines and Limitations • BIGDOT is the default optimizer of topometry optimization since topometry optimization

usually involves many thousands of design variables. BIGDOT requires a Topology Optimization license. For SOL 200 design optimization clients without access to topology optimization, optimizer MSCADS, method=4 (SUMT) is recommended through the optimization control Bulk Data entry DOPTPRM. • Since SOL 200 adjoint design sensitivity analysis method does not support element responses

(such as stress), a direct design sensitivity analysis method is automatically selected for problems with element response constraints. In this case, topometry optimization with element response constraints are slow due to many design variables. Fully stressed design (FSD) can be used for certain problems. • Topology optimization can be used for analysis model properties PDAMP, PELAS, PMASS,

PBUSH, PVISC, PGAP, NSM, NSM1, PACBAR and PFAST. Topology optimization is limited to analysis properties that can reference material property MAT1. • P2 > 13 on DOPTPRM prints design variables in *.f06.

Example 1 - Three-bar Truss (tomex1.dat) A simple sizing optimization example three-bar truss (a TPL file DSOUG1.dat) is used here to demonstrate topometry optimization solved by the fully stressed design algorithm. Figure 8-1 shows the three-bar truss that must be built to withstand two separate loading conditions. The objective is to minimize structural weight and subjected to displacement and stress constraints. The sizing design variables are the cross-sectional areas. The detailed descriptions of analysis model and design

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264 MD Nastran R3 Release Guide Topometry Optimization

optimization model can be seen in Chapter 7 of the MD Nastran Design Sensitivity and Optimization User's Guide.

Figure 8-1

Three Bar Truss

The goal of this example is to show an alternate method of setting design variables by a TOMVAR entry. The objective and constraints are not changed. In conventional sizing optimization, the set of DESVAR and DVPREL1 entries define the relations Ai=1.0Xi (i=1, 2, 3) where A is the rod element crosssectional area and X is the design variable. In DSOUG1.dat, we have: $...DESIGN VARIABLE DEFINITION $DESVAR ID LABEL XINIT XLB XUB DELXV(OPTIONAL) DESVAR 1 A1 1.0 0.1 100.0 DESVAR 2 A2 2.0 0.1 100.0 DESVAR 3 A3 1.0 0.1 100.0 $ $...DEFINITION OF DESIGN VARIABLE TO ANALYSIS MODEL PARAMETER $RELATIONS $DVPREL1 ID TYPE PID NAME PMIN PMAX C0 + $+ DVID1 COEF1 DVID2 COEF2 ... DVPREL1 10 PROD 11 A 1 1.0 DVPREL1 20 PROD 12 A 2 1.0 DVPREL1 30 PROD 13 A 3 1.0

In DSOUG1.dat, rod elements 11 and 12 have different property groups. Then, the DLINK entry is used to explicitly link the design variables 1 and 3 together. In this example, we try to do element-by-element optimization. Thus, we take three design variables (rod element cross-sectional areas) as independent variables. The rod elements 1 and 3 have the same property group (PROD=1). TOMVAR entry 1

Main Index

CHAPTER 8 265 Optimization

(Listing 8-6) is used to define two independent design variables with an initial value = 1.0 (and element cross-sectional area = 1.0) for rod element 11 and 13 respectively. This is equivalent to four entries in DSOUG1.dat: DESVAR 1 DESVAR 3 DVPREL1 10 1 DVPREL1 30 3

A1 A3 PROD 1.0 PROD 1.0

1.0 2.0 11

0.1 0.1 A

13

A

100.0 100.0

TOMVAR entry 2 (Listing 8-6) is used to define one independent design variable with an initial value = 2.0 (and element cross-sectional area = 2.0) for rod element 12. This is equivalent to two entries in DSOUG1.dat: DESVAR 2 DVPREL1 20 2

A2 PROD 1.0

2.0 12

0.1 A

100.0

Input The input data for this example is given in Listing 8-6. Listing 8-6

Input File for Example 1

ID MSC TOMEX1 $ TIME 10 $ SOL 200 $ OPTIMIZATION CEND TITLE = THREE BAR TRUSS TOPOMETRY OPTIMIZATION SUBTITLE = 3 CROSS SECTIONAL AREAS AS DESIGN VARIABLES ECHO = SORT SPC = 100 DISP = ALL STRESS = ALL DESOBJ(MIN) = 20 $ (DESIGN OBJECTIVE = DRESP ID) DESSUB = 21 $ DEFINE CONSTRAINT SET FOR BOTH SUBCASES ANALYSIS = STATICS SUBCASE 1 LABEL = LOAD CONDITION 1 LOAD = 300 SUBCASE 2 LABEL = LOAD CONDITION 2 LOAD = 310 BEGIN BULK $ $-----------------------------------------------------------------------$ ANALYSIS MODEL $-----------------------------------------------------------------------$ $ GRID DATA $ 2 3 4 5 6 7 8 9 10 GRID 1 -10.0 0.0 0.0 GRID 2 0.0 0.0 0.0 GRID 3 10.0 0.0 0.0 GRID 4 0.0 -10.0 0.0 $ SUPPORT DATA

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266 MD Nastran R3 Release Guide Topometry Optimization

SPC1 100 123456 1THRU3 $ ELEMENT DATA CROD 1 11 1 4 CROD 2 12 2 4 CROD 3 11 3 4 $ PROPERTY DATA PROD 11 1 1.0 PROD 12 1 2.0 MAT1 1 1.0E+7 0.33 0.1 $ EXTERNAL LOADS DATA FORCE 300 4 20000. 0.8 -0.6 FORCE 310 4 20000. -0.8 -0.6 $ $-----------------------------------------------------------------------$ DESIGN MODEL $-----------------------------------------------------------------------$ $...DESIGN TOPOMETRY DESIGN DEFINITION $TOMVAR, ID, PRYPE, PID, PNAME, XINIT, XLB, XUB, DELXV(OPTIONAL) TOMVAR, 1 , PROD, 11, 4 , 1., .1 , 100.0 TOMVAR, 2 , PROD, 12, 4 , 2., .1 , 100.0 $ $...STRUCTURAL RESPONSE IDENTIFICATION $DRESP1 ID LABEL RTYPE PTYPE REGION ATTA ATTB ATT1 + $+ ATT2 ... DRESP1 20 W WEIGHT DRESP1 21 U4 DISP 12 4 DRESP1 23 S1 STRESS PROD 2 11 12 $...CONSTRAINTS $DCONSTR DCID RID LALLOW UALLOW DCONSTR 21 21 -0.20 0.20 DCONSTR 21 23 -15000. 20000. $ $...OPTIMIZATION CONTROL (FULLY STRESSED DESIGN): $ DOPTPRM FSDMAX 20 DESMAX 0 P1 1 P2 15 $ $.......2.......3.......4.......5.......6.......7.......8.......9.......0 ENDDATA

Main Index

CHAPTER 8 267 Optimization

Output A regular SOL 200 output can be found as:

*************************************************************** S U M M A R Y O F D E S I G N C Y C L E H I S T O R Y *************************************************************** (HARD CONVERGENCE ACHIEVED) NUMBER OF FINITE ELEMENT ANALYSES COMPLETED NUMBER OF FULLY STRESSED DESIGN CYCLES COMPLETED NUMBER OF OPTIMIZATIONS W.R.T. APPROXIMATE MODELS

17 16 0

OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY -------------------------------------------------------------------------------------------------------------------------------OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT ------------------------------------------------------------------------------------------------------------------------------INITIAL 3.234952E-01

4.828427E+00 1

FSD

3.862742E+00

N/A

-1.543690E-01 2

FSD

3.225798E+00

N/A

-7.883203E-03 . 16

FSD

2.741757E+00

N/A

1.664062E-04 DESIGN VARIABLE HISTORY --------------------------------------------------------------------------------------------------------------------------------------------------------------------INTERNAL | EXTERNAL | | DV. ID. | ELEMENT ID | LABEL | INITIAL : 1 : 2 : 3 : 4 : 5 : ----------------------------------------------------------------------------------------------------------------------------------------------------------------1 | 1 | TOMVAR | 1.0000E+00 : 8.0000E-01 : 6.8794E-01 : 6.8306E-01 : 6.9978E01 : 7.2284E-01 : 2 | 2 | TOMVAR | 2.0000E+00 : 1.6000E+00 : 1.2800E+00 : 1.0240E+00 : 8.1920E01 : 6.5536E-01 : 3 | 3 | TOMVAR | 1.0000E+00 : 8.0000E-01 : 6.8794E-01 : 6.8306E-01 : 6.9978E01 : 7.2284E-01 : -------------------------------------------------------------------------------------------------------------------------------

Example 2 – Car Model Topometry Design A real complex example car body is used here to demonstrate topometry optimization for graphical postprocessing. This example also shows that SOL 200 is able to deal with very large optimization problems. The objective is to minimize structural compliance and keep weight unchanged. SOL 200 produces an element thickness distribution file *.des that can be used by Patran or other post-processors to view topometry optimization results.

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268 MD Nastran R3 Release Guide Topometry Optimization

Figure 8-2

Main Index

Optimal Thickness Distribution of Car Model - Note that this figure is meaningful only when viewed in color.

CHAPTER 8 269 Optimization

Topography (Bead or Stamp) Optimization Introduction Topography optimization (also called bead or stamp optimization) is used to generate a design proposal for reinforcement bead patterns. In MD Nastran R3, topography optimization is treated as a special shape optimization and built on SOL 200 shape optimization technology. In topography optimization, finite element grids are moved in as normal vectors to the shell surface or the user's given direction. New algorithms were developed to generate shape design variables and shape basis vectors automatically based on the user's provided bead dimension (minimum bead width, maximum bead height, and draw angle). Since many design variables are generated in the topography optimization, the adjoint design sensitivity analysis method and large scale optimizer play key roles in solving topography optimization problems.

Benefits • Topography optimization is particularly powerful for designing sheet metal parts. • Topography optimization can be used for all SOL 200 analysis types such as statics, normal

modes, buckling, complex eigenvalue, dynamic frequency response, and aeroelastic analyses.

Input The BEADVAR Bulk Data entry is used to define topography design regions. N

2

3

4

5

6

7

8

9

BEADVAR

ID

PTYPE

PID

MW

MH

ANG

BF

SKIP

NORM/XD

YD

ZD

CID

XLB

XUB

DELXV

“DESVAR”

10

“GRID” NGSET DGSET

Main Index

Field

Contents

ID

Unique topography design region identification number. (Integer > 0)

PTYPE

Property entry type. Used with PID to identify the element nodes to be designed. (Character: “PSHELL”, “PSHEAR”, “PCOMP”, or “PCOMPG”.)

PID

Property entry identifier. See Remark 1. (Integer > 0)

MW

Minimum bead width. This parameter controls the width of the beads. The recommended value is between 1.5 and 2.5 times the average element width. See Remark 2. (Real > 0.0)

MH

Maximum bead height (Real > 0.0). This parameter sets the maximum height of the beads when XUB=1.0 (as Default). See Remark 2.

270 MD Nastran R3 Release Guide Topography (Bead or Stamp) Optimization

Main Index

Field

Contents

ANG

Draw angle in degrees (0.0 < Real < 90.0). This parameter controls the angle of the sides of the beads. The recommended value is between 60 and 75 degrees.

BF

Buffer zone ('yes' or 'no'; Default='yes'). This parameter creates a buffer zone between elements in the topography design region and elements outside the design region when BF='yes'. See Remark 3.

SKIP

Boundary skip (“bc”, “load”, “both”, or “none”; Default = “both”). This parameter indicates which element nodes are excluded from the design region. “bc” indicates all nodes referenced by “SPC” and “SPC1” are omitted from the design region. "load" indicates all nodes referenced by “FORCE”, “FORCE1”, “FORCE2”, “MOMENT”, “MOMENT1”, “MOMENT2”, and “SPCD” are omitted from the design region. “both” indicates nodes with either “bc” or “load” are omitted from the design region. “none” indicates all nodes associated with elements referencing PID specified in field 4 are in the design region.

“DESVAR”

Indicates that this line defines bead design variables that are automatically generated.

NORM/XD, YD, ZD

Bead vector (draw direction). Norm indicates the shape variables are created in the normal directions to the elements. If XD, YD, and ZD are provided, the shape variables are created in the direction specified by the xyz vector defied by XD/YD/ZD that is given in the basic coordinate system or CID. See Remark 4. (Character or Real, Default = blank = norm).

CID

Coordinate system ID used for specifying draw direction (Blank or Integer > 0; Default = blank = basic coordinate system)

XLB

Lower bound. (Real < XUB or blank; Default = blank = 0.0). This ensures the lower bound on grid movement equal to XLB*MH. See Remark 5.

XUB

Upper bound. (Real > XLB or blank; Default = 1.0). This sets the upper bound of the beads equal to XUB*MH. See Remark 5.

DELXV

Fractional change allowed for the design variable during approximate optimization. See Remark 3. (Real > 0.0; Default = 0.2)

“GRID”

Indicates this line defines what element nodes can be added and/or removed from topography design regions.

NGSET

All grids listed on Bulk Data entry SET1 = NGSET are removed from topography design regions.

DGSET

All grids listed on Bulk Data entry SET1 = DGSET are added to topography design regions.

CHAPTER 8 271 Optimization

Remarks: 1. Multiple BEADVAR’s are allowed in a single file. Combined topometry, topology, topography, sizing, and shape optimization is supported in a single file. 2. The user can provide allowable bead dimensions. MW

MH ANG

Bead Dimensions 3. It is recommended to set buffer zone = yes to maintain a good quality of mesh during topography optimization. Design elements No buffer zone

Buffer zone

Nondesign elements

Nondesign elements

4. The grids moves in the normal direction. All element grids referenced by one BEADVAR entry must follow the right hand rule. Element normal vectors

Optimized surface

Baseline surface

Element Normal

Main Index

272 MD Nastran R3 Release Guide Topography (Bead or Stamp) Optimization

User defined draw vector

Baseline surface

Optimized surface

User’s Provided Draw Direction

5. To force the grids to move only in the positive bead vector direction (one side of the surface), use XLB = 0.0. To force the grids to move only in the negative bead vector direction (another side of the surface), use XUB = 0.0. To allow girds to move in both positive and negative bead vector directions, use XLB < 0.0 and XUB > 0.0. For example, Bead Vector Bead Vector

Base Surface

Optimized Surface

(a) XLB = 0.0 and XUB = 1.0

Optimized Surface

(b) XLB = -1.0 and XUB = 0.0

(c) XLB = -1.0 and XUB = 1.0

6. The jobname.op2 has topography results (shape change) that can be viewed in Patran. The text file jobname.pch also has updated grid coordinates that can be copied to replace the grids in the original file, and imported to Patran on other post-processors to view topography optimization results.

Outputs A regular SOL 200 design history summary table is produced. The jobname.op2 (with PARAM,POST,1) and jobname.pch can be imported to Patran and other post-processors to view topography optimization results.

Main Index

CHAPTER 8 273 Optimization

Guidelines and Limitations • BIGDOT is the default optimizer of topography optimization since topography optimization

usually involves many design variables. BIGDOT requires a Topology Optimization license. For SOL 200 design optimization clients without access to topology optimization, the optimizer MSCADS method=4 (SUMT) is recommended through the optimization Bulk Data entry DOPTPRM. • Since SOL 200 adjoint design sensitivity analysis method does not support element responses

(such as stress), a direct design sensitivity analysis method is automatically selected for problems with element response constraints. In this case, topography optimization with element response constraints are slow. • Since adjoint design sensitivity analysis does not support rigid body elements (RBE1, RBE2,

RBE3, RROD, RBAR, RTRPLT, RSPLINE), all grids connected to rigid body elements must be fixed in topography optimization for static and dynamic frequency response analyses. • The minimum bead width and maximum bead height have significant effects on optimal

designs. A smaller minimum bead width results in more small beads. • Mesh distortion is a challenge for topography optimization. It is recommended that a relatively

coarse mesh be used for highly curved areas. • P2 > 13 on DOPTPRM prints design variables in *.f06

Example 3 – A Square (togex1.dat) A square model shown in Figure 8-3 is used to demonstrate MD Nastran R3 topography optimization capabilities. The square is modeled with quadrilateral plate elements (CQUAD4) and is fixed at all four edges. The objective is to maximize the first frequency of the structure with a given bead dimension (minimum bead width = 10.0, maximum bead height = 20.0, draw angle = 70.0).

Figure 8-3

Main Index

A Square

274 MD Nastran R3 Release Guide Topography (Bead or Stamp) Optimization

Input The input data for this example is given in Listing 8-7. The Bulk Data entry 1 defines the topography designable region. It is noticed that element normals are used for bead vectors (draw direction) and all grids associated with the boundary condition are fixed during optimization. PARAM, POST, -1 outputs results for Patran. Listing 8-7

Input File for Example 2

$Topography opt example one SOL 200 CEND TITLE = MD Nastran job created on 28-Nov-07 ECHO = NONE $ Direct Text Input for Global Case Control Data DESOBJ(MAX) = 1 SUBCASE 1 $ Subcase name : Default SUBTITLE=Default SPC = 2 METHOD = 1 DISPLACEMENT(SORT1,REAL,PLOT)=ALL ANALYSIS=MODES BEGIN BULK EIGRL,1,,,20 $ Direct Text Input for Bulk Data $ Elements and Element Properties for region : ps1 $ $ BEADVAR, ID, TYPE, PID, MW, MH, ANG, BF, SKIP. $ BEADVAR, 1 , PSHELL, 1, 10., 20.0, 70.0, YES, BOTH DRESP1, 1, MODES, FREQ,,,1 PARAM POST -1

Output Figure 8-4 shows the topography optimized result by using Patran. The first frequency has increased from

0.568HZ at the initial design to 4.78 HZ.

Figure 8-4

Main Index

Topography Optimal Design of A Square

CHAPTER 8 275 Optimization

Permanent Glued Contact Modeling in SOL 200 Permanent glued contact released in MD Nastran R2 and R3 is defined as a special type of contact model which imposes the condition that there is no relative normal or tangental motion between the contacting surfaces. In MD Nastran R3, the permanent glued contact capability is supported in all SOL 200 solutions including sizing, shape, topology, topometry, and topography optimization. SOL 200 supports all permanent glued contacts including edge-to- edge, edge-to-surface, and surfaceto-surface.

Benefits The primary benefit of the permanent glued contact in an optimization design task is the joining of two dissimilar meshes, with the potential to save significant modelling time.

Input No new input. The input associated with permanent glued contact are mentioned in both the MD Nastran R2 Release Guide and MD Nastran R3 Release Guide.

Output None.

Guidelines and Limitations 1. BCPROP (contact region by element properties) cannot reference topology and/or topometry designed element properties.Topology and/or topometry designed element IDs can be referenced by BSURF entries. 2. If the glue border elements are allowed in the topography optimization (BEADVAR), then the model may fail GROUNDCHECK (see Adaptive Meshing (Ch. 2)). With the removal of those glue border elements from topography designable regions, then the model will pass GROUNDCHECK.

Example 4 - A Solid Beam (topoug5.dat) The problem has two solids glued together along a transverse plane to form a cantilever. The composite cantilever is used to demonstrate topology optimization with glued contact. The objective is to minimize the compliance subject to mass constraint of 0.3 (70% weight reduction). The loading and boundary conditions are shown in Figure 8-5. The structure is modeled with 1683 CHEXA elements of PSOLID=1 property and 975 CHEXA elements with PSOLID=2 property.

Main Index

276 MD Nastran R3 Release Guide Permanent Glued Contact Modeling in SOL 200

Figure 8-5

Composite Cantilever with two solids permanently glued

Input The input data for this example related to topology optimization model is given in Listing 8-8. Two TOPVAR entries are used to define two topological design regions identified by PSOLID=1 and PSOLID=2. XINIT=0.3 on the TOPVAR entries match the mass target constraint so that the initial design is feasible. The rest of the values on the TOPVAR entry are default values for general topology optimization applications. Type one design responses DRESP1, 2 and 10 identify fractional mass and compliance respectively. DCONSTR = 1 specifies the mass target. DESOBJ = 10 in Case Control command selects the DRESP1=10 entry to be used as a design objective (minimization as default) and DESGLB selects the design constraint DCONSTR= 1 to be applied in this topology optimization task. Case Control command BCONTACT =888 selects the Bulk Data entry BCTABLE. Value 1 in field 5 of first line in BCTABLE entry indicates that 1 set of slave/master entries is entered. “Slave” indicates touching body and “master” indicates touched body. Presence of BCONTACT above the Subcase and value of 1 in field 8 (IGLUE) of “Slave” line in BCTABLE entry indicates that there is Permanent Glued Contact between the two bodies. The first entries 1001 and 2001 in “Slave” and “Master” lines respectively in BCTABLE entry are referenced by the two BCBODY entries with the corresponding IDs. Field 5 in BCBODY entries contains the IDs of BSURF entries which define the deformable surfaces identified by element IDs. In this problem deformations are small and linear. Listing 8-8 DESOBJ = 10 DESGLB = 1

Main Index

Input File for Glued Contact Topology Optimization

CHAPTER 8 277 Optimization

BCONTACT = 888 smethod=element ANALYSIS = STATICS $ Direct Text Input for Global Case Control Data SUBCASE 1 $ Subcase name : Default SUBTITLE=Default SPC = 2 LOAD = 2 DRSPAN = 1 BEGIN BULK $-------2-------3-------4-------5-------6-------7-------8-------9-----BCTABLE 888 1 + + SLAVE 1001 0.1 1 + + MASTER 2001 $ $-------2-------3-------4-------5-------6-------7-------8-------9-----BCBODY 1001 3D DEFORM 3 0 BCBODY 2001 3D DEFORM 4 0 $$ DCONSTR 1 2 .3 TOPVAR 1 PSOLID PSOLID .3 1 TOPVAR 2 PSOLID PSOLID .3 2 DRESP1 2 FRM FRMASS DRESP1 10 COMP COMP $ Direct Text Input for Bulk Data $ Elements and Element Properties for region : p1 PSOLID 1 1 0 BSURF 3 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 $......................... BSURF 4 1798 1799 1800 1801 1802 1803 1804 1805 1806 1807 1808 1809 1810 1811 1812 $.........................

Output Figure 8-6 shows the topology optimized result by using Patran without smoothing.

Figure 8-6

Main Index

Glued Contact Topology Design

278 MD Nastran R3 Release Guide Randomization of an Input Data File

Randomization of an Input Data File Introduction The stochastic capability in MD Nastran is the first step toward a complete and automatic selfrandomization of a finite element model. The current capability offers the possibility to automatically distribute tolerances and uncertainties with minimum effort. This dramatically reduces the complexity of large-scale stochastic simulations. In fact, once the stochastic option is triggered, the entire Bulk Data file is automatically randomized without further user intervention. The resulting model, which needs to be incorporated in a Monte Carlo Simulation loop (there are numerous off-the-shelf products which support this capability) possesses unprecedented levels of realism. In order to make full use of this new capability, it is necessary to use a multi-run environment which can spawn a certain number of independent MD Nastran executions, collect the results, and perform statistical postprocessing. With the self-randomization capability in MD Nastran, the user need only define the outputs to be monitored, such as stresses, Eigenfrequencies, temperatures, displacements, etc. There is no need to define inputs, as these are defined automatically by MD Nastran. The Randomization of an Input Data File functionality was a pre-release capability in MD Nastran R2.1. For MD Nastran R3 this is now a production capability.

Benefits It is sometimes assumed that the inputs to an MD Nastran analysis are known exactly, and thus the computed responses are exact. This is an invalid assumption since there will always be some uncertainty in the input values with a corresponding variation in the results. MD Nastran R2 provides a way of introducing this uncertainty into the analysis process by automatically randomizing user input real numbers based on the input values and statistical quantities that characterize the variation.

Input The randomization capability is driven by a new STOCHASTICS Case Control command, as described in the MD Nastran Quick Reference Guide. If STOCHASTICS=ALL is used, all real quantities on connectivity (those starting with C), material, and property Bulk Data entries, as well as any loads and SPCD quantities, are modified based on a covariance factor of 0.05. A Gaussian distribution is used to randomly select the perturbed quantity with the restriction than the value can be no more that a specified number of standard deviations from the user input mean value. The default number of maximum standard deviations is three. Alternatively, the STOCHASTICS Case Control command can point to a STOCHAS Bulk Data entry that provides the ability to selectively randomize different types of input quantities by means of userspecified covariance values and user-prescribed numbers of allowed standard deviations. In this case, only the types of input specified are randomized so that, for example, it is possible to randomize the load inputs while leaving the property values unchanged.

Main Index

CHAPTER 8 279 Optimization

Output There is no new output produced by this capability.

Guidelines and Limitations The randomization algorithm involves using a random number generator, a Gaussian distribution, a prescribed covariance, and a mean value based on user input to determine a randomized value that is to be used in the analysis. In order to avoid physically meaningless properties, the random value is prescribed to be within m standard deviations of the input value, where m is a user input value with a default value of 3.0. The product of m * COV should not be greater than 1.0 to eliminate the possibility of the property changing sign. Any real value in the Bulk Data file will be randomized unless otherwise specified by the user. To keep a particular field or fields from being randomized, the user must set them equal to a value of 0.0.

Main Index

280 MD Nastran R3 Release Guide Random Elimination of Element Types

Random Elimination of Element Types Introduction There has been a long-standing capability in MD Nastran that allows the user to specify the random elimination of a specified percentage of the CWELD elements contained in a bulk data file. This was done using the PARAM CWRANDEL entry, with an additional CWDIAGP PARAM providing the option of printing the IDs of the deleted elements. In the current release, this capability has been extended to the CELASi, CFAST, CSEAM, and 1-D mass (CMASSi, CONM1, and CONM2) elements. In addition, the user interface has been changed from the NASTRAN statement to the MDLPRM entry. The Random Elimination of Element Types functionality was a pre-release capability in the MD Nastran R2.1 release. For MD Nastran R3 this is now a production capability.

Benefits The ability to randomly delete various 1-D elements provides the user with some assessment of the integrity of the design being modeled. For instance, if randomly deleting 20% of, say, of the CWELD elements from a model caused a negligible change in the first ten natural frequencies, this was taken as an indication of the robustness of the structure. Extending this approach to other element types provides more options in this type of analysis. Placing the input on the MDLPRM entry consolidates that input so that the user does not have to deal with the PARAM entry.

Input The MDLPRM entry has ten new PARAMi names that support this capability. Five of these names (e.g, DELELAS) select the element type to which the random elimination applies and the ratio to be deleted, while an additional five names (e.g., PRTELAS) provide control as to whether the IDs of the deleted elements are to be printed. The default is that the IDs will not be printed.

Output There is no new output produced by this capability.

Guidelines and Limitations The deletion ratio is input as a real number between 0.0 and 1.0, with 0.0 indicating that no deletion is to take place, while 1.0 eliminates all elements of the specified type. It is possible that the elimination of a series of elements will introduce mechanisms in the structure that will cause the analysis to fail. It is the user’s responsibility to determine whether this failure has occurred. A likely scenario for the use of this capability would be to submit the same file multiple times and determine the variation in the results. MSC does not offer an automated way of doing this at this time.

Main Index

CHAPTER 8 281 Optimization

Enhancements in SOL 200 Optimization Introduction Capabilities of SOL 200 have been expanded to support: • Using properties on PCOMPG as design variables • Using responses from exterior acoustic as design constraints • Using responses from fluid model • A modified objective function

Benefits PCOMPG The implementation provides a simple user interface to design and to track a particular ply over many PCOMPGs which has the potential to significantly increase the productivity of engineers and designers. Exterior Acoustics By being able to use responses from exterior acoustic analysis in SOL 200, the automotive engineer has the design tool to produce the optimized products which satisfy pass-by noise regulation. Fluid Modes Fluid modes can be utilized as design constraints in the optimization. Objective Function Modification Frequently, auto and aircraft manufacturers use SOL 200 to design just a tiny portion of the structure. The mass of design portion can be 3 to 4 orders of magnitude smaller than the full structural mass. Modifying the objective function provides a quick way avoid premature convergence.

Input PCOMPG as Design Variables The following KEYWORDs are added to the TYPE field of DVPREL1 Bulk Data entry.

Main Index

1

2

3

4

5

6

7

8

DVPREL1

ID

TYPE

PID

PNAME/ FID

PMIN

PMAX

C0

DVPREL1

100

PCOMPG PID or or GPLY GPLYID

9

10

282 MD Nastran R3 Release Guide Enhancements in SOL 200 Optimization

For type=PCOMPG, PID field should have the ID of the PCOMPG entry and the PNAME/FID field can have input of property name of fields or field number. For type=GPLY, PID field should have the GPLYID on the continuation lines of PCOMPG and the PNAME/FID field can only have T or THETA as input. It should be noted that: 1. When DVPREL1 has TYPE=GPLY, all PCOMPG entries with GPLYID will participate in the design. The relationship between design variable and properties are defined by the following equation P i Z C0 H ( T0 i or THETA0 i ) ⋅

∑ ( DVID j ⋅ COEF j )

T0 or THETA0 is the original thickness or THETA angle on PCOMPG which is determined automatically from the PCOMPG entry and is utilized as multiplier to the design variables. This formulation allows a ply with same GPLYID on different PCOMPG’s to change in tandem percentage-wise. 2. For THETA0 with original value equal to 0.0, THETA0 is taken as 1.0 and it is recommended to have XINIT of DVID set to 0.0.

Example $ $ DESVAR 1 $ DVPREL1 1 1

$ $ T100000 1.00 GPLY 1.0

$ 0.01

100000

$

100.0

$

$

$

T

Exterior Acoustic Responses as Design Constraints 1 DRESP1

Main Index

2

3

4

ID

LABEL

RTYPE

ATT2

-etc.-

5

6

PTYPE REGION

7

8

9

ATTA

ATTB

ATT1

10

CHAPTER 8 283 Optimization

New Keyword Entry for RTYPE Field

Response Attributes

PTYPE ATTA

ATTB

ATTi

ACPWR – acoustic power radiated through a panel

Panel name (Blank for total)

Blank

Frequency value (Blank for all forcing frequency, Real > 0.0)

Blank

ACINTS – acoustic intensity

Blank

Blank

Frequency value (Blank for all forcing frequency, Real > 0.0)

Grid ID of wetted surface

AFPRES – Acoustic pressure for AFPM

AFPMID – Acoustic Field Point Mesh ID (Integer > 0)

Acoustic Pressure Component (Integer = 1 or 7)

Frequency value (Blank for all forcing frequency, Real > 0.0)

Grid ID of AFPMID

AFINTS – Acoustic Intensity for AFPM

AFPMID – Acoustic Field Point Mesh ID (Integer>0)

Component Code 0-normal to AFPM, 1-xdir 2-y-dir 3-z-dir

Frequency value (Blank for all forcing frequency, Real > 0.0)

Grid ID of AFPMID

AFVLELO – Velocity for AFPM

AFPMID – Acoustic Field Point Mesh ID (Integer>0)

Component Code 11-Real/Mag in x-dir 12-Real/Mag in y-dir 13-Real/Mag in z-dir 71-Img/Ph in x-dir 72-Img/Ph in y-dir 73-Img/Ph in z-dir

Frequency value (Blank for all forcing frequency, Real > 0.0)

Grid ID of AFPMID

AFPWR – Acoustic Power for AFPM

AFPMID – Acoustic Field Point Mesh ID (Integer > 0)

Blank

Frequency value (Blank for all forcing frequency, Real > 0.0)

Blank

Example $ $ $ $ $ $ DRESP1 with new RTYPE $ ACPWR - ACoustic PoWeR dresp1 5200 APOW ACPWR dresp1 5201 APOW2 ACPWR dresp1 5202 APOW3 ACPWR LFDOOR $ $ ACINTS - ACoustic INTenSity dresp1 5300 AINT acints dresp1 5301 Aint2 acints $ $ AFPRES - Acoustic PRESsure for AFPM dresp1 5400 afprs AFPRES 100 dresp1 5401 afprs2 AFPRES 100 $ $ AFINTS - Acoustic INTenSity for AFPM dresp1 5501 afint2 AFINTS 100 $ $ AFVELO - Acoustic VELOcity for AFPM

Main Index

$

$

$

$

30.

30.

5 5

1 1

30.

194 189

1

30.

189

284 MD Nastran R3 Release Guide Enhancements in SOL 200 Optimization

dresp1 dresp1 $ $ AFPWR dresp1 dresp1

5600 5601

afvel afvel2

AFVELO AFVELO

100 100

11 11

194 189

30.

- Acoustic PRESsure for AFPM 5700 afpwr AFPWR 100 5701 afpwr2 AFPWR 100

30.

Fluid Modes as Design Constraints 1

2

3

4

DRESP1

ID

LABEL

RTYPE

ATT2

-etc.-

RTYPE EIGN or FREQ

New Option for PTYPE Field STRUC or FLUID

5

6

PTYPE REGION

7

8

9

ATTA

ATTB

ATT1

10

Response Attributes ATTA Normal Modes Number

ATTB

ATTi

Approximation code

With RTYPE=EIGN or FREQ, the default for PTYPE field is ‘STRUC’. Objective Function Modification New parameter OBJMOD for DOPTPRM is implemented as a flag for objective function modification. With DOPTPRM,OBJMOD,1, the original objective function value will be reset to 0.0. From the second cycle onward, the objective function value represents the change of objective function with respect to the original design. The default value for OBJMOD is 0, meaning the total objective function value will be used.

Output Output for the previous new features of SOL 200 is presented in the following paragraph. New features are highlighted in BOLD characters. PCOMPG as Design Variables A single set of DESVAR/DVPREL1 with GPLY will cover multiple PCOMPG entries which has a ply with GPLYID. The output of comparison of analysis and design model, will then look like:

-----

COMPARISON BETWEEN INPUT PROPERTY VALUES FROM ANALYSIS AND DESIGN MODELS -----

---------------------------------------------------------------------------------------------------------------------------PROPERTY PROPERTY PROPERTY ANALYSIS DESIGN LOWER UPPER DIFFERENCE SPAWNING TYPE ID NAME VALUE VALUE BOUND BOUND FLAG FLAG ---------------------------------------------------------------------------------------------------------------------------GPLY 12 T 5.400000E-03 5.400000E-03 N/A N/A NONE GPLY 22 T 5.400000E-03 5.400000E-03 N/A N/A NONE GPLY 33 T 5.400000E-03 5.400000E-03 N/A N/A NONE

Main Index

CHAPTER 8 285 Optimization

In the previous output, the number printed under the ‘PROPERTY ID’ column is the ID of PCOMPG. Exterior Acoustic Responses as Design Constraints A sample of sensitivity for exterior acoustic responses is shown as follows. The output is produced via the DSAPRT Case Control command.

**************************************************************************** * * * D E S I G N S E N S I T I V I T Y M A T R I X O U T P U T * * * * * * R E S P O N S E S E N S I T I V I T Y C O E F F I C I E N T S * * * **************************************************************************** ------------------------------------------------------------------------------------------------------------------------------DRESP1 ID= 5200 RESPONSE TYPE= ACPWR PANEL NAME= -TOTALSEID= 0 SUBCASE RESP VALUE FREQ/TIME DESIGN VARIABLE COEFFICIENT ------------------------------------------------------------------------------------------------------------------------------1 6.2096E-05 3.0000E+01 1 T1 -1.5862E-05 1 6.2140E-05 3.2000E+01 1 T1 -1.6007E-05 ------------------------------------------------------------------------------------------------------------------------------DRESP1 ID= 5300 RESPONSE TYPE= ACINTS GRID ID= 5 COMP NO= 0 SEID= 0 SUBCASE RESP VALUE FREQ/TIME DESIGN VARIABLE COEFFICIENT ------------------------------------------------------------------------------------------------------------------------------1 6.1866E-05 3.0000E+01 1 T1 -1.6807E-05 1 6.1936E-05 3.2000E+01 1 T1 -1.6807E-05 ------------------------------------------------------------------------------------------------------------------------------DRESP1 ID= 5501 RESPONSE TYPE= AFINTS GRID ID= 189 COMP NO= 1 SEID= 0 AFPM ID= 100 SUBCASE RESP VALUE FREQ/TIME DESIGN VARIABLE COEFFICIENT ------------------------------------------------------------------------------------------------------------------------------1 -2.1149E-07 3.0000E+01 1 T1 8.6521E-03 ------------------------------------------------------------------------------------------------------------------------------DRESP1 ID= 5600 RESPONSE TYPE= AFVELO GRID ID= 194 COMP NO= 11 SEID= 0 AFPM ID= 100 SUBCASE RESP VALUE FREQ/TIME DESIGN VARIABLE COEFFICIENT ------------------------------------------------------------------------------------------------------------------------------1 -7.0853E-05 3.0000E+01 1 T1 2.4374E-05 1 -5.8033E-05 3.2000E+01 1 T1 2.0518E-05 ------------------------------------------------------------------------------------------------------------------------------DRESP1 ID= 5700 RESPONSE TYPE= AFPWR GRID ID= 0 COMP NO= 0 SEID= 0 AFPM ID= 100 SUBCASE RESP VALUE FREQ/TIME DESIGN VARIABLE COEFFICIENT ------------------------------------------------------------------------------------------------------------------------------1 -1.0058E-03 3.0000E+01 1 T1 6.8219E-04 1 -9.9851E-04 3.2000E+01 1 T1 6.9616E-04

Fluid Modes as Design Constraints A sample of sensitivity for fluid mode responses is shown as follows. The output is produced via the DSAPRT Case Control command.

**************************************************************************** * * * D E S I G N S E N S I T I V I T Y M A T R I X O U T P U T * * * * * * R E S P O N S E S E N S I T I V I T Y C O E F F I C I E N T S * * * **************************************************************************** ------------------------------------------------------------------------------------------------------------------------------DRESP1 ID= 101 RESPONSE TYPE= FREQ MODE ID= 1 FLUID SEID= 0 SUBCASE RESP VALUE DESIGN VARIABLE COEFFICIENT ------------------------------------------------------------------------------------------------------------------------------1 8.6023E+01 1 T 1.4641E-01 ------------------------------------------------------------------------------------------------------------------------------DRESP1 ID= 102 RESPONSE TYPE= FREQ MODE ID= 2 FLUID SEID= 0 SUBCASE RESP VALUE DESIGN VARIABLE COEFFICIENT ------------------------------------------------------------------------------------------------------------------------------1 2.6020E+02 1 T 4.4286E-01

Main Index

286 MD Nastran R3 Release Guide Enhancements in SOL 200 Optimization

Objective Function Modification With DOPTPRM,OBJMOD,1, objective function modification algorithm is activated. A sample of objective function history is shown as follows. The output is available for all optimization jobs.

OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY --------------------------------------------------------------------------------------------------------------OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT -------------------------------------------------------------------------------------------------------------->>> OBJECTIVES in COLUMN 2/3 ARE INCREMENTAL TO OBJECTIVE OF ORIGINAL DESIGN = 1.0000E+05 <<< >>> ADD INCREMENTAL OBJECTIVE TO ORIGINAL TO ARRIVE AT REAL OBJECTIVE OF EACH CYCLE <<< --------------------------------------------------------------------------------------------------------------INITIAL

0.000000E+00

1.249923E+00

1

8.947921E-03

7.812500E-03

1.453339E-01

9.368142E-01

2

-1.010694E-02

-7.812500E-03

-2.936888E-01

1.003581E+00

3

-1.317651E-02

-1.562500E-02

1.567034E-01

3.951643E+00

4 -1.562500E-02 -1.562500E-02 0.000000E+00 3.951643E+00 ---------------------------------------------------------------------------------------------------------------

Guidelines • For type=GPLY, the recommended values for fields of DESVAR and DVPREL1 are

Bulk Data Entry

Field Name

Recommended Value

DESVAR

X0

1.0

DVPREL1

C0

0.0

DVPREL1

COEF1

1.0

• The design model for exterior acoustic must be part of main input file which is after the ‘BEGIN

BULK’ entry. Any design model entries placed after ‘BEGIN BULK AFPM=xxxx’ are ignored. • The effectiveness of DOPTPRM,OBJMOD,1 is not consistent. Hence, it is recommended only

for optimization problems that design just a tiny portion of the full structure.

Limitations • DVPREL2 must not be used to link design variable and properties of PCOMPG. • Properties associated with ‘MICRO’ feature of PCOMPG are not supported in SOL 200.

Example PCOMPG as Design Variables A simple file, d200pcg1, with multiple PCOMPG entries is utilized here to demonstrate the features implemented for PCOMPG support in SOL 200. Some key bulk data entries are shown as follows: $

Main Index

CHAPTER 8 287 Optimization

DESVAR $ DVPREL1 DVPREL1

1

T100000 1.00

0.01

1 1 2 1

GPLY 1.0 PCOMPG 0.0054

100000

T

12

T2

100.0

$ pcompg,12,,,5000.,hill,0.0,,, ,100000, 1, .0054, 45., yes, ,400000, 1, .0054, 90., yes, ,500000, 1, .0054, 90., yes, ,600000, 1, .0054, 0.0, yes ,700000, 1, .0054,-45., yes ,800000, 1, .0054, 45., yes pcompg,22,,,5000.,hill,0.0,,, ,100000, 1, .0054, 45., yes, ,300000, 1, .0054, 0.0, yes, ,400000, 1, .0054, 90., yes, ,500000, 1, .0054, 90., yes ,600000, 1, .0054, 0.0, yes ,800000, 1, .0054, 45., yes pcompg,33,,,5000.,hill,0.0,,, ,100000, 1, .0054, 45., yes, ,200000, 1, .0054,-45., yes, ,300000, 1, .0054, 0.0, yes, ,400000, 1, .0054, 90., yes ,500000, 1, .0054, 90., yes ,800000, 1, .0054, 45., yes $

DVPREL1,1 links the thickness of ply 100000 in PCOMPG 12, 22 and 33 to DESVAR,1 and DVPREL1,2 connects the thickness of PLY 400000 in PCOMPG,12 to DESVAR,1. Note that DVPREL1,2 uses the existing equation for relation between design variables and properties while DVPREL1,1 uses the new one shown in INPUT section. PCOMPG entries corresponding to the new design are shown as follows,

Main Index

288 MD Nastran R3 Release Guide Enhancements in SOL 200 Optimization

$ ************************************************************* $ * * $ * CONTINUOUS DESIGN CYCLE NUMBER = 4 * $ * * $ ************************************************************* $ $ $ UPDATED DESIGN MODEL DATA ENTRIES $ DESVAR * 1T100000 3.37500000E+00 9.99999978E-03+D *D 1V 1.00000000E+02 $ $ UPDATED ANALYSIS MODEL DATA ENTRIES $ PCOMPG* 12 0.00000000E+00 5.00000000E+03* * HILL 0.00000000E+00 0.00000000E+00 * * 100000 1 1.82250012E-02 4.50000000E+01* * YES * * 400000 1 1.82250012E-02 9.00000000E+01* * YES * * 500000 1 5.40000014E-03 9.00000000E+01* * YES * * 600000 1 5.40000014E-03 0.00000000E+00* * YES * * 700000 1 5.40000014E-03 -4.50000000E+01* * YES * * 800000 1 5.40000014E-03 4.50000000E+01* * YES PCOMPG* 22 0.00000000E+00 5.00000000E+03* * HILL 0.00000000E+00 0.00000000E+00 * * 100000 1 1.82250012E-02 4.50000000E+01* * YES * * 300000 1 5.40000014E-03 0.00000000E+00* * YES * * 400000 1 5.40000014E-03 9.00000000E+01* * YES * * 500000 1 5.40000014E-03 9.00000000E+01* * YES * * 600000 1 5.40000014E-03 0.00000000E+00* * YES * * 800000 1 5.40000014E-03 4.50000000E+01* * YES PCOMPG* 33 0.00000000E+00 5.00000000E+03* * HILL 0.00000000E+00 0.00000000E+00 * * 100000 1 1.82250012E-02 4.50000000E+01* * YES * * 200000 1 5.40000014E-03 -4.50000000E+01* * YES * * 300000 1 5.40000014E-03 0.00000000E+00* * YES * * 400000 1 5.40000014E-03 9.00000000E+01* * YES * * 500000 1 5.40000014E-03 9.00000000E+01* * YES * * 800000 1 5.40000014E-03 4.50000000E+01* * YES

1V

Exterior Acoustic as Design Constraints – TPL test file: d200exac.dat Portions of this example are shown in the preceding Sections Input, 281 and Output, 284. Fluid Modes as Design Constraints – TPL test file: d200fmd1.dat The output section shows results from this file.

Main Index

CHAPTER 8 289 Optimization

Objective Function Modification Test file, d200zobj, is used. The design model covers just a tiny portion of the structure. The original file produced following optimization history.

OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY --------------------------------------------------------------------------------------------------------------OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT --------------------------------------------------------------------------------------------------------------INITIAL

1.000000E+05

1.249923E+00

1

1.000000E+05

1.000000E+05

0.000000E+00

9.361193E-01

2

1.000000E+05

1.000000E+05

0.000000E+00

1.003858E+00

3

1.000000E+05

1.000000E+05

0.000000E+00

3.077129E+00

4 1.000000E+05 1.000000E+05 0.000000E+00 3.077129E+00 ---------------------------------------------------------------------------------------------------------------

From column 3 of the previous output, the change in objective function is not visible at all. The same output from d200zobj with DOPTPRM,OBJMOD,1 is shown as follows

OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY --------------------------------------------------------------------------------------------------------------OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT -------------------------------------------------------------------------------------------------------------->>> OBJECTIVES in COLUMN 2/3 ARE INCREMENTAL TO OBJECTIVE OF ORIGINAL DESIGN = 1.0000E+05 <<< >>> ADD INCREMENTAL OBJECTIVE TO ORIGINAL TO ARRIVE AT REAL OBJECTIVE OF EACH CYCLE <<< --------------------------------------------------------------------------------------------------------------INITIAL

0.000000E+00

1.249923E+00

1

8.947921E-03

7.812500E-03

1.453339E-01

9.368142E-01

2

-1.010694E-02

-7.812500E-03

-2.936888E-01

1.003581E+00

3

-1.317651E-02

-1.562500E-02

1.567034E-01

3.951643E+00

4 -1.562500E-02 -1.562500E-02 0.000000E+00 3.951643E+00 ---------------------------------------------------------------------------------------------------------------

Column 3 of the previous table shows the change of objective function. The original objective function value can be found on the first line bracketed by ‘>>>’ and ‘<<<’. Note that the change of objective function is 8 orders of magnitude smaller than the original objective function value.

Main Index

290 MD Nastran R3 Release Guide Optimization of Nonlinear Structural Responses (Pre-release)

Optimization of Nonlinear Structural Responses (Prerelease) Introduction MSC Software’s SOL 200 is a gradient-based multidisciplinary design optimization capability and has been widely used by clients in applying optimization techniques to linear structural analyses (Ref. 1.). Its success has led to the desire to extend these techniques to nonlinear structural analyses. Studies have been done to apply both gradient and non-gradient based approaches to the nonlinear structural analysis problems. The gradient approach involves design sensitivity analysis of nonlinear responses and mathematical programming. It provides accurate solutions but requires sensitivity calculations that are either too difficult in derivation, too expensive numerically or that become problematic due to the potential discontinuities in the responses as a function of design variables. Non-gradient based approaches often use Response Surface Methods to construct a surrogate model and the mathematical programming techniques are applied to the surrogate model (Refs.2.-7.). This approach is very general but is limited in the size of the design problems. An Equivalent Static Loads (ESL) based approach has been developed that transforms the original problem into an iterative solution of linear sub-optimization problems (Refs. 8.-10.). The most attractive attribute of this approach is that it shares the best features in gradient and non-gradient based approaches and avoids the disadvantages of each approach. Therefore, it is able to solve small- or large-scale problems more efficiently. Furthermore, the approach can be implemented with the existing highly developed nonlinear analysis (e.g., SOL 400) and linear response optimization software systems (e.g., SOL 200). However, its limitation is that it may not support general design statement due to limited support of nonlinear response and element types and nonlinear analysis disciplines because it requires that any supporting nonlinear response type must have the equivalent response type in the linear system. The new nonlinear response optimization capability in MD Nastran R3 (ESLNRO) is based on the ESL concept and implemented within SOL 400. This is the first attempt to introduce nonlinear response optimization capability into MD Nastran and the new capability will be a beta release. In this release, only nonlinear displacement and stress responses are supported. It is expected that more experience in ESLNRO applications will lead to future enhancements. The following describes the current status of the ESLNRO for MD Nastran R3. What is supported: • Analysis = NLSTATIC, RTYPE = DISP and STRESS, WEIGHT, VOLUME • DRESP2 • Geometry nonlinear (large displacement) • Material nonlinear

What is not supported: • Boundary nonlinear (contact) • Marc elements

Main Index

CHAPTER 8 291 Optimization

• TOPVAR, TOMVAR, BEADVAR • DVMREL1,2 and DVCREL1,2

Benefits • Enables design optimization tasks to include structural nonlinear responses • Leverages the existing linear multidisciplinary design optimization capability in SOL 200 • Is able to solve small- or large-scale nonlinear response optimization tasks

Theory Basic Optimization Statement A general nonlinear response optimization problem can be stated as follows:

Find:

X

Minimize:

F ( X, U N L )

Subject to:

g ( X, U N L ) < 0 XL < X < XU

ESLNRO The ESL based approach converts the above problem into an iterative solution of linear sub-optimization problems through use of Equivalent Static Loads (ESL). The essence of the approach can be described in Figure 8-7:

Main Index

292 MD Nastran R3 Release Guide Optimization of Nonlinear Structural Responses (Pre-release)

K ( X, U N L )U N L Z P

Pe q Z KL UN L

Nonlinear analysis

Transformation to ESL

ESLNRO Loop K L ( X )U L Z P e q

Find:

X

Minimize:

F ( X, U L )

Subject to:

K L ( X )U L Z P e q Allowable

Linear analysis with ESL

UL ≤ U Allowable σL ≤ σ σD L Z α ⋅ σ L, σ Z σ N L ⁄ σ L Notice U L Z U NL and σ L Z σ NL at start of linear response optimization

Linear response optimization (Inner Loop)

Figure 8-7 where subscript NL refers a nonlinear system,

Peq

equivalent static loads and L a linear system.

First, a nonlinear analysis is carried out. Next, the equivalent static loads (ESL) are computed from the nonlinear solutions. Then, the ESL is applied to a linear system and mathematical programming techniques are carried out on this linear system. The new design from the linear optimization is used to start a new ESLNRO loop. The process continues until the convergence criteria are satisfied. It is the ESL that establishes a platform to perform nonlinear response optimization without actually calculating the sensitivities of nonlinear responses. One key ingredient in the ESLNRO is the generation of the equivalent static loads. According to Ref. 8., for a particular nonlinear response, a required ESL should produce an equivalent and identical linear response at the start of the linear response optimization. The displacement-based ESL is computed by multiplying the linear stiffness matrix and nonlinear displacement solution and satisfies the requirement. For the stress-based ESL, Ref. 8. has used a more involved approach by solving an extra linear system with the nonlinear stress field as the initial condition without external loading. Then, the extra displacement solution is multiplied with the linear stiffness matrix to generate the stress-based ESL. Furthermore, a stress ratio scheme is introduced to ensure the linear stress filed will be identical to the nonlinear stress field. Notice that the ESLNRO in MD Nastran R3 directly uses the displacement-based ESL as the stress-based ESL to avoid the extra linear analysis. However, the stress ratio scheme is still applied to ensure that the linear stress responses are identical to the nonlinear stress response at the start of the linear response optimization.

Main Index

CHAPTER 8 293 Optimization

As shown in Figure 8-7, an ESL-based nonlinear response optimization task involves two types of loops. An inner loop (or a SOL 200 loop) is carried out in the linear response optimization and follows all the rules in a SOL 200 job. The ESLNRO loop is the outer loop that brings the nonlinear analysis and linear response optimization together. Like the inner loop carried out in SOL 200, the ESLNRO loop also has its own design move limit and the convergence criteria. Design Move Limits in ESLNRO In the ESLNRO, the actual nonlinear response optimization is solved by iterative solutions of linear suboptimization problems. Although the linear responses at the beginning of the linear system optimization are identical to the nonlinear responses, there is no guarantee that the nonlinear responses evaluated with the proposed design are the same as those linear response evaluated with the same design. The design proposed by a linear sub-optimization solution may be too aggressive to affect convergence negatively. Ref. 8. has proposed a scaled-back scheme to limit the design move at each design cycle. Its main idea is to scale back the design move proposed by a linear sub-problem solution: *

1

X k Z X k Ó 1 H ( X k Ó 1 Ó X k Ó 1 ) ⋅ DELXESL where

*

Xk

is the design variable for the k-th design cycle,

Xk Ó 1

is the design variable at (k-1)th design

cycle, X 1k Ó 1 is the proposed design from the linear optimization solution at (k-1)th design cycle and DELXES is the fractional change allowed in each design variable during the ESLNRO loop. An alternate to the scaled-back scheme is to limit the design move by posing more restrictive lower and upper bounds on each design variable. The following equations are used to update the design variable bounds. Subscript k indicates k-th design cycle, o indicates the initial design cycle, i indicates i-th design variable, L lower bound and U upper bound. The initial design variable bounds are those specified on the DESVAR entries and DXMIN is a DOPTPRM parameter and is the same parameter used in a SOL 200 run. Xk

L

= max ( X o , X i Ó MOVE )

L

Xk

U

= min ( X o , X i H MOVE )

MOVE

= max ( DXMIN,abs ( X i ) ⋅ DELXESL )

U

It has been found that each scheme is effective in certain applications. Therefore, a user selection is provided.

Main Index

294 MD Nastran R3 Release Guide Optimization of Nonlinear Structural Responses (Pre-release)

Convergence Criteria in ESLNRO An ESLNRO job will be terminated if either of the following conditions is met: 1. It reaches the maximum number of design cycle or 2. When the changes in each design variable between the current and previous design cycles must be less than a given tolerance and the requirement will further be satisfied in two consecutive design cycles.

Implementation The ESLNRO capability is implemented in MD Nastran environment with nonlinear solver SOL 400, a comprehensive and sophisticated nonlinear solution sequence that can deal with general applications with geometric, material and boundary nonlinearities (12-14). The design logic for ESLNRO is shown in Figure 8-8. Note that only a single user input file is required that specifies the nonlinear analysis model as well as the design model with its design variables and constraints. However, internally, a multiple Nastan invocation strategy is used to bring SOL 400 and SOL 200 together to provide an integrated solution to the design task. Specifically, a dashed frame as shown in Figure 8-8 forms the main ESLNRO loop in which the iterative solutions of linear sub-optimization problems are obtained through SOL 200 and SOL 400. The communication between the main driver, the SOL 400 and SOL 200 runs are established through various intermediate files. Outputs, 298 and Guidelines and Limitations, 279 will describe them and discuss how to manage these files.

Main Index

CHAPTER 8 295 Optimization

A User Submits a Single Input File (SOL 400 + Design Model)

ESLNRO loop

The single file is partitioned into two files: fn_nlsol400.dat and fn_eslsol200.dat k=0

Launch SOL 400 to perform nonlinear analysis

Generate Equivalent Static Loads

X(new)

Launch SOL 200 to perform a linear response optimization

Update Design Variable Bounds ΔDVi ≤ ξ?, i Z 1, ndv * or k > DSMXESL?

Yes

Create design history table and clean up files.

STOP

No, k=k+1

* This condition must be satisfied in two consecutive design cycles. Figure 8-8

Program Flowchart

Input In general, the required user input to perform an ESLNRO task is to add a design model definition to an existing SOL 400 job. The detailed description will be shown in Examples, 302. Here, several new types of input, that may be required to perform ESLNRO tasks are described. 1. Activation of ESLNRO To invoke ESLNRO, you are required to specify a Nastran ESLOPT statement.

Main Index

296 MD Nastran R3 Release Guide Optimization of Nonlinear Structural Responses (Pre-release)

System Cell Name (Number)

Function and Reference

ESLOPT (443)

Flag to invoke ESLNRO concept of Equivalent Static Loads 0 – No ESLNRO, default 1 – Turn on ESLNRO

Example, to activate ESLNRO, use Nastran ESLNRO = 1 or Nastran system(443) = 1 2. Control parameters for ESLNRO tasks New parameters, DELXESL and DSMXESL are added to the DOPTPRM entry. DELXESL is used to control how much a design variable can move during a ESLNRO design cycle while DSMXESL is the maximum allowable number of design cycles. Name

Description, Type, and Default Value

DELXESL

Fractional change allowed in each design variable during the ESLNRO loop (Real > 0.0, Default = 0.5)

DSMXESL

Maximum number of design cycles applied to the ESLNRO loop (Integer > 0, Default = 20).

3. Definition of designed properties Element property entries such as PBEAM, PROD, PSHELL and PTUBE can be specified on a DVPRELi entry. The associated nonlinear element types are: CBEAM(94), CONROD(92), CQUAD4(90), CQUADR(173), CROD(89), CTRIA3(88), CTRIAR(174), CTUBE(87). The property names on these entries that can be referenced on a DVPRELi entry shown in the following table: Property Entry

Property

PBEAM

(A(i), I1(i), I2(i), I12(i), J(i), NSM(i), C1(i), C2(i), D1(I), D2(i), E1(i), E2(i), F1(i), F2(i), (i=A, B, 1 ... 9)), K1, K2, S1, S2, (NSI(j), CW(j), M1(j), M2(j), N1(j), N2(j), j=A, B)

PROD

^I=gI=`I=kpj

PSHELL

T, 12I/T**3, TS/T, NSM, Z1, Z2 (The 12I/T**3 term can be designed but must be referenced by Field ID=6 rather than by name.)

PTUBE

OD, T, NSM

DVMRELi and DVCRELi entries are not supported.

Main Index

CHAPTER 8 297 Optimization

4. New input for defining nonlinear responses with a DRESP1 Bulk Data entry The displacement response is identified on a DRESP1 by RTYPE=DISP while the stress response is identified by RTYPE=STRESS. The same way to define a linear displacement response on a DRESP1 can be used to define a nonlinear displacement response. However, defining nonlinear stress response requires specifying a nonlinear stress item code on the ATTA field of a DRESP1 entry. These stress item codes can be found in Element Stress (or Strain) Item Codes (p. 877) in the MD Nastran Quick Reference Guide (Ref. 15.). For this release, the stress responses from the following nonlinear elements are supported: CONROD(92), BEAM(94), TUBE(87), QUAD4(90), TRIA3(88), QUADR(172), TRIAR(173), HEXA(93), PENTA(91), TETRA(85). In order to ensure to support the nonlinear stress responses that have the equivalent linear stress responses, the nonlinear element stresses are categorized into three groups: a. the stress having the same name and same meaning as those in the linear element stresses; b. the stress having the different name but having the same meaning; and c. the stress having the different name and different meaning. Only the stresses in groups 1 and 2 can be specified on a DRESP1 entry. The following lists the stresses from Groups 2 and 3 for supported nonlinear elements. For example, the Equivalent Stress is a group2 stress because it is equivalent to the von Mises stress in a linear element although their names are different. However, total strain, effective plastic strain and effective creep strain (as shown in bold) cannot be specified on a DRESP1 entry because they do not have linear equivalents. Nonlinear 1D element CONROD (92) (equivalent stress) (total strain, effective plastic strain, effective creep strain) Beam (94) (equivalent stress), (total strain, effective plastic strain, effective creep strain) Tube (87)

(equivalent stress) (total strain, effective plastic strain, effective creep strain)

Nonlinear 2D QUAD4 (90) (equivalent stress) (effective plastic strain, effective creep strain) TRIA3(88) (equivalent stress) (effective plastic strain, effective creep strain) QUADR(172) (equivalent stress) (effective plastic strain, effective creep strain) TRIAR(173) (equivalent stress) (effective plastic strain, effective creep strain) Nonlinear 3D Hexa (93) (effective stress), (effective plastic strain, effective creep strain) Penta (91) (effective stress), (effective plastic strain, effective creep strain) Tetra (85) (effective stress), (effective plastic strain, effective creep strain) 5. New Bulk Data Parameters Option to save ESLNRO intermediate files on disk PARAM,ESLFSAV,character string (character, Default = NO)

Main Index

298 MD Nastran R3 Release Guide Optimization of Nonlinear Structural Responses (Pre-release)

ESLFSAV = YES requests that all the intermediate files from an ESLNRO job be saved on disk. The destination of these files can be directed with the ‘sdir=’ option on a Nastran submittal command line. Selection of move limit schemes PARAM,ESLMOVE,Integer, Default = 0 ESLMOVE = 0 selects a move limit scheme that poses restrict lower and upper bounds on design variables during the linear response optimization. ESLMOVE = 1 selects a move limit scheme that scales back the design move proposed from a linear response optimization. User-supplied RC file PARAM,ESLRCF,filename (Char*8, must be lower case). Default = blank New Bulk Data parameter entry, PARAM,ESLRCF,filename allows the user-supplied RC file for the internally spawned jobs where filename is a character string up to 8 characters. Only lower case is supported. Example: PARAM,ESLRCF,myrc where myrc is the name of the user-supplied RC file with the following contents: MEM=200m EXE=~local_path/MDNASTRAN DEL=~local_path/SSS The example shows a user-supplied RC file that requests each spawned SOL 200 or SOL 400 job be run with memory allocation of 200 million words per run and with executable and delivery database. Option to save ESLNRO intermediate files on disk PARAM,ESLFSAV,character string (Character, Default = NO) ESLFSAV = YES requests that all the intermediate files from an ESLNRO job be saved on disk. The destination of these files can be directed with the ‘sdir=’ option on a Nastran submittal command line.

Outputs During the ESLNRO job, in addition to the primary Nastran result files (e.g., .f06, .f04 and log), files are generated internally for communications between the main driver and nonlinear analyses (SOL 400 run) and linear response optimizations (SOL 200 runs). These are temporary files and will be removed at the job’s completion by default. However, the user can use PARAM,ESLFSAV,YES to save them on the disk if necessary. These two types of files will be described using a user input file named deslo.dat.

Main Index

CHAPTER 8 299 Optimization

The Primary Nastran Result Files (deslo.f06, .f04, log, etc.) These are regular output files from a Nastran job and follow the Nastran naming conventions such as .f04, .f06 and log files. The .f06 file contains certain messages that are unique to an ESLNRO job. For example, the following information messages are printed in the .f06 file for each design cycle to provide a brief description of the ESLNRO process:

***************************************************** * * E S L N R O D E S I G N C Y C L E = 11 * * *****************************************************

* *

^^^ A NONLINEAR ANALYSIS JOB INITIATED WITH FOLLOWING COMMAND: /nast/md20071t1/linux64/nastran /scratch/./deslo_nlsol400 scr=yes bat=no rcf=my.rc out=/scratch/./deslo_nlsol400 ^^^ A NONLINEAR ANALYSIS JOB FOR THE ESLNRO COMPLETED. ^^^ A LINEAR OPTIMIZATION JOB INITIATED WITH FOLLOWING COMMAND: /nast/md20071t1/linux64/nastran /scratch/./deslo_eslsol200 scr=yes bat=no rcf=my.rc out=/scratch/./deslo_eslsol200 ^^^ A LINEAR OPTIMIZATION JOB FOR THE ESLNRO COMPLETED. ^^^ NO HARD CONVERGENCE IS ACHIEVED IN THE ESLNRO LOOP. JOB CONTINUES

If a nonlinear analysis job is unable to converge and is terminated at design cycle 11 in the ESLNRO loop, the following User Information Message 6464 will be printed out in the deslo.f06 file. In addition, the deslo.f06 will also include the additional information on the lack of convergence is printed in the regular SOL 400 .f06 file (not shown).

*** USER INFORMATION MESSAGE 6464 (DELSOPT) RUN TERMINATED DUE TO NONLINEAR ANALYSIS JOB UNABLE TO CONVERGE AT DESIGN CYCLE = 11.

In addition, for initial design cycle and final design cycle, the results from nonlinear analysis tasks and the optimization output data controlled by P1 and P2 on the DOPTPRM entry are always printed out in the .f06 file. However, no results output are printed in the .f06 file for the intermediate design cycles. At the end of the design cycle, a summary of design cycle history and design variable history are printed in the .f06 file. If you are familiar with a SOL 200 job, they look very much like the design history tables from an SOL 200 task. Here is the sample printout of the summary of design cycle history.

****************************************************************** S U M M A R Y O F D E S I G N C Y C L E H I S T O R Y ****************************************************************** (HARD CONVERGENCE ACHIEVED) NUMBER OF NONLINEAR FINITE ELEMENT ANALYSES COMPLETED NUMBER OF OPTIMIZATIONS W.R.T. LINEAR MODELS

38 37

OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY -----------------------------------------------------------------------------------------------------OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE LINEAR MODEL EXACT OF OF NUMBER OPTIMIZATION ANALYSIS LINEAR MODEL CONSTRAINT -----------------------------------------------------------------------------------------------------INITIAL 2.630691E-01 4.676274E-01 1 3.190933E-01 2.742739E-01 1.634111E-01 1.778786E-01

Main Index

300 MD Nastran R3 Release Guide Optimization of Nonlinear Structural Responses (Pre-release)

The Internally Spawned Files Two user input files, one for the SOL 400 run and one for the SOL 200 run are internally generated derived from the primary user input file: deslo_nlsol400.dat and deslo_eslsol200.dat. deslo is the name of the primary user input file and _nlsol400 and _eslsol200 are suffixes to distinguish a SOL 400 job from a SOL 200 job. Each has a unique Executive Control Section and a Case Control Section. Each file also has unique Bulk Data entries and shares a portion of common Bulk Data entries. Detailed descriptions of two user input files are as follows. Notice multiple INCLUDE entries are used to facilitate sharing common Bulk Data entries among two jobs, updating DESVAR entries or GRID entries for shape optimization at the end of each design cycle without the need to changing the actual input files. Description of a SOL 400 Input File (deslo_nlsol400.dat) SOL 400 CEND include '$sdir/deslo_nlsub.cas' $ = original subcase contents minus DESOBJ/DESSUB/DRSPAN BEGIN BULK include ‘$sdir/deslo_grid.blk' $ = all GRID entries. Original entries for initial design cycle and updated entries for design cycle>1. include ‘$sdir/deslo_desmod.blk' $ = all design model Bulk Data entries except DESVAR entries include ‘$sdir/deslo_desvar.blk' $ = all DESVAR entries include '$sdir/deslo_nlmat.blk' $ = nonlinear material entries such as MATS1, MATEP,MATF, NLPARM include '$sdir/deslo_loads.blk' $ = the original loading Bulk Data entries. include ‘$sdir/deslo_model’ $ = the remaining portion of the original Bulk Data entries ENDDATA Description of a SOL 200 Input File (deslo_eslsol200.dat) SOL 200 CEND include '$sdir/deslo_eslsub.cas' $ = ESL Subcases + DESOBJ/DESSUB/DRSPAN BEGIN BULK include ‘$sdir/deslo_grid.blk' $ = all GRID entries. Original entries for initial design cycle and updated entries for design cycle>1. include '$sdir/deslo_desmod.blk' $ = all design model entries except DESVARs include '$sdir/deslo_desvar.blk' $ = all DESVARs entries include ‘$sdir/deslo_esl’ $ = Equivalent Static Loads Bulk Data entries include ‘$sdir/deslo_model’ $ = the remaining portion of the original bulk data entries All the intermediate files are stored in the same Nastran scratch directory defined by environment variable $sdir. It could be reset on the Nastran command line with sdir=local-path-directory. If SCR option is set to Yes, they will be removed from the directory after the ESLNRO job is complete. If SCR is set to No, they will be saved in the directory.

Main Index

CHAPTER 8 301 Optimization

Descriptions of Individual Include Files deslo_nlsub.cas

This file contains the original contents of the Case Control Section used by a SOL 400 run.

deslo_eslsub.cas

This file defines SUBCASES that reference load cases corresponding to the same number of Equivalent Static Loads. It is generated by the SOL 400 run and will be used by a SOL 200 job.

deslo_desmod.blk

This file contains all the design entries except DESVAR entries and is used by both a SOL 200 job and a SOL 400 job.

deslo_desvar.blk

This file contains all the initial DESVAR entries for the initial design cycle. For design cycle > 1, it contains updated DESVAR entries. The file is used by both SOL 200 and SOL 400 runs.

deslo_grid.blk

The file contains all the initial GRID entries at the initial design cycle. For shape optimization it contains the updated GRID entries for design cycle > 1. It is used by both jobs.

deslo_loads.blk

The file contains the loads Bulk data entries from the original user input file. It is only used by a SOL 400 job.

deslo_esl.blk

The file contains the loads Bulk data entries for the Equivalent Static Loads. It is generated by a SOL 400 run at every design cycle and is only used by a SOL 200 job.

deslo_nlmat.blk

The file contains nonlinear analysis specific data such as nonlinear material entries that are supported by this project such as MATEP, MATF, MATS1 and NLPARM and is used only by SOL 400 job.

deslo_model

This file contains the remaining Bulk Data entries after the entries in deslo_grid.blk, deslo_nlmat.blk and deslo_desmod.blk, deslo_desvar, deslo_loads are excluded from the original Bulk Data Section and is used by both jobs.

Guidelines and Limitations • The current release of the ESLNRO capability supports nonlinear analyses with geometry and

material nonlinearities but not nonlinear boundary applications such contact problems. It is limited to static analysis with design constraints on displacements and element stresses. Both sizing and shape design variables are supported where sizing design variables are limited to the quantities that can be specified on a DVPRELi entry. Topology, Topometry and Topography are not supported. • To invoke the ESLNRO capability, set NASTRAN ESLOPT = 1 at the top of your input file.

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302 MD Nastran R3 Release Guide Optimization of Nonlinear Structural Responses (Pre-release)

• An ESLNRO job requires a single user input file consisting of a regular SOL 400 job and a

design model definition. Various intermediate files are generated from those separate SOL 400 and SOL 200 runs that perform nonlinear analysis and linear response optimization. You can use SDIR= option to redirect these files to your desired location. Use SCR=no if you want to keep them on the disk at the end of the job. • When you start an ESLNRO job, make sure the directory that will store the intermediate files

does not contain any intermediate files from the previous ESLNRO run. • You can specify your own RC file for these internally spawned SOL 200 or SOL 400 jobs using

PARAM,ESLRCF, RC_ File_Name to allocate more memory or for other purposes. • After an ESLNRO job is complete, a complete Bulk Data Section with updated element

properties entry or GRID and DESVAR entries for the last design cycle will be saved in the PCH file. In addition, the history of design objective, maximum constraints and design variables are also saved in the PCH file from which XY-Plots can be generated using spreadsheet program such as Microsoft Excel. • The capability is characterized as “pre-release” or “beta” because it is a new functionality that

requires considerable use and, perhaps, refinement to become a mature production tool. The user community is invited to exercise this capability and provide MSC with feedback as to its performance and usefulness.

Examples 10 Bar Truss (test library problem: deslo.dat)

50 GPa

200 GPa

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CHAPTER 8 303 Optimization

(cross sectional areas)

Find: Minimize:

Weight

Subject to:

σ j ≤ 220 MPa

(j = 1, ..., 10)

δ a l l ≤ 100.0 mm (both x and y directions of all nodes 2

78.5 mm ≤ X i ≤ 2826.0 mm

2

(i = 1, ..., 10)

This example demonstrates an ESLNRO optimization problem involving both geometric and material nonlinear behavior. The design task is to minimize the structural weight while maintaining nonlinear nodal displacements and element stresses within allowable limits. It is solved using MD Nastran R3. As stated above, SOL 400 and SOL 200 are combined in a single process for nonlinear analysis and linear response optimization. The optimizer in SOL 200 is MSCADS, a modified version of the ADS code (Ref. 1.). The job is terminated due to hard convergence to a feasible design. The following data compare the results between the initial design and the final design. Although both initial nonlinear displacement and stress constraints are violated, the final design is a feasible design. • Max Deflection:

Optimized: -99.85, Initial -146.76 (lower limit is -100.0)

• Max Axial Stress: Optimized: -218.26, Initial -283.99 (upper limit is 220.00) Figure 8-9 shows the design history where an ESLNRO design cycle represents a nonlinear analysis followed by a linear optimization task. Each linear optimization task typically has its own series of design cycles as in a standard SOL 200 run. The blue line is for weight while the red line is for the maximum constraint. It is seen that a feasible design is attained after 10 design cycles but that the weight continues to decrease so that ultimately 37 design cycles are performed. Even for this small problem, it should be obvious that the number of nonlinear analyses required to solve the problem are much fewer than would be required if a response surface method approach had been used.

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304 MD Nastran R3 Release Guide Optimization of Nonlinear Structural Responses (Pre-release)

Figure 8-9 Joined Wing A joined-wing model is used here to demonstrate the capability. It was provided to MSC by the Air Force Institute of Technology (Ref. 11.). The airplane has a half span of 38 meters and is operating under 11 load conditions that result in a maximum tip deflection of 20 meters.

Figure 8-10

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Joined-wing configuration

CHAPTER 8 305 Optimization

The optimization problem is formulated as: ( i Z 1, …2559 )

Find:

ti

to minimize:

Mass

subject to:

σ j ≤ σ allowable

( j Z 1, …, 2559 )

0.001016m ≤ t skin part ≤ 0.227m 0.000127m ≤ t tip wing part ≤ 0.227m 0.000254m ≤ t wing spars and ribs ≤ 0.227 m This problem is solved by MD Nastran. SOL 400 is used for nonlinear analysis. Figure 8-11shows the initial full scan displacement and the stress contour.

Initial Deflection Figure 8-11

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Initial Stress Contour

306 MD Nastran R3 Release Guide Optimization of Nonlinear Structural Responses (Pre-release)

Furthermore, a special snap over buckling behavior has been observed at approximate 50% load. See Figure 8-12.

∼ 50%

0% load

100% load

Figure 8-12 Again, SOL 200 is used for linear response optimization. The BIGDOT optimizer licensed from VR&D is used here to solve large scale linear response optimization problem. The following data compares the normalized results between the initial and final design. Figure 8-13 shows the final displacement and stress contour plots. • Max Deflection:

Optimized: 1.0, Initial: 5.96

• Max equivalent stress: Optimized: 1., Initial: 23.30 • Snap over buckling effect is eliminated

Optimized Deflection

Optimized Stress Contour

Figure 8-13 Figure 8-14 shows the history of the joined wing design. The blue line is for weight while the red line is for maximum constraint. The job converges at 36 design cycles with constrain value of 0.05. This is a fairly hard problem to solve considering it includes more than 2500 design variables and 2000 plus constraints. Here it shows that it is possible to design a joined-wing problem under large deformation with thousands of design variables and nonlinear stress constraints, something that is impossible to solve by the RSM approaches.

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CHAPTER 8 307 Optimization

Figure 8-14

References 1. MD Nastran R1 Design Sensitivity and Optimization User’s Guide, 2006. 2. Arora’s paper: Sensitivity Based Nonlinear Response Optimizations 3. G. E. P. Box and N. R. Draper, Empirical Model-Building and Response Surfaces, Wiley, New York, 1987. 4. R. H. Myers and D. C. Montgomery, “Response Surface Methodology: Process and Product Optimization Using Designed Experiments,” Wiley-Interscience, February 5, 2002. 5. W. J. Roux, N. Stander and R.T. Haftka, “Response Surface Approximations for Structural Optimization,” International Journal for Numerical Methods in Engineering, 42, 517{534 (1998) 6. N. Stander et al., “LS-OPT User’s Manual Design Optimization Software for the Engineering Analyst,” April, 2003 Version 2, Livermore Software Technology Corporation 7. H. Thomas, “NASOPT: A Flexible Optimization Capability for MSC/NASTRAN.’ Proceedings of the MSC User Conference, 1995 8. M.K. Shin, K.J. Park and G.J. Park, “Optimization of Structures with Nonlinear Behavior Using Equivalent Loads,” Computer Methods in Applied Mechanics and Engineering, 196 (2007) 1154–1167. 9. Y.I. Kim, G.J. Park, R.M. Kolonay, M. Blair and R.A. Canfield, “Nonlinear Response Structural Optimization of a Joined-Wing Using Equivalent Loads,” submitted to AIAA J. 10. W.S. Choi and G.J. Park (1999), "Transformation of Dynamic Loads into Equivalent Static Loads Based on Modal Analysis," International Journal for Numerical Methods in Engineering, August, Vol. 46, pp. 29-43.

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308 MD Nastran R3 Release Guide Optimization of Nonlinear Structural Responses (Pre-release)

11. C.C. Rasmussen, R.A. Canfield, M. Blair, “Joined-Wing Sensor-Craft Configuration Design,” 45th AIAA/ASME/AHS/ASC Structures, Structural Dynamics and Material Conference, 2004 (AIAA 2004-1760). 12. MD Nastran R1 Release Guide, 2006. 13. MD Nastran R2 Release Guide, 2007. 14. MD Nastran R3 Release Guide, 2008. 15. MD Nastran R3 Quick Reference Guide, 2008

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Chapter 9: Aeroelasticity and Rotor Dynamic Improvements

9

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MD Nastran R3 Release Guide

Aeroelasticity and Rotor Dynamic Improvements 

A New Aerodynamic Interpolation Method



External Spline Server



Blade Vibration Analysis

310 MD Nastran R3 Release Guide A New Aerodynamic Interpolation Method

A New Aerodynamic Interpolation Method Introduction Solution of the flutter equations entails interpolation to compute the aerodynamics at the exact reduced frequency of the flutter solution as a function of the aerodynamics that have been computed explicitly based on the ‘k’ (reduced frequency) values input on the MKAEROi entries. For many years, the available interpolation schemes have been adaptations of the beam and surface spline methods used in the splining of displacements and forces in aeroelasticity. Chapter 2.6 of the MSC Nastran Aeroelastic Analysis User’s Guide documents these methods. All of these methods perform their interpolation based only on the ‘k’ values and each term in the generalized aerodynamics matrix is weighted in the same way. For MD Nastran R3, an alternative interpolation is provided that interpolates each term in the generalized aerodynamic matrix individually.

Inputs The existing FLUTTER Bulk Data entry contains an IMETH field that allows the user to select between L (linear interpolation on k-only) and S (surface interpolation on Mach number and k) methods. Under this enhancement, an additional option (TCUB) has been provided to invoke a termwise cubic interpolation technique. For legacy purposes, if the FLUTTER entry has a METH field of “PK”, “PKNL”, “PKS” or “PKNLS” and the IMETH field is blank, S or L, the linear beam spline is used to interpolate the aerodynamics as a function of reduced frequency. If IMETH is TCUB, the termwise cubic spline technique is employed. Any other value of IMETH results in an error. If the flutter method is “K” or “KE”, IMETH=S selects a surface spline on Mach and reduced frequency and IMETH=L selects a linear method on reduced frequency and using the Mach number that is closest to the Mach number specified on the FLFACT entry. It is an error to select METH = “K” or “KE” and IMETH=”TCUB”

Outputs There are no new outputs as a result of this implementation.

Guidelines and Limitations The interpolation scheme involves determining weighting coefficients using cubic spline techniques based on the k values entered on the MKAEROi entries and the generalized aerodynamics computed at these k’s. During the PK flutter analysis, an estimate of the k value is made. The interpolation is then performed using: 3

2

1

Q i j ( k e s t ) Z Q i j ( k 0 ) H ( ( C i j ⋅ Δk H C i j ) ⋅ Δk H C i j ) ⋅ Δk

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CHAPTER 9 311 Aeroelasticity and Rotor Dynamic Improvements

where: Qi j

= A term in the generalized aerodynamic matrix. Real and imaginary terms are splined separately

ke s t

= k at which aerodynamics are required

k0

= largest k value from the MKAEROi input that is

k

=

1, 2, 3 C ij

< ke s t

ke s t Ó k o

= Interpolation coefficients determined using a cubic spline (1,2,3 are superscripts, not exponents.)

If only one k value is provided for the MKAEROi input, no interpolation is performed and the aerodynamics are invariant. If the k e s t value falls outside the range of k’s input using the MKAEROi entries, no extrapolation is performed. Instead, the aerodynamics at the lowest input k value are used if the desired k is lower than the input k’s and the aerodynamics at the highest input k value are used if the desired k is higher than any input k’s. For sensitivity analysis, it is necessary to provide the sensitivity of the aerodynamics due to a change in k . Differentiation of the equation above gives: dQ i j ( k e s t ) 3 2 1 JJJJJJJJJJJJJJJJJJJJJJJJJ J Z ( 3.0 ⋅ C i j ⋅ Δk H 2.0 ⋅ C i j ) ⋅ Δk H C i j dk If only one k value is provided of if the k e s t falls outside the range of MKAEROi values, the sensitivity is zero. A convenient way to check interpolation using the TCUB method with the beam spline method (IMETH=L) is to perform a flutter analysis with two subcases with the only difference being the IMETH value. The flutter summary results should be close, but not identical. DIAG 39 can be turned on around the FA1 module to provide debug data for the flutter analysis while DIAG 30 will print even more data. Turning DIAG 30 and DIAG 39 on around the DSFLTE module in the FLUTSENS dmap will provide information on the sensitivity analysis. It is cautioned that the output is particularly voluminous for the sensitivity diagnostics. IMETH=TCUB is only supported for the ‘PK’ method of flutter analysis and its variants, i.e., it is not supported for the ‘K’ and ‘KE’ methods.

Examples Two examples are available with the release demonstrating this new capability. The first is named csint.dat and is a variation of the simple HA145A example found in the MSC Nastran Aeroelasticity User’s Guide. An extra subcase has been provided that repeats the PK flutter analysis of the example

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312 MD Nastran R3 Release Guide A New Aerodynamic Interpolation Method

while setting IMETH to TCUB. A comparison of the flutter summary results for the two examples show virtually identical results. The second example is entitled cintopt.dat and is a variation of the HA200B example from the same User’s Guide. In this case, the flutter subcases have been converted from using the beam spline interpolation to using the new TCUB interpolation. Again, there is virtually no change in the results.

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CHAPTER 9 313 Aeroelasticity and Rotor Dynamic Improvements

External Spline Server Introduction The external spline evaluation capability that was introduced with MD Nastran R2.1 required that every term in the server-generated spline matrix be stored in memory. This limited the capability since very large, but very sparse, spline matrices would not fit into the available memory. With this release, the API was updated to allow the spline matrix to be stored in a sparse format. The fully-populated spline matrix format is still supported.

Inputs No changes were made to the Nastran input file or to how the external spline server is used.

API Changes The interface between Nastran and an external spline server was modified to support the sparse matrix format. Two changes were made to the calling sequence of the main spline server interface routine (sxsevd.c), they are noted in bold and a slightly larger font: void sxsevd ( INTEGER group_id, INTEGER spline_id, INTEGER *usage, INTEGER n_int_data, INTEGER *int_data, INTEGER n_real_data, MACHINEPRECISION *real_data, INTEGER n_char_data, INTEGER *char_data, INTEGER n_dep_grid, INTEGER *dep_grid_id, MACHINEPRECISION *dep_grid_xyz, INTEGER n_indep_grid, INTEGER *indep_grid_id, MACHINEPRECISION *indep_grid_xyz, INTEGER n_dep_elem, INTEGER *dep_elem, INTEGER n_indep_elem, INTEGER *indep_elem, char *command_line, char *connect_data,

INTEGER *ginfo, MACHINEPRECISION **gmat, INTEGER *error) {

/* /* /* /* /* /* /* /* /* /* /* /* /* /* /* /* /* /* /* /* /* /* /* /*

Group id */ Spline id */ Usage string (stored as hollerith) */ Number of integer data */ Integer data */ Number of real data */ Real data */ Number of character data */ Character data (stored as hollerith) */ Number of dependent grids */ Dependent grid ids */ Dependent grid x,y,z locations */ Number of independent grids */ Independent grid ids */ Independent grid x,y,z locations */ Number of dependent elements */ Dependent element table */ Number of independent elements */ Independent element table */ Optional command line argument */ Optional connect data */ Output information about the spline matrix */ The computed spline matrix */ Error code */

1. A new integer parameter called ginfo is now output. This variable stores the total number of nonzero terms in the spline matrix if it is stored in the sparse format. ginfo should have a value of zero if the spline matrix is stored in the fully-populated format.

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314 MD Nastran R3 Release Guide External Spline Server

2. Previous versions of Nastran allocated the memory for the spline matrix on the client (Nastran) side of the problem. With the new version, the client does not know if the server will be storing the spline matrix in the sparse or full formats. Therefore, it is now the server’s responsibility to allocate the memory to store the spline matrix. As a result of this change, the gmat variable, which was previously a pointer is now a pointer to a pointer.

Sparse Matrix Format If the sparse format is used to store the spline matrix, then the data must be stored in gmat in triplets of (row number, column number, value) for each nonzero term in the spline matrix: Row number for value 1 Collumn number for value 1 Value 1 Row number of value 2 Column number for value 2 Value 2

gmat Z

. . . Row number for value n Column number for value n Value n The ginfo variable must store the number of nonzero terms (n) in the spline matrix. The sparse gmat will store ( 3 × n ) numbers total.

Upgrading an Existing Spline Server This section provides one method for upgrading an MD Nastran R2.1 spline server to be compatible with R3. The experienced C programmer may wish to implement the changes differently. It will be assumed that the spline matrix will be stored in the fully-populated format. 1. Update the calling arguments of sxsevd.c to be exactly as listed above. 2. Declare a local variable to store the spline matrix: MACHINEPRECISION *server_gmat=NULL; 3. Set the value of ginfo: *ginfo = 0; 4. Allocate the memory to store the spline matrix.

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CHAPTER 9 315 Aeroelasticity and Rotor Dynamic Improvements

Blade Vibration Analysis In prior versions of Nastran; MD Nastran R2 and 2007 r1, special options were added to SOL 106 to support blade vibration analysis but were not documented in the MD Nastran Release Guide or MD Nastran Quick Reference Guide. The options are documented here for your convenience. • Frequency (Forced) Response Analysis - in addition to the current normal modes analysis in

SOL 106, the user can request a frequency response analysis. Both the normal modes and frequency response analysis are requested with a separate subcase followed by the Case Control commands ANALYSIS=MODES (Ch. 4) and ANALYSIS=DFREQ (Ch. 4) in the MD Nastran Quick Reference Guide. • “Hot-to-Cold” Analysis - allows the user to input the “stressed” or “hot” (deformed) geometry

using standard Bulk Data input and then “unload” the structure to determine the “unstressed” or “cold” shape. See the description of the Case Control command ANALYSIS=HOT2COLD (Ch. 4) in the MD Nastran Quick Reference Guide and user parameters HTOCITS (Ch. 5), HTOCPRT (Ch. 5), and HTOCTOL (Ch. 5) in the MD Nastran Quick Reference Guide. • Tangential Acceleration and Coriolis Follower Forces in Frequency Response Analysis - Include

the effects of the tangential acceleration and Coriolis follower forces in the nonlinear differential stiffness matrix to be used frequency (forced) response analysis. See the description of user parameter CORITAN (Ch. 5) in the MD Nastran Quick Reference Guide. These options enable the analyses of a rotating nonsymmetrical structure connected to a nonsymmetrical stationary structure. The rotating component will be assumed to be spinning at a constant rate. The procedure permits dynamic response calculations of the bypass fan, compressor, and turbine blades for aerojet engines. It also allows analyses of rotating wing aircraft. The methodology can also be used for dynamic response of the crankshaft/engine block of a reciprocating engine.

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316 MD Nastran R3 Release Guide Blade Vibration Analysis

Main Index

Chapter 10: SCA User Services

10

SCA User Services 

Main Index

MD Nastran R3 Release Guide

User Defined Services

318 MD Nastran R3 Release Guide SCA User Services

User Defined Services Introduction This new capability in MD Nastran gives you a mechanism to utilize your own subroutines or applications within a MD Nastran execution process. There are many benefits to this new feature, such as embedding proprietary element formulations, or extending MD Nastran element formulations that may not be flexible enough for a specific type of analysis. A specific case of this problem is when rotordynamics users would like to provide their own formulation of Squeeze Film Dampers in MD Nastran. In this version of MD Nastran, nonlinear force elements are equipped with an external implementation in the form of a User Defined Service.

Example The complete process of creating a user defined nonlinear force and incorporating it into MD Nastran is described in the User Defined Services User’s Guide. The example presented here demonstrates how an external implementation of a nonlinear force can be used in the same way as a built in MD Nastran nonlinear force. Below is a simple illustration of a MD Nastran model with the relevant information highlighted in bold. connect service mysub 'SCA.MDSolver.Util.UDS' $ id msc, rotnlt01.dat SOL senlharm $ CEND $ … $ BEGIN BULK $ … nlrsfd, 4001, 105, 205, YZ, 4.2, .95, .005, short, ,1.0e-6, 1.0, 1, 10., 180., , , 201, , , ,mysub,again ,1.0e3 … enddata

In order to identify the service, you have to create a connection between the service name and a service identifier. This is done through the connect statement in the FMS statement—highlighted in bold. The connect statement above takes the service “SCA.MDSolver.Util.UDS” and gives it a service-identifier name called “mysub”. Next, to associate the required NLRSFD entry in the model with the service identifier, we set the GROUP_NAME field to “mysub”. The presence of the GROUP_NAME on the NLRSFD Bulk Data entry triggers the call to the User Defined Service.

Main Index

CHAPTER 10 319 SCA User Services

The new NLRSFD entry is follows: NLRSFD

SID

GA

GB

PLANE

BDIA

BLEN

BCLR

SOLN

VISCO

PVAPCO

NPORT

PRES1

THETA1

PRES2

THETA2

NPNT

OFFFSET1

OFFSET2

GRPNAME

EVALNAME

PARM1

PARM2

PARM3

PARM4

PARM5

PARM6

PARM7

PARM8

You must of course have an implementation of the “SCA.MDSolver.Util.UDS” service based on the interface definition given below:

/******************************************************************************* Copyright (c) 2008, MSC.Software Corporation. All Rights Reserved. The skeleton for this file was generated by the MSC.Software SCA IDL compiler version 25.0 from 'test.sdl' This file contains the implementation for the service object 'Nlrsfd' *******************************************************************************/ #include "Nlrsfd.h" namespace Test { // Constructor Nlrsfd::Nlrsfd(SCAINlrsfdFactoryAccess* factoryAccess) : NlrsfdBase(factoryAccess) { } // Destructor Nlrsfd::~Nlrsfd() { } SCA::SCAResult Nlrsfd::runNlrsfd(const SCA::SCAInt32 sid,const SCA::SCAInt32 ga, const SCA::SCAInt32 gb,const SCA::SCAString plane, const SCA::SCAReal32 bdia,const SCA::SCAReal32 blen, const SCA::SCAReal32 bclr,const SCA::SCAString soln, const SCA::SCAReal32 visco,const SCA::SCAReal32 pvapco, const SCA::SCAInt32 nport,const SCA::SCAReal32 pres1, const SCA::SCAReal32 theta1,const SCA::SCAReal32 pres2, const SCA::SCAReal32 theta2,const SCA::SCAInt32 npnt, const SCA::SCAReal32 offset1,const SCA::SCAReal32 offset2, const SCA::SCAString evalname,const SCA::SCAReal32 time, const SCA::SCAReal64 xx,const SCA::SCAReal64 yy, const SCA::SCAReal64 xdt,const SCA::SCAReal64 ydt, const SCA::SCAReal64 xb,const SCA::SCAReal64 yb, const SCA::SCAReal64 xbt,const SCA::SCAReal64 ybt, SCA::SCAReal64& fx,SCA::SCAReal64& fy,SCA::SCAInt32& fuseit, SCA::SCAInt32& bisect,SCA::SCAReal32& parm1, SCA::SCAReal32& parm2,SCA::SCAReal32& parm3, SCA::SCAReal32& parm4,SCA::SCAReal32& parm5, SCA::SCAReal32& parm6,SCA::SCAReal32& parm7, SCA::SCAReal32& parm8,const SCA::SCAReal32 omega) { return SCA::SCASuccess; } }

To build the service, you will need MSC’s build environment which consists of a set of tools to compile and link all necessary files. You must also obtain the appropriate compiler and compiler version on the particular platform you are working on. The following table gives the list of appropriate compilers and options for various MD Nastran supported platforms.

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320 MD Nastran R3 Release Guide SCA User Services

Requirements Platforms HP (Intel IA-64)

HP (RISC PA2.0)

IBM (Power) Linux (Intel x86-32) Linux (Intel IA-64) Linux (Intel/AMD x86_64) SGI (MIPS) SUN (Sparc) SUN (x86-64) Windows (Intel x86-32)

OS Level HPUX 11.23

HPUX 11.00

AIX 5.1 RHEL 4 RedHat AS 3

Compiler Fortran

F90 2.8.7

C

A.05.44

C++

A.06.02

aC++

A.06.02

Fortran

F90 2.9.2.

C

B.11.11.16

C++

B.11.11.06

aC++

A.03.50

Fortran

XLF 8.1.1.4

C++

CC 6.0.0.7

Fortran

Intel 9.1.036

C++

Intel 9.1.043

Fortran

Intel 10.1.012

C++

Intel 10.1.012

RedHat RHEL 4.3 Fortran Irix64 6.5 Solaris 10 Solaris 10

Intel 9.1.043

Fortran

F90 7.4

C++

Cc 7.3

Fortran

F90 8.3

C++

CC 5.9

Fortran

F90 8.3

C++

CC 5.9

Windows 2000 sp4 Fortran Windows 2000 sp4 Fortran C++

Main Index

Intel 9.1.036

C++

C++ Windows (Intel x86-64)

Compiler Versions

Intel 9.1.024 Intel 9.1.022 Intel 9.1.024 Intel 9.1.022