Modal Analysis With Glued Contact

Chapter 25: Modal Analysis with Glued Contact

25

Modal Analysis with Glued Contact 

Summary



Introduction



Requested Solutions



FEM Solutions



Modeling Tips



Input File(s)



Video

454

448 449

449 454 454

449

448 MD Demonstration Problems CHAPTER 25

Summary Title

Chapter 25: Modal Analysis with Glued Contact

Contact features

• Glued Contact between two bodies with dissimilar meshes • Stress Free Projection • Contact tolerance bias factor = 0.0

Geometry

• • • •

Shroud outside diameter = 0.46 m Hub diameter = 0.26 m Width = 0.12 m Shroud thickness = 0.02 m

t

d2

d1

w

Material properties

9

E = 210 10 Pa ,  = 0.3 ,  = 7850kg  m 3

Linear elastic material Analysis type

Modal analysis using SOL 103

Boundary conditions

• Free-Free • Glued contact between vanes and shroud

Applied loads

None

Element type

• 8-node hexahedral elements • 10-node tetrahedral elements

FE results

Natural frequencies and mode shapes Mode Shape 7 @ 1,130 Hz

Mode Shape 8 @ 1,131 Hz

Mode Shape 9 @ 1,168 Hz

Mode Shape 10 @1,774 Hz

CHAPTER 25 449 Modal Analysis with Glued Contact

Introduction The shrouded vanes shown in Figure 25-1, consisting of twelve vanes with a central hub and an outer shroud, uses contact to join dissimilar meshes during a modal analysis. The hub and vanes contain higher-order tetrahedral elements while the shroud has linear hexahedral elements. The glued contact parameters preclude separation after initial contact and change the original coordinates of the nodes in contact to insure stress free contact between the dissimilar meshes.

Figure 25-1

Shrouded Vanes Model

Requested Solutions The modal analysis assumes free-free boundary conditions and returns ten natural frequencies and their associated mode shapes of which the lowest six correspond to rigid body motion.

FEM Solutions An eigenvalue analysis has been performed with MD Nastran’s SOL 103 for the element mesh shown in Figure 25-2. The vanes and the hub are modeled using higher order tetrahedral elements while the shroud is modeled using linear hexahedral elements. Contact body ID 1 is identified as all the elements making the vanes and hub whereas contact body ID 2 is identified as the elements making the shroud respectively as: BCBODY BSURF ...

1 1

3D 10000

DEFORM 10001

1 10002

0 10003

10004

10005

10006

2 2

3D 100000

DEFORM 100001

2 100002

0 100003

100004

100005

100006

and BCBODY BSURF ...

450 MD Demonstration Problems CHAPTER 25

Figure 25-2

FEA Mesh for the Shrouded Vanes Model

The BCTABLE entries shown below identify that these bodies are glued to each other: BCTABLE

BCTABLE

0 SLAVE

2 1 MASTERS 1 1 SLAVE 2 1 MASTERS 1

0. 1

1 0. 0

0.

0.

1

0. 1

1 0. 0

0.

0.

1

The BCTABLE option shows that contact body ID 2, the shroud, has been selected as the touching body, the SLAVE, whereas contact body ID 1, the vanes, has been selected as the touched body, the MASTERS. This selection is due to the fact the average element size for the vanes in the contact area is slightly larger than that of the shroud as shown in Figure 25-3. The IGLUE parameter of the BCTABLE option activates the glue option. The JGLUE parameter is turned off to ensure that no nodes separate once in contact. Additionally, the ICOORD parameter is turned on to modify the coordinates of the nodes in contact to ensure stress-free initial contact. The BCPARA entries activate the quadratic contact option and indicate that a bias factor of 0 (actually a small nonzero number of 1 x 10-16) has been selected: BCPARA 0 NBODIES 2 MAXENT IBSEP 2 BIAS 1.-16

13824

MAXNOD

18348

CHAPTER 25 451 Modal Analysis with Glued Contact

Figure 25-3

Relative Element Size Between the Shroud and Vanes in the Contact Area

The vanes and the shroud are both modeled using the same material. The material properties are isotropic and elastic with Young’s modulus, Poisson’s ratio, and density defined as $ Referenced Material Records $ Material Record : inner_mat $ Description of Material : MAT1 1 2.1+11 $ Material Record : outer_mat $ Description of Material : MAT1 2 2.1+11

.3

7.85+3

.3

7.85+3

The Lanczos procedure is selected for the real eigenvalue problem using the METHOD and EIGRL entries in which ten modes are desired: METHOD=13 ... EIGRL,13,,,10

The obtained modes are listed in Table 25-1. The first six modes are rigid body modes. Mode shapes 7 to 10 are shown in Figure 25-4. Table 25-1

Obtained Modes and Frequencies

Mode

Frequency (Hz)

1

6.911939E-04

2

6.290693E-04

3

4.908829E-04

4

4.434468E-04

5

2.943299E-04

6

7.051053E-05

452 MD Demonstration Problems CHAPTER 25

Table 25-1

Obtained Modes and Frequencies (continued)

Mode

Frequency (Hz)

7

1.130332E+03

8

1.131441E+03

9

1.168441E+03

10

1.774218E+03

Mode Shape 7 @ 1,130 Hz

Mode Shape 8 @ 1,131 Hz

Mode Shape 9 @ 1,168 Hz

Mode Shape 10 @1,774 Hz

Figure 25-4

Mode Shapes and Corresponding Frequencies

CHAPTER 25 453 Modal Analysis with Glued Contact

To check the efficacy of gluing dissimilar messes on natural frequencies, Test 53 (Selected Benchmarks for Natural Frequency Analysis, Abbassian, F, Dawswell, D J, and Knowles, N C, NAFEMS Ref R0015, 1987) was performed on glued mesh below. Title

Simply-Supported Solid Annular Plate, Axisymmetric Vibration

Contact features

Glued Contact between two bodies with dissimilar meshes Stress Free Projection

Geometry and Mesh Geometry

θ

A

R A o

α = 10

Z

4.2 m

0.6 m 1.6 m

Gluing Surface

Mesh

Material properties

9

E = 200 10 Pa ,  = 0.3 ,  = 8000kg  m 3

Linear elastic material Analysis type

Modal analysis using SOL 103

Boundary conditions

u = 0

Element type

10-node tetrahedral elements, 20-node hexahedral elements

for all nodes on axial planes of symmetry. u z = 0 along section AA

FE results fref

=

18.583 Hz

fref

fMD =

18.666 Hz

fMD = 140.03 Hz

z

= 140.15 Hz

fref

z

R

=

358.29 Hz

fref

=

629.19 Hz

fMD =

362.71 Hz

fMD =

658.97 Hz

R

R

Flexural Mode 5

R

Extensional Mode 3

z

Flexural Mode 4

224.56 Hz

R

Flexural Mode 2

z

224.16 Hz

r

Flexural Mode 1 fref

=

fMD =

454 MD Demonstration Problems CHAPTER 25

Modeling Tips Glued contact with no separation ensures that nodes do not separate once in contact. Stress-free initial contact modifies the coordinates of the nodes in contact to close any gaps between the two bodies. Quadratic contact allows midside nodes to participate in the glued contact. Insuring that the dissimilar meshes join properly requires there are no artificial stresses induced by nodes slightly off the contact surface, and the displacement field is completely continuous across the contact surface. This technique of “gluing” dissimilar meshes together facilitates faster model building by not requiring the meshes to be contiguous across all nodes. Furthermore, as in this application example, joining different element types assists modeling flexibility.

Input File(s) File

Description

nug_25_1.dat

Linear Hexahedral and Parabolic Tetrahedral Elements

nug_25_2.dat

Glued Annular Plates NAFEMS Test #53

Video Click on the image or caption below to view a streaming video of this problem; it lasts approximately two minutes and explains how the steps are performed.

Figure 25-5

Video of the Above Steps