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