disable Displacement but not freedom of rotation

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Trexabyte
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disable Displacement but not freedom of rotation

Post by Trexabyte »

Dear Elmer specialists, I would like to do an eigenvalue simulation in Elmer. Before I can start the simulation, the examined geometry (plate) must be fixed at its four corners in such a way that no more shifts in the coordinate directions are possible. However, freedom of rotation around the axes must be retained.
My question is how to design the plate (the mesh of the plate) to realize an articulated support.
If you need more information, let me know.
Many thanks for your help!
kevinarden
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Re: disable Displacement but not freedom of rotation

Post by kevinarden »

You can use target nodes to restrain the corners. In a plate mesh it would just be 1 corner node at each corner. In a solid element mesh you would have to target the node at the midplane of each corner.

Boundary Condition 1
Target Nodes(4) = n1 n2 n3 n4
Displacement 1 = 0
Displacement 2 = 0
Displacement 3 = 0
end

where n1 n2 n3 n4 are the for corner node labels
corner_nodes.png
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raback
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Re: disable Displacement but not freedom of rotation

Post by raback »

Hi

Actually for eigen analysis you do not necessarily need to fix the rigid body motion for numerical reasons. It just means that you should regard the eigenmodes corresponding to the smallest eigenvalues (6 in 3D, 3 in 2D) as rigid body motions. Of course if you have real BCs they should be set.

-Peter
Trexabyte
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Re: disable Displacement but not freedom of rotation

Post by Trexabyte »

Thank you for the explanations! I was able to implement the boundary condition.
I designt the model so that the plate is articulated on all sides. For this I introduced the boundary condition 1. Im now wondering why the result is larger than it should be. The first 20 calculated eigenvalues are:


EigenSolve: 1: 1.403521E+06 0.000000E+00 -> 188,55 Hz
EigenSolve: 2: 5.556234E+06 0.000000E+00 -> 375,15 Hz
EigenSolve: 3: 1.178240E+07 0.000000E+00 -> 546,31 Hz
EigenSolve: 4: 1.805627E+07 0.000000E+00 -> 676,29 Hz
EigenSolve: 5: 2.193725E+07 0.000000E+00 -> 745,44 Hz
EigenSolve: 6: 4.536385E+07 0.000000E+00
EigenSolve: 7: 5.138703E+07 0.000000E+00
EigenSolve: 8: 5.338072E+07 0.000000E+00
EigenSolve: 9: 7.309379E+07 0.000000E+00
EigenSolve: 10: 8.999617E+07 0.000000E+00
EigenSolve: 11: 1.107895E+08 0.000000E+00
EigenSolve: 12: 1.197722E+08 0.000000E+00
EigenSolve: 13: 1.620869E+08 0.000000E+00
EigenSolve: 14: 1.655623E+08 0.000000E+00
EigenSolve: 15: 1.797881E+08 0.000000E+00
EigenSolve: 16: 1.979719E+08 0.000000E+00
EigenSolve: 17: 2.252866E+08 0.000000E+00
EigenSolve: 18: 2.525581E+08 0.000000E+00
EigenSolve: 19: 2.861556E+08 0.000000E+00
EigenSolve: 20: 3.016710E+08 0.000000E+00

but they should be:

1. -> 48,5 Hz
2. -> 97,5 Hz
3. -> 144,9 Hz
4. -> 179,1 Hz
5. -> 193,9 Hz
6. -> 275,5 Hz

My Solver-Sif-File looks like:

Header
CHECK KEYWORDS Warn
Mesh DB "." "."
Include Path ""
Results Directory ""
End

Simulation
Max Output Level = 5
Coordinate System = Cartesian
Coordinate Mapping(3) = 1 2 3
Simulation Type = Steady state
Steady State Max Iterations = 1
Output Intervals = 1
Timestepping Method = BDF
BDF Order = 1
Coordinate Scaling = 0.001
Solver Input File = case.sif
Post File = case.vtu
End

Constants
Gravity(4) = 0 -1 0 9.82
Stefan Boltzmann = 5.670374419e-08
Permittivity of Vacuum = 8.85418781e-12
Boltzmann Constant = 1.380649e-23
Unit Charge = 1.6021766e-19
End

Body 1
Target Bodies(1) = 1
Name = "Body 1"
Equation = 1
Material = 1
End

Solver 1
Equation = Linear elasticity
Procedure = "StressSolve" "StressSolver"
Eigen System Select = Smallest magnitude
Variable = -dofs 3 Displacement
Eigen Analysis = True
Eigen System Values = 20
Exec Solver = Always
Stabilize = True
Bubbles = False
Lumped Mass Matrix = False
Optimize Bandwidth = True
Steady State Convergence Tolerance = 1.0e-5
Nonlinear System Convergence Tolerance = 1.0e-7
Nonlinear System Max Iterations = 1
Nonlinear System Newton After Iterations = 3
Nonlinear System Newton After Tolerance = 1.0e-3
Nonlinear System Relaxation Factor = 1
Linear System Solver = Direct
Linear System Direct Method = Umfpack
End

Equation 1
Name = "Equation 1"
Active Solvers(1) = 1
End

Material 1
Name = "Aluminium (generic)"
Density = 2676.0
Heat expansion Coefficient = 23.1e-6
Poisson ratio = 0.33
Mesh Poisson ratio = 0.33
Heat Conductivity = 237.0
Sound speed = 5000.0
Heat Capacity = 897.0
Youngs modulus = 70.59e9
End

Boundary Condition 1
Target Nodes(156) = 10 11 7 3 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468
Displacement 1 = 0
Displacement 2 = 0
Displacement 3 = 0
end

Do you have any idea what mistake I might have made? The element size of my mesh is one sixth of a wavelenght.
Thank you very much for your help!
Greetings, Alex from Germany :)
kevinarden
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Joined: 25 Jan 2019, 01:28
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Re: disable Displacement but not freedom of rotation

Post by kevinarden »

High eigenvalues are generally due to mesh quality and element type. Linear triangles are poor for linear elastic regardless of mesh size. You can use
Element = "P:2"
in the solver section to use higher order elements to see if the eigenvalues come down.
Trexabyte
Posts: 5
Joined: 14 Sep 2022, 11:57
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Re: disable Displacement but not freedom of rotation

Post by Trexabyte »

you are absolutely amazing! Just modified and the results agree (approximately) with the analytical solution. Thanks very much! I will mention you in my draft. Best regards, Alex
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