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This test lets you check analysis results for a simply-supported thin square plate, in the context of a free frequency case. You will use 2D meshes. This test proposed by NAFEMS is used to validate the following attributes:
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Reference: NAFEMS-Glasgow, BENCHMARK newsletter, Report No. E1261/R002, February 1989, p.21. |
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Length: |
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Thickness: |
Young Modulus (material): |
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Poisson's Ratio (material): |
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Density: |
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Restraints (User-defined): Tx = Ty = Rz = 0
at all nodes |
You will find here the results for different finite elements:
Mode |
Reference frequency [Hz] |
Parabolic triangle shell (32 x 32 elements) |
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Frequency [Hz] |
Error [%] |
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1 |
2.377 |
2.377 |
0.013 |
2 |
5.942 |
5.943 |
0.019 |
3 |
5.942 |
5.943 |
0.021 |
4 |
9.507 |
9.516 |
0.095 |
5 |
11.884 |
11.882 |
0.013 |
6 |
11.884 |
11.883 |
0.010 |
7 |
15.449 |
15.467 |
0.118 |
8 |
15.449 |
15.469 |
0.126 |
To visualize the convergence of parabolic triangle shell
elements with other mesh refinements, click
here.
Mode |
Reference frequency [Hz] |
Linear triangle shell (64 x 64 elements) |
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Frequency [Hz] |
Error [%] |
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1 |
2.377 |
2.378 |
0.022 |
2 |
5.942 |
5.947 |
0.082 |
3 |
5.942 |
5.947 |
0.084 |
4 |
9.507 |
9.520 |
0.133 |
5 |
11.884 |
11.904 |
0.167 |
6 |
11.884 |
11.904 |
0.171 |
7 |
15.449 |
15.483 |
0.218 |
8 |
15.449 |
15.483 |
0.221 |
To visualize the convergence of linear triangle shell
elements with other mesh refinements, click
here.
Mode |
Reference frequency [Hz] |
Parabolic quadrangle shell (16 x 16 elements) |
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Frequency [Hz] |
Error [%] |
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1 |
2.377 |
2.376 |
0.022 |
2 |
5.942 |
5.940 |
0.026 |
3 |
5.942 |
5.940 |
0.026 |
4 |
9.507 |
9.503 |
0.038 |
5 |
11.884 |
11.880 |
0.034 |
6 |
11.884 |
11.880 |
0.034 |
7 |
15.449 |
15.442 |
0.049 |
8 |
15.449 |
15.442 |
0.049 |
To visualize the convergence of parabolic quadrangle shell elements with other mesh refinements, click here.
Mode |
Reference frequency [Hz] |
Linear quadrangle shell (32 x 32 elements) |
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Frequency [Hz] |
Error [%] |
||
1 |
2.377 |
2.378 |
0.030 |
2 |
5.942 |
5.954 |
0.203 |
3 |
5.942 |
5.954 |
0.203 |
4 |
9.507 |
9.523 |
0.171 |
5 |
11.884 |
11.952 |
0.568 |
6 |
11.884 |
11.952 |
0.568 |
7 |
15.449 |
15.510 |
0.392 |
8 |
15.449 |
15.510 |
0.392 |
To visualize the convergence of linear quadrangle shell elements with other mesh refinements, click here.
To Perform the Test:
The Free_vibrations_simply_Thin_Square_Plate.CATAnalysis document presents a complete analysis of this case, computed with a mesh formed of 16 elements per edge, and parabolic quadrangle elements (QD8).
To compute the case with other mesh sizes and element types, proceed as follow:
Open the CATAnalysis document.
In the Advanced Meshing Tools workbench, replace the mesh size and element type.
In the Generative Structural Analysis workbench, compute the case, and activate the image called Deformed mesh.