OS-V: 0200 Simply-Supported Thin Square Plate
Test No. 13OptiStruct is used to investigate the repeated eigenvalues.
Figure 1.
Benchmark Model
The 2nd order and 1st order quad elements are used to model the square plate of thickness 0.05m. The z-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x=0 and x=10 and y-rotation is fixed along the edge y=0 and y=10.
The material properties are:
- Young’s Modulus
- 200 x 109 N/m2
- Poisson’s Ratio
- 0.3
- Density
- 8000 kg/m3
Modal Analysis Results
The frequency of each targeted mode is normalized with the closed form solution.
f*- Closed form solution
| Mode 1 | Mode 2 and 3 | Mode 4 | |||
|---|---|---|---|---|---|
|
|
|
|||
f* |
2.377 Hz | f* |
5.942 Hz | f* |
9.507 Hz |
| HOE | 1.021926053 | HOE | 1.066977913 | HOE | 1.076061121 |
| LOE | 1.013646055 | LOE | 1.015552897 | LOE | 1.053290494 |
| Mode 5 and 6 | Mode 7 and 8 | ||
|---|---|---|---|
|
|
||
f* |
11.884 Hz | f* |
15.449 Hz |
| HOE | 1.176750173 | HOE | 1.175007606 |
| LOE | 1.002869198 | LOE | 1.065889334 |
Model Files
The model files used in this problem include:
<install_directory>/hwsolvers/demos/optistruct/verification
- Test13HOE.fem
- Test13LOE.fem
Reference
NAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish Enterprise Technology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.