OS-V: 0470 Simply-Supported Thick Square Plate
Test 21OptiStruct is used to investigate the repeated eigenvalues and the effect of ‘secondary’ restraints.
Figure 1. FE Model with Boundary Conditions and Loadcases
Model Files
Before you begin, copy the file(s) used in this problem
to your working directory.
Benchmark Model
The 2nd order and 1st order quad elements are used to model the square plate of thickness 1.0 m. 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:
- Material Properties
- Value
- Young’s Modulus
- 200 × 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 | Modes 2 and 3 | Mode 4 | |||
|---|---|---|---|---|---|
|
|
|
|||
f* |
45.897 Hz | f* |
109.44 Hz | f* |
167.89 Hz |
| HOE | 1.013827837 | HOE | 1.044863043 | HOE | 1.046793653 |
| LOE | 1.005851414 | LOE | 1.002363027 | LOE | 1.034589005 |
| Modes 5 and 6 | Modes 7 and 8 | ||
|---|---|---|---|
|
|
||
f* |
204.51 Hz | f* |
256.50 Hz |
| HOE | 1.125821617 | HOE | 1.094829757 |
| LOE | 0.993823531 | LOE | 1.051061511 |
Reference
NAFEMS R0015 - Selected benchmarks for natural frequency analysis