OS-V: 0200 Simply-Supported Thin Square Plate

Test No. 13OptiStruct is used to investigate the repeated eigenvalues.

図 1. FE Model with Boundary Conditions and Loadcases

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:
Material Properties
Young’s Modulus
200 x 109 N/m2
Poisson’s Ratio
8000 kg/m3

Modal Analysis Results

The frequency of each targeted mode is normalized with the closed form solution.
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:
  • Test13HOE.fem
  • Test13LOE.fem


NAFEMS R0015 - Selected benchmarks for natural frequency analysis