OS-V: 0465 Simply-Supported Thin Square Plate

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

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 0.05 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
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


NAFEMS R0015 - Selected benchmarks for natural frequency analysis