OS-V: 0210 Simply-Supported Thick Square Plate

Test 21OptiStruct is used to investigate the repeated eigenvalues and the effect of ‘secondary’ restrains.

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 1.0m. 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 × 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 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

Model Files


The model files used in this problem include:
  • Test21HOE.fem
  • Test21LOE.fem


NAFEMS R0015 - Selected benchmarks for natural frequency analysis