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
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


NAFEMS R0015 - Selected benchmarks for natural frequency analysis