OS-V: 0365 Simply-Supported Thin Square Plate Transient Forced Vibration Response

Test 13T OptiStruct is used to investigate the Peak Displacement in z-direction, the time at the peak displacement, extreme fiber bending stress at undamped Natural Frequency and the Static displacement at the center of the plate.



Figure 1.

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. A suddenly applied step load F0=100 N/m2 is induced in the z-direction. For modal analysis solution, a damping ratio of 0.02 is applied in all 16 modes at a time step of 0.002 secs and for direct solution, Rayleigh damping factor α1=0.299 and α2=1.339×10-3 at a time step of 0.002 secs are given.

The material properties are:
Young’s Modulus
200 × 109 N/m2
Poisson’s Ratio
0.3
Density
8000 kg/m3

Frequency Response Summary

The frequency of each targeted mode is normalized with the closed form solution.
f*
Closed form solution
  Peak Displacement (mm) Time at Peak Displacement (sec) Peak Stress (N/mm2) Static Displacement (mm)
Reference Solution 3.523 0.210 2.484 1.817
HOE:        
Direct Solution 3.637 0.212 2.784 1.832
Normalized 0.968655485 0.990566038 0.892241379 0.991812227
Modal Solution 3.643 0.210 2.820 1.832
Normalized 0.967060115 1 0.880851064 0.991812227
LOE:        
Direct Solution 3.465 0.210 2.244 1.780
Normalized 1.016738817 1 1.106951872 1.020786517
Modal Solution 3.454 0.214 2.203 1.779
Normalized 1.019976838 0.981308411 1.127553336 1.021360315

Model Files

The model files used in this problem include:

<install_directory>/hwsolvers/demos/optistruct/verification
  • /Test13THOED.fem
  • /Test13THOEM.fem
  • /Test13TLOED.fem
  • /Test13TLOEM.fem

Reference

NAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish Enterprise Technology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.