Simply-Supported Solid Square Plate

NAFEMS Benchmark, Test No. FV52:

$image\fv52.gif$

Summary

Test No. FV52 is a well-established solid square plate, which contains 3 rigid modes with the given boundary condition. The test is used to examine the performance of OptiStruct normal modes analysis on 3D solid elements.

Benchmark Model

The HEXA 8-node and HEXA 20-node solid elements are used in test FV52. An 8x8x3 mesh configuration is used for HEXA 8-node elements, and a 4x4x1 mesh configuration is used with HEXA 20-node elements. The z-directional displacement is constrained at Z = -5m plane along the four edges of the plate. The material properties for the solid plate are: $image\evp.gif$ .

Modal Analysis Results

The frequency of each targeted mode is normalized with the closed form solution.

f* = closed form solution

Mode 4		Modes 5 & 6		Mode 7
$image\fv52a_high.gif$		$image\fv52b_high.gif$		$image\fv52c_high.gif$
f* HEXA20 HEXA8	45.897 Hz 0.9760 0.9874	f* HEXA20 HEXA8	109.44 Hz 1.0101 1.0413	f* HEXA20 HEXA8	167.89 Hz 1.0072 1.0322

Mode 8		Modes 9 & 10
$image\fv52d_high.gif$		$image\fv52e_high.gif$
f* HEXA20 HEXA8	193.59 Hz 1.0017 1.0164	f* HEXA20 HEXA8	206.19 Hz 1.0022 1.0164

Reference

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

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