OS-V: 0425 Clamped Thin Rhombic Plate

Test No. FV15 The behavior of distorted thin elements in normal modes analysis is examined using OptiStruct.

Benchmark Model

The 4-node quad elements with 12x12 mesh configuration are used to model the thin rhombic plate. The x-translation, y-translation displacements, and z-rotational displacements are fixed for all of the nodes. In addition, the z-translation, x-rotational and y-rotational are fixed for the nodes along the four edges.

The material properties are:

Property: Value
E: 200 x 10⁹ N/m²
$υ$: 0.3
$ρ$: 8000 kg/m³

Modal Analysis Results

The frequency of each targeted mode is normalized with the closed form solution. If a closed form solution is not available, the target values for H.O.E. are used instead. All benchmarked results are normalized with target values.

f*: Closed form solution

Mode 1		Mode 2		Mode 3

`f*` CQUAD4	7.938 Hz 0.9798	`f*` CQUAD4	12.835 Hz 1.0079	`f*` CQUAD4	17.941 Hz 1.0182

Mode 4		Mode 5		Mode 6

`f*` CQUAD4	19.133 Hz 0.9629	`f*` CQUAD4	24.009 Hz 1.0339	`f*` CQUAD4	27.922 Hz 1.0036

Model Files

The model file used in this problem includes:

<install_directory>/hwsolvers/demos/optistruct/verification/fv15.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.