OS-V: 0420 Free Thin Square Plate

Test No. FV12 A thin square plate model, which contains three rigid body modes. OptiStruct investigates the repeated eigenvalues and kinematically incomplete suppressions of the thin plate in Normal Modes Analysis.

Benchmark Model

The 4-node quad elements with 8x8 mesh configuration are used to model the plate. The x-translation, y-translation displacements and z-rotational displacements are fixed for all nodes.

The material properties are:

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. The closed form solution is not available for mode 10, use target value for H.O.E. instead.

f*: Closed form solution

Mode 4		Mode 5		Mode 6

`f*` CQUAD4	1.622 Hz 0.9964	`f*` CQUAD4	2.360 Hz 1.0145	`f*` CQUAD4	2.922 Hz 1.0231

Modes 7 and 8		Mode 9		Mode 10

`f*` CQUAD4	4.233 Hz 0.9978	`f*` CQUAD4	7.416 Hz 1.0496	F[HOE] CQUAD4	7.392 Hz 1.1746

Model Files

The model files used in this problem include:

<install_directory>/hwsolvers/demos/optistruct/verification/fv12.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.