OS-V: 0455 Simply-Supported Solid Square Plate

Test No. FV52 A well-established solid square plate, which contains three rigid modes with the given boundary condition. The test examines 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 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.

f*: Closed form solution.

Mode 4 Modes 5 and 6 Mode 7

Mode 4	Modes 5 and 6	Mode 7

`f*` HEXA20 HEXA8	45.897 Hz 0.9760 0.9874	`f*` HEXA20 HEXA8	109.44 Hz 1.0101 1.0413	`f*` HEXA20 HEXA8	265.81 Hz 1.0072 1.0322

f*

HEXA20

HEXA8

45.897 Hz

0.9760

0.9874

f*

HEXA20

HEXA8

109.44 Hz

1.0101

1.0413

f*

HEXA20

HEXA8

265.81 Hz

1.0072

1.0322

Mode 8 Modes 9 and 10

Mode 8	Modes 9 and 10

`f*` HEXA20 HEXA8	193.59 Hz 1.0017 1.0164	`f*` HEXA20 HEXA8	206.19 Hz 1.0022 1.0164

f*

HEXA20

HEXA8

193.59 Hz

1.0017

1.0164

f*

HEXA20

HEXA8

206.19 Hz

1.0022

1.0164

Model Files

The model files used in this example include:

<install_directory>/demos/hwsolvers/optistruct/verification

/fv52_HOE.fem
/fv52_LOE.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.