# 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:
Property
Value
E
200 x 109 N/m2
$\upsilon$
0.3
$\rho$
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
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
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 problem include:
• fv52_HOE.fem
• fv52_LOE.fem

## Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis