# OS-V: 0470 Simply-Supported Thick Square Plate

Test 21OptiStruct is used to investigate the repeated eigenvalues and the effect of ‘secondary’ restraints.

## Model Files

Before you begin, copy the file(s) used in this problem
to your working directory.

## Benchmark Model

The 2nd order and 1st order quad elements are used to model the square plate of thickness 1.0 m. The z-rotation and x, y translations are fixed for all the nodes, z-translation is fixed along all four edges, x-rotation is fixed along the edge x = 0 and x = 10 and y-rotation is fixed along the edge y = 0 and y = 10.

The material properties are:

**Material Properties****Value**- Young’s Modulus
- 200 × 10
^{9}N/m^{2} - Poisson’s Ratio
- 0.3
- Density
- 8000 kg/m
^{3}

## Modal Analysis Results

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

`f*`

- Closed form solution

Mode 1 | Modes 2 and 3 | Mode 4 | |||
---|---|---|---|---|---|

`f*` |
45.897 Hz | `f*` |
109.44 Hz | `f*` |
167.89 Hz |

HOE | 1.013827837 | HOE | 1.044863043 | HOE | 1.046793653 |

LOE | 1.005851414 | LOE | 1.002363027 | LOE | 1.034589005 |

Modes 5 and 6 | Modes 7 and 8 | ||
---|---|---|---|

`f*` |
204.51 Hz | `f*` |
256.50 Hz |

HOE | 1.125821617 | HOE | 1.094829757 |

LOE | 0.993823531 | LOE | 1.051061511 |

## Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis