# OS-V: 0010 Elliptic Membrane

Test No. LE1 The model is a thin plate of thickness 0.1m subjected to a uniform pressure for linear static analysis. OptiStruct examines the direct stress ${\sigma}_{yy}$ at the point on inside the ellipse on the x-axis.

## Benchmark Model

Second order Hexahedral, Penta, Tetra, Quad and Tria elements are used to create the coarse and fine mesh. A uniform outward pressure of 10 MPa is applied on the outer face. The pressure is converted to force and is applied to the nodes for Quad8 and Tria6 elements.

**Material Properties****Value**- Young's Modulus
- 210 x 10
^{3}MPa - Poisson's Ratio
- 0.3

## Linear Static Analysis Results

Direct Stress ${\sigma}_{yy}$ at Point D (MPa) | Normalized with the Target Value | |
---|---|---|

Solid Hexahedral: | ||

Hex8 coarse | 63.15 | 1.467933492 |

Hex20 coarse | 87.46 | 1.059913103 |

Hex8 fine | 79.8 | 1.161654135 |

Hex20 fine | 91.01 | 1.018569388 |

Solid Wedges: | ||

Penta6 coarse | 48.68 | 1.904272802 |

Penta15 coarse | 95.21 | 0.973637223 |

Penta6 fine | 67.3 | 1.377414562 |

Penta15 fine | 94.28 | 0.983241409 |

Solid Tetrahedral: | ||

Tetra4 coarse | 53.34 | 1.737907762 |

Tetra10 coarse | 95.96 | 0.966027511 |

Tetra4 fine | 66.56 | 1.392728365 |

Tetra10 fine | 95.28 | 0.972921914 |

Quad Shells: | ||

Quad4 coarse | 61.83 | 1.499272198 |

Quad8 coarse | 86.67 | 1.069574247 |

Quad4 fine | 79.7 | 1.163111669 |

Quad8 fine | 91.48 | 1.013336248 |

Triangular Shells: | ||

Tria3 coarse | 54.06 | 1.714761376 |

Tria6 coarse | 97.07 | 0.954980942 |

Tria3 fine | 74.21 | 1.249157795 |

Tria6 fine | 96.64 | 0.959230132 |

## Model Files

Refer to Access the Model Files to download the required model file(s).

- LE1Hex8C.fem
- LE1Hex20C.fem
- LE1Hex8F.fem
- LE1Hex20F.fem
- LE1Pen6C.fem
- LE1Pen15C.fem
- LE1Pen6F.fem
- LE1Pen15F.fem
- LE1Tet4C.fem
- LE1Tet10C.fem
- LE1Tet4F.fem
- LE1Tet10F.fem
- LE1Quad4C.fem
- LE1Quad8C.fem
- LE1Quad4F.fem
- LE1Quad8F.fem
- LE1Tria3C.fem
- LE1Tria6C.fem
- LE1Tria3F.fem
- LE1Tria6F.fem

## Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis