# OS-V: 0070 Solid Cylinder/Taper/Sphere - Temperature

Test No. LE11 The model is a thick solid cylinder subjected to linear temperature gradient in the radial and axial direction. OptiStruct examines the direct stress ${\sigma}_{yy}$ at the point A inside the cylinder on the y axis for linear static analysis.

## Model Files

## Benchmark Model

Second order Hexahedral, Penta and Tetra elements are used to create the coarse and fine mesh. A Linear temperature gradient of T°C = (x2 + y2)1/2 + z is applied in the radial and axial direction from the center of the cylinder. Only one quarter of the cylinder is considered.

**MAT1 Isotropic**- Young's Modulus
- 210 x 10
^{3}MPa - Poisson's Ratio
- 0.3
- Coefficient of Thermal Expansion
- 2.3 x 10
^{-4}/°C

## Linear Static Analysis Results

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

Solid Hexahedral: | ||

Hex20 coarse | -93.21 | 1.126488574 |

Hex20 fine | -99.12 | 1.059322034 |

Solid Wedges: | ||

Penta15 coarse | -100.3 | 1.046859422 |

Penta15 fine | -103.7 | 1.012536162 |

Solid Tetrahedral: | ||

Tetra10 coarse | -91.97 | 1.141676634 |

Tetra10 fine | -98.68 | 1.064045399 |

## Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis