# 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.

## 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.

The material properties are:
MAT1 Isotropic
Young's Modulus
210 x 103 MPa
Poisson's Ratio
0.3
Coefficient of Thermal Expansion
2.3 x 10-4/°C

## Linear Static Analysis Results

All results are normalized with the target value ${\sigma }_{zz}$ (-105 MPa).
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

## Model Files

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

The model files used in this problem include:
• LE11Hex20C.fem
• LE11Hex20F.fem
• LE11Pyr15C.fem
• LE11Pyr15F.fem
• LE11Tet10C.fem
• LE11Tet10F.fem

## Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis