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 $σ_{y y}$ $σ_{y y}$ at the point A inside the cylinder on the y axis for linear static analysis.

Model Files

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

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

σ_{z z}

$σ_{z z}$ (-105 MPa).

	Direct Stress $σ_{z z}$ $σ_{z z}$ 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