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 at the point A inside the cylinder on the y axis for linear static analysis.



Figure 1.

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 (-105 MPa).
  Direct Stress σ z z MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadQhacaWG6baabeaaaaa@39E3@ 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

The model files used in this problem include:

<install_directory>/hwsolvers/demos/optistruct/verification
  • /LE11Hex20C.fem
  • /LE11Hex20F.fem
  • /LE11Pyr15C.fem
  • /LE11Pyr15F.fem
  • /LE11Tet10C.fem
  • /LE11Tet10F.fem

Reference

NAFEMS Ltd, The Standard NAFEMS BENCHMARKS TNSB Rev. 3, NAFEMS Ltd, Scottish Enterprise Technology Park, Whitworth Building, East Kilbride, Glasgow, United Kingdom, 1990.