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. FE Model with Boundary Conditions and Loadcases


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 zz MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadQhacaWG6baabeaaaaa@39E3@ (-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

Reference

NAFEMS R0015 - Selected benchmarks for natural frequency analysis