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Verification Problems
This manual presents solved verification models including NAFEMS problems.
NAFEMS Linear Elastic
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.

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Verification Problems
This manual presents solved verification models including NAFEMS problems.
- NAFEMS Linear Elastic
  - OS-V: 0010 Elliptic Membrane
    Test No. LE1 The model is a thin plate of thickness 0.1m subjected to a uniform pressure for linear static analysis. OptiStruct examines the direct stress $σ_{y y}$ at the point on inside the ellipse on the x-axis.
  - OS-V: 0020 Cylinder Shell Patch
    Test No. LE2 OptiStruct examines the outer surface tangential stress $θ - θ$ at point E for linear static analysis.
  - OS-V: 0030 Radial Point Load on a Hemisphere
    Test No. LE3 The model is a hemispherical shell subjected to concentrated radial loads at its free edges. It examines the performance of the three-dimensional shell to model local bending behavior under conditions where the deformations are primarily due to bending.
  - OS-V: 0040 Z-Section Cantilever
    Test No. LE5 OptiStruct examines the axial (x-x) stress (compression) at mid-surface, point A for linear static analysis.
  - OS-V: 0050 Skew Plate Normal Pressure
    Test No. LE6 OptiStruct examines the maximum principal stress on the lower surface at the plate center point E for linear static analysis.
  - OS-V: 0060 Thick Plate Pressure
    Test No. LE10 The model is a thick plate subjected to uniform normal pressure of 1 MPa on the upper surface of the plate. OptiStruct examines the direct stress $σ_{y y}$ at the point D for linear static analysis.
  - 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.
  - OS-V: 0080 Buckling of Shells and Composites with Offset
    A test of influence of offset on buckling solution for shells, including composite with offset Z0 and element offset ZOFFS.
  - OS-V: 0085 Plane Strain: Analysis of Pressure Vessel
    This problem examines the expansion of a pressure vessel due to an internal pressure.
- NAFEMS Thermo-elastic
- NAFEMS Heat Transfer
- NAFEMS Nonlinear Static Analysis
- NAFEMS Dynamic Response Analysis
- NAFEMS Random Response Analysis
- NAFEMS Normal Modes Analysis
- NAFEMS Composites
- Response Spectrum Analysis
- Elements
- Materials
- Fatigue Analysis
- Rotor Dynamics
- Frequency Response Analysis
- Explicit Dynamic Analysis
- Aeroelastic Analysis
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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_{z z}

(-105 MPa).


	Direct Stress $σ_{z z}$ 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