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NAFEMS Linear Elastic
OS-V: 0085 Plane Strain: Analysis of Pressure Vessel
This problem examines the expansion of a pressure vessel due to an internal pressure. OptiStruct examines the principal stresses in the pressure vessel, due to the applied loading and boundary conditions.

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- 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. OptiStruct examines the principal stresses in the pressure vessel, due to the applied loading and boundary conditions.
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OS-V: 0085 Plane Strain: Analysis of Pressure Vessel

This problem examines the expansion of a pressure vessel due to an internal pressure. OptiStruct examines the principal stresses in the pressure vessel, due to the applied loading and boundary conditions.

Two-dimensional plane strain element will be used for this analysis.

図 1. FE Model of with Boundary Conditions and Loadcases

Model Files

開始前に、この問題で使用するファイルを作業ディレクトリにコピーしてください。

Pressure_Vessel_LS.fem

Benchmark Model

Quad4 Plane Strain elements are used to model the quarter symmetric slice of the pressure vessel of radius 0.1m and thickness 0.020m. Internal pressure of 10,000 Pa which is converted to force and applied on the nodes of the inner surface of the pressure vessel. A Linear Static analysis is performed on this model.

The material properties are:

Material Properties: Value
Young's Modulus: 207 x 10⁹ Pa
Poisson's Ratio: 0.27

Linear Static Analysis Results


Model	Hoop Stress (Pa)	Radial Stress (Pa)
Theoretical	55455	-10000
OptiStruct	54710	-9205.6
Normalized	1.013	1.086

図 2. First Principle Stress (Hoop Stress)

図 3. Third Principle Stress (Radial Stress)

¹

¹ MacDonald, Bryan J., "Practical Stress Analysis with Finite Elements" (2nd Ed), page 327-329