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

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
Young's Modulus
207 x 109 Pa
Poisson's Ratio

Linear Static Analysis Results

Model Hoop Stress


Radial Stress


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)

Model Files


The model file used in this problem includes:


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