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# Validation Case: Hollow Cylinder in Plane Strain Condition

This plane strain condition validation case belongs to solid mechanics. This test case aims to validate the following parameters:

• Distributed pressure
• Symmetry boundary condition
• Nodal displacement
• Strains and Nodal stresses

The simulation results from SimScale were compared to the analytical results presented in [SSLV04]$$^1$$.

## Geometry

The geometry used for the case is as follows:

The 3D geometry is a 45-degree section of a hollow cylinder with dimensions as tabulated below:

## Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Static linear

Mesh and Element Types: The meshes used in this project were created using the standard meshing tool on the SimScale platform. In Table 2 you will find a summary of the mesh characteristics.

Find below the manually refined 1st order standard mesh used in case A:

## Simulation Setup

Material:

• Steel (linear elastic)
• $$E$$ = 200 $$GPa$$, $$v$$ = 0.3

Boundary Conditions:

• Constraints
• Face EFE’F’ zero normal-displacement
• Face ABA’B’ zero y-displacement
• Face ABEF and face A’B’E’F’ zero z-displacements fixed
• The pressure of 60 $$MPa$$ on Face AEA’E’

## Reference Solution

The analytical solution is given by the equations presented under Reference Solution$$^1$$.

## Result Comparison

The results obtained from SimScale for displacements, stresses, and strains at point A are compared with those presented in SSLV04.

Find in Figure 3 below the case B results for the total strain $$\epsilon_{yy}$$ distributed across the cylinder:

Last updated: July 21st, 2021