# OS-V: 0085 Plane Strain: Analysis of Pressure Vessel

This problem examines the expansion of a pressure vessel due to an internal pressure.

## Model Files

When running a CAE analysis, using the plane strain assumption can lead to considerable savings in computational time and file storage. The simplification to a 2D mesh allows you to use a finer mesh resulting in a more accurate analysis than a coarsely 3D meshed full model. A typical example of plane strain application is for the analysis of pressure vessels.

## Benchmark Model

Plane Strain elements are used to model the quarter symmetric slice of the pressure vessel with a radius of 100 mm and thickness of 20 mm. The internal pressure of 10 MPa is applied on the nodes of the inner surface of the pressure vessel and a Linear Static analysis is performed.

- The model must be in the XY or XZ plane, meaning for the XY plane all nodes must have Z coordinates equal to zero and for the XZ plane all Y coordinates are zero.
- All element normals are pointed in the positive Z or Y direction.
- CTPSTN and CQPSTN are used as the element property.
- PPLANE is used as the card image for the property.
- The 10 MPa load is applied using PLOADE1 type and selecting the internal edge of the model.

- ${\sigma}_{c}$
- Stress in circumferential direction (MPa, psi).
- ${\sigma}_{r}$
- Stress in radial direction (MPa, psi).
- ${p}_{i}$
- Internal pressure in the tube or cylinder (MPa, psi).
- ${p}_{o}$
- External pressure in the tube or cylinder (MPa, psi).
- ${r}_{i}$
- Internal radius of tube or cylinder (mm, in).
- ${r}_{o}$
- External radius of tube or cylinder (mm, in).
- $r$
- Cylinder wall radius where stress is calculated (mm, in) ( ${r}_{i}$ < $r$ < ${r}_{o}$ ).

## Linear Static Analysis Results

Model | Hoop Stress (Pa) |
Radial
Stress (Pa) |
---|---|---|

Theoretical | 55455 | -10000 |

OptiStruct | 54710 | -9205.6 |

Normalized | 1.013 | 1.086 |

^{1}

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