# OS-V: 0510 Wrapped Thick Cylinder

Test No: R0031/2 OptiStruct examines the hoop stress in the inner and outer cylinder at different radius for linear static analysis.

## Model Files

Before you begin, copy the file(s) used in this problem
to your working directory.

## Benchmark Model

Ply laminates are created using Quad4 elements for one quarter model of the cylinder. For Case 1 an internal pressure of 200 MPa is applied and for the Case 2 together with the internal pressure, a temperature rise of 130 °C is applied.

The material properties are:

**Inner Cylinder (Isotropic)**- E
- 2.1 × 10
^{5}MPa - $\upsilon $
- 0.3
- α
- 2.0 × 10
^{-5}°C^{-1}

**Outer Cylinder (Circumferentially wound)**- E
_{1} - 1.3 × 10
^{5}MPa -
$\upsilon $
_{12} - 0.25
- E
_{2} - 5.0 × 10
^{3}MPa - α
_{1} -
3.0 × 10

^{-6}°C^{-1} - α
_{2} - 2.0 × 10
^{-5}°C^{-1} - G
_{12} - 1.0 × 10
^{4}MPa - G
_{33} - 5.0 × 10
^{3}MPa

## Linear Static Analysis Results

Target (MPa) | OptiStruct Results (MPa) | Normalized with the Target Value | |
---|---|---|---|

Case 1: | |||

Hoop stress in inner cylinder at r = 23 | 1565.3 | 1659.4 | 0.94329276 |

Hoop stress in inner cylinder at r = 25 | 1429.7 | 1659.4 | 0.86157647 |

Hoop stress in outer cylinder at r = 25 | 874.7 | 792.6 | 1.10358314 |

Hoop stress in outer cylinder at r = 27 | 759.1 | 792.6 | 0.95773404 |

Case 2: | |||

Hoop stress in inner cylinder at r = 23 | 1381.0 | 1392.05 | 0.99206207 |

Hoop stress in inner cylinder at r = 25 | 1259.6 | 1392.05 | 0.90485256 |

Hoop stress in outer cylinder at r = 25 | 1056.0 | 1059.92 | 0.99630161 |

Hoop stress in outer cylinder at r = 27 | 936.1 | 1059.92 | 0.88317986 |

## Reference

NAFEMS R0031 - Composite Benchmarks, Hardy 2001