# 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.

## Benchmark Model

Ply laminates are created using Quad4 elements for one quarter model of the cylinder. For Case 1 an internal pressure of 200MPa 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 × 105 MPa
$\upsilon$
0.3
α
2.0 × 10-5°C-1
Outer Cylinder (Circumferentially wound)
E1
1.3 × 105 MPa
$\upsilon$ 12
0.25
E2
5.0 × 103 MPa
α1

3.0 × 10-6°C-1

α2
2.0 × 10-5°C-1
G12
1.0 × 104 MPa
G33
5.0 × 103 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

## Model Files

The model files used in this problem include:
• compwtcq4c1.fem
• compwtcq4c2.fem

## Reference

NAFEMS R0031 - Composite Benchmarks, Hardy 2001