OS-V: 0532 Laminated Shell Strength Analysis Mechanical Load 2
This problem analyzes the strength of laminated composite shells when subjected to a more general combination of membrane and bending load.
The model and boundary conditions are described by Hopkins (2005). The resulting ply failure indices, reserve factor and midplane strains are compared against analytical solutions from classical lamination theory (CLT). 5 The results indicate a good correlation between OptiStruct and CLT.
Benchmark Model
800 mesh elements of CQUAD4 element type were used in this study. The model is fixed at point A using a SPC card; a uniform longitudinal force per unit length (Nx) of 23.125 N/m, uniform transverse force per unit length (Ny) of 25.0 N/m and shear force per unit length (Nxy) of 5 N/m are applied using a FORCE card. Bending moments per unit length (Mx = 0.4 N and My = -0.75 N) and torsional load per unit length (Txy = -0.175 N) are applied along the edges of the laminate using a MOMENT card.
- Property
- Value
- Longitudinal Young’s Modulus, El (GPa)
- 207.0
- Transverse Young’s Modulus, Et (GPa)
- 7.6
- Longitudinal Shear Modulus, Glt (GPa)
- 5.0
- Major Poisson’s ratio, 12
- 0.3
- Longitudinal Tensile Strength, lt (MPa)
- 500.0
- Longitudinal Compressive Strength, lc (MPa)
- 350.0
- Transverse Tensile Strength, tt (MPa)
- 5.0
- Transverse Compressive Strength, tc (MPa)
- 75.0
- In-plane shear strength, lt (MPa)
- 35.0
Ply | Orientation (°) | Thickness ( m) |
---|---|---|
1 | 90.0 | 0.05 |
2 | -45.0 | 0.05 |
3 | 45.0 | 0.05 |
4 | 0.0 | 0.05 |
- Dimension
- Value
- Length (m)
- 0.2
- Breadth (m)
- 0.1
Results
Midplane Strains | Theory | OptiStruct Result |
---|---|---|
x | -1.732 x 10-3 | -1.732 x 10-3 |
y | -5.552 x 10-4 | -5.552 x 10-4 |
xy | -3.928 x 10-4 | -3.928 x 10-4 |
Failure Criteria | Ply 1 | Ply 2 | Ply 3 | Ply 4 | ||||
---|---|---|---|---|---|---|---|---|
Theory | OptiStruct Result | Theory | OptiStruct Result | Theory | OptiStruct Result | Theory | OptiStruct Result | |
Tsai-Wu | -2.35980 | -2.36000 | -2.54390 | -2.54400 | -1.90380 | -1.90400 | -1.13300 | -1.13300 |
Hill | 0.75736 | 0.75740 | 0.22681 | 0.22680 | 0.06410 | 0.06415 | 0.49058 | 0.49060 |
Hoffman | -2.68970 | -2.69000 | -2.35430 | -2.35400 | -1.80170 | -1.80200 | -1.30400 | -1.30400 |
Reserve Factor | Ply 1 | Ply 2 | Ply 3 | Ply 4 | ||||
---|---|---|---|---|---|---|---|---|
Theory | OptiStruct Result | Theory | OptiStruct Result | Theory | OptiStruct Result | Theory | OptiStruct Result | |
Tsai-Wu | 1.8527 | 1.853 | 4.0967 | 4.096 | 7.344 | 7.343 | 2.5661 | 2.566 |
Hill | 1.1491 | 1.149 | 2.0997 | 2.100 | 3.9483 | 3.948 | 1.4277 | 3.038 |
Hoffman | 2.0359 | 2.036 | 3.4277 | 3.428 | 5.6690 | 5.669 | 3.0381 | 1.428 |
This document addresses the verification of numerical results for the criteria and does not address the merits of a particular criteria. For details of particular failure criteria. 2 3 4
Model Files
The model files used in this problem include:
- /lssam2_tsai.fem
- /lssam2_hill.fem
- /lssam2_hoff.fem