OS-V: 0530 Composite Shell Bending
This problem discusses the composite shells two- or three-layer plate subjected to a sinusoidal distributed load, as described by Pagano (1969).
The resulting transverse shear and axial stresses through the thickness of the plate are compared to analytical solutions using classical laminated plate theory (CPT) and linear elasticity theory.
Model Files
Before you begin, copy the file(s) used in this problem
to your working directory.
Benchmark Model
Two models have been considered - composite plate with two and three-ply layers.
- For the two-layer model, the top layer is in 90° orientation and the bottom layer is in 0° orientation.
- For the three-layer model, the top and bottom layer are in 0° orientation and the middle ply is in 90° orientation.
The material properties are:
- Property
- Value
- E_{L}
- 25*10^{6} lb/in^{2} (172.4 GPa)
- E_{T}
- 1.0*10^{6} lb/in^{2} (6.90 GPa)
- G_{LT}
- 0.5*10^{6} lb/in^{2} (3.45 GPa)
- G_{TT}
- 0.2*10^{6} lb/in^{2} (0.2 GPa)
- V_{LT} = V_{TT}
- 0.25
Where,
- L
- Signifies the direction parallel to the fibers
- T
- Signifies the transverse direction
Limit stresses and limit strains used are:
Stress Value | X_{t} | X_{c} | Y_{t} | Y_{c} | S |
---|---|---|---|---|---|
GPa | 2.07*10^{-4} | -8.28*10^{-5} | 3.45*10^{-6} | -1.03*10^{-5} | 6.89*10^{-6} |
lb/in^{2} | 30.0 | -12.0 | 0.5 | -1.5 | 1.0 |
Results
For plate with S = 4:
Reference
Exact Solutions for Composite Laminates in Cylindrical Bending by N.J. Pagano, Washington University, St. Louis, MO (May 7, 1969)
Nonlinear finite element shell formulation accounting for large membrane strains by Thomas J.R. Hughes and Eric Carnoy, Stanford University (1982)