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.
Figure 1. Composite Shell Subjected to Uniformly Varying Sine
Load
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
EL
25*106 lb/in2 (172.4 GPa)
ET
1.0*106 lb/in2 (6.90 GPa)
GLT
0.5*106 lb/in2 (3.45 GPa)
GTT
0.2*106 lb/in2 (0.2 GPa)
VLT = VTT
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
Xt
Xc
Yt
Yc
S
GPa
2.07*10-4
-8.28*10-5
3.45*10-6
-1.03*10-5
6.89*10-6
lb/in2
30.0
-12.0
0.5
-1.5
1.0
Results
For plate with S = 4: Figure 2. Maximum Displacement versus Span to Thickness Ratio
of Two-layer 2nd Order Plate Figure 3. Axial Stress Distribution through the Thickness of
Two-layer 2nd Order Plate Figure 4. Transverse Shear Stress Distribution through the
Thickness of Two-layer 2nd Order Plate Figure 5. Maximum Displacement versus Span to Thickness Ratio
of Three-layer 1st Order Plate Figure 6. Axial Stress Distribution through the Thickness of
Three-layer 1st Order Plate Figure 7. Transverse Shear Stress Distribution through the
Thickness of Three-layer 1st Order Plate
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)
