The basis for all calculations is classical laminated plate theory which can be found in a number of standard textbooks:

Composites Design Guide: Analytic Design Methods, Center for Composite Materials, Vol. 2, 1983.

Ashton, J. E., Halpin, J. C. and Petit, P. H., Primer on Composite Materials: Analysis, Technomic Publishing Co., Inc., Stamford, Connecticut, 1969.

Jones, R. M., Mechanics of Composite Materials, McGraw-Hill Book Company, New York, 1975.

Tsai, S. W. and Hahn, H. T., Introduction to Composite Materials, Technomic Publishing Co., Inc., Stamford, Connecticut, 1980.

Whitney, J. M., Daniel, I. M. and Pipes, R. B., Experimental Mechanics of Fiber Reinforced Composite Materials, Society for Experimental Stress Analysis, Monograph No. 4, Brookfield Center, CN,1982.


The basic assumptions of laminated plate theory require that each individual layer obey linear stress-strain relations and that an approximate state of plane stress exist within the laminate. The following assumptons are made with respect to the cartesian coordinate system shown in Figure 1, where the displacements in the x, y and z directions are denoted u, v and w:

1. The plate is constructed of an arbitrary number of layers of orthotropic sheets bonded together. However, the orthotropic axes of material symmetry of an individual layer need not coincide with the x-y axes of the plate.
2. The plate is thin, i.e., the thickness h is much smaller than the other physical dimensions.
3. The displacements u, v, and w are small compared to the plate thickness.
 

Figure 1. Coordinate System of Plate


4. In-plane strains are small compared to unity.
5. In order to include inplane force effects nonlinear terms in the equations of motion involving products of stresses and plate slopes are retained. All other nonlinear terms are neglected.
6. Transverse shear strains are negligible.
7. Tangential displacements u and v are linear functions of the z coordinate.
8. The transverse normal strain is negligible.
9. Each ply obeys Hooke's law.
10. The plate has constant thickness.
11. Rotary inertia terms are negligible.
12. There are no body forces.
13. Transverse shear stresses vanish on the surfaces z = ± h/2.

Lamination theory is appropriate for "thin laminates" in which strains vary linearly through the thickness and interlaminar deformations may be considered negligible at interior regions. Interlaminar stresses, however, do not vanish at geometric discontinuities such as free edges. This boundary layer phenomenon is a region where stress transfer between lamina is accomplished by interlaminar stresses, which violates the basic assumptions of lamination theory. A simple rule of thumb which defines interior regions where lamination theory is valid is that the boundary layer diminishes within one laminate thickness from the geometric discontinuity.
CREDITS

CONTENT AND ORGANIZATION
R. L. McCullough

COMPUTATIONAL ALGORITHMS
J. W. Gillespie, Jr

PROGRAMMING
Tae-Ki Kim

GRAPHICS & DESIGN
Brian Banks
Mark A. Deshon

CONTACT
J. W. Gillespie, Jr., Director

Center for Composite Materials
University of Delaware
Newark DE 19716

GILLESPIE@CCM.UDEL.EDU