Linear analysis of laminated composite plates using a higher-order shear deformation theory

A higher-order shear deformation theory is used to analyze laminated anisotropic composite plates for deflections, stresses, natural frequencies, and buckling loads. The theory accounts for parabolic distribution of the transverse shear stresses, satisfies the stress-free boundary conditions on the top and bottom planes of the plate, and, as a result, no shear correction coefficients are required. Even though the displacements vary cubically through the thickness, the theory has the same number of dependent unknowns as that of the first-order shear deformation theory of Whitney and Pagano.

Exact solutions for cross-ply and anti-symmetric angle-ply laminated plates with all edges simply-supported are presented. A finite element model is also developed to solve the partial differential equations of the theory. The finite element model is validated by comparing the finite element results with the exact solutions. When compared to the classical plate theory and the first-order shear deformation theory, the present theory, in general, predicts deflections, stresses, natural frequencies, and buckling loads closer to those predicted by the three dimensional elasticity theory.