Analytical solutions for the statics and dynamics of rectangular laminated composite plates using shearing deformation theories

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Virginia Polytechnic Institute and State University


The Levy-type analytical solutions in conjunction with the state-space concept are developed for symmetric laminated composite rectangular plates. Combinations of simply-supported, free and clamped boundary conditions are considered. The solutions are obtained for the first-order and higher-order theories in predicting the transverse deflections and stresses. Numerical results are presented for various boundary conditions, aspect ratios, lamination schemes and different loadings.

The developments of these theories accomplished in general coordinates allow one to fulfill both the invariance requirements and to derive the relevant equations in any convenient planar systems of coordinates.

The dynamic response problems are analyzed in the framework of higher order theories where the effects of transverse normal stress and rotary inertia forces are evaluated.

The comparison between the theories as well as previously reported results is reported.