Enhanced single-layer variational formulation for transverse shear effects in laminated orthotropic beams and plates

A recently derived Reissner inspired mixed formulation technique has been used to present an alternative theory for modeling the important three-dimensional structural aspects of plates in a two-dimensional form. By integrating the classical Cauchy's equilibrium equations with respect to the thickness co-ordinate, and enforcing continuity of shear and normal stresses at each ply interface, condenses the effect of the thickness. Two coupled partial differential equations in two variables, transverse displacement and potential function are shown to condense to a single fourth order partial differential equation in transverse displacement subject to general loading. Shear deformation is captured by incorporating second order differential terms of the transverse pressure into the governing field equation with shear correction factors as coefficients. The theory degenerates to classical composite plate analysis for thin configurations. Significant deviations from classical plate theory are observed when the thickness becomes comparable with the in-plane dimensions.