On the effect of transverse normal stresses inclusion in shearbased enhanced single-layer variational formulations for orthotropic beams

A recently derived Reissner inspired mixed formulation technique based on the effect of transverse shear stresses was used to present an alternative theory for modeling the important threedimensional structural aspects of plates in a two-dimensional form. In the present study, the effect of including normal transverse stresses is quantified. The model is enhanced 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. Two modified coupled partial differential equations in two variables, transverse displacement and bending moment are shown to condense to a single sixth order ordinary differential equation in transverse displacement subject to general loading. Transverse normal deformation is captured by incorporating second and fourth order differential terms of the transverse pressure into the governing field equation. Generalized shear correction factors are presented. The theory degenerates to classical composite plate analysis for thin configurations. Predominance of newly included terms is observed when the thickness becomes comparable with the span dimensions.