Unified Geometrically Nonlinear Formulation of All Higher-order Shear Deformation Theories for Cross-ply Plates

Several higher-order shear deformation theories have been proposed for laminated plates, based on the expansions of displacements across the thickness, which are the same for all layers. In this study, a unified formulation of all higher-order theories is presented for cross-ply laminated plates based on polynomial expansions of displacements in the thickness coordinate z. It includes all the models available in literature. The governing equations for linear static and free vibfation response, and for buckling under inplane load are derived. The expressions for the stiffness matrix, inertia matrix, geometric stiffness matrix, and the load vector are developed for a simply supported rectangular plate using Navier's solution. A general purpose, single programme has been developed for all higher-order laminated plate theories