Exact model for the response of moderately thick laminates to transverse forces

Abstract

Under the premise of homogeneous force, or curvature-gradient, distribution, a solution for transverse-shear strains and stresses, warping functions, and through-thickness displacements is derived by satisfying all relations and conditions of linear elasticity. Only for calculating the substitute-plate transverse-stiffness matrix the principle of the minimum of the total potential energy is used as a scheme for correctly combining energetically conjugate components of stresses and strains for the entries of the substitute-plate transverse stiffness matrix. The model is valid for all laminate and sandwich designs. The said premise renders the model a point theory rather than a structural theory, so that it is a complement to the classical theory of laminated plates in the sense of mapping substitute-plate properties and distribution of state variables through the laminate thickness. This paper explains the modeling ideas and derivations in detail. Predictions of the responses for a set of sample laminates of varying complexity, and comparison of stiffness values with those obtained by a dedicated FEM formulation, verify the model.