In-plane Strain and Stress Fields in Theories of Shearable Laminated Plates Subject to Transverse Loads

Abstract

The predictions of a new theory of orthotropic laminated plates are compared with those of two other theories equally based on a Reissner-Mindlin Ansatz for the displacement field, either layer by layer [5] or for the whole plate [4]. A well-known merit of such an Ansatz is to allow and account for transverse shearings. What we are after here is to determine how well in-plane strain and stress fields are described. For definiteness, we consider circular plates that are axi-symmetrically loaded, whose layers are made of transversely isotropic materials and are symmetrically located with respect to the midplane of the plate. The new theory allows for an explicit analytic solution of this problem, as the simpler of the two theories considered for comparison does, but shows an accuracy closer to the other more complex theory, whose governing equations we solve numerically; as a benchmark, we use a numerical solution of the corresponding three-dimensional equilibrium problem; the results of our comparison are summarized graphically in the final section. While the new theory allows for an explicit analytic solution of this simple problem, the governing equations of the other two theories are solved numerically; as a benchmark, we use a numerical solution of the corresponding three-dimensional equilibrium problem; the results of our comparison are summarized graphically in the final section.