Three-dimensional analytical elasticity solution for the mechanical analysis of arbitrarily-supported, cross and angle-ply composite plates under patch loads

Abstract

Patch-type discontinuous loads lead to highly localized stresses which are three-dimensional (3D) in nature and can initiate failures. Their accurate characterization is of primal importance for composite and sandwich structures. The present contribution elaborates a 3D analytical elasticity solution for the mechanical analysis of cross and angle-ply composite plates under transverse patch loads and arbitrary support conditions. For the solution, the Reissner-type, mixed variational principle is used to derive the governing equations. Analytical solutions are obtained using the multiterm, extended Kantorovich method, by dividing the plate into loaded and unloaded parts. The present analytical solution exactly satisfies inter-segment, inter-layer continuity and edge support conditions, treating stresses and displacements as primal variables. Its accuracy is established by direct comparisons with existing analytical – where available – and 3D finite element results, both for cross-ply and angle-ply designs, for different boundary conditions. Extensive analysis is performed to quantify the effect of thickness, angle-ply and patch load position on the composite mechanical performance. Through thickness stress asymmetries are identified and quantified, along with angle-ply designs that can smoothen stress concentrations in the vicinity of patch loads. The methodology can be used as a reference solution in the design of multilayer anisotropic plates under discontinuous loads.