3-D Elasticity Solutions of Simply Supported Laminated Rectangular Plates in Uniform Temperature Field

Abstract

Based on the exact three dimensional (3-D) thermoelasticity theory, the elasticity solution of the simply supported laminated rectangular plates subjected to uniform temperature load is studied. An analytical method is presented to obtain the stress and displacement fields in the plate. First, the general solutions of a single-layer simply supported rectangular plate, which satisfies the governing differential equations and the boundary conditions at the lateral edges of the plate, is derived. Then, the displacement and stress relationships between the upper surface and the lower surface in the single-layer plate are obtained. According to the continuity of displacements, normal stress and shear stresses on the interface of two adjacent layers, the recursive formulae of displacements and stresses between the lowest layer and the top layer of the laminated plate are derived out by using the transfer matrix method. Finally, the unknown coefficients in the solutions are determined by the use of the upper surface and lower surface conditions of the plate. The distributions of displacements and stresses in the plate are obtained by substituting the unknown coefficients back to the recursive formulae and the solutions. The solutions obtained show excellent convergence. Comparing the numerical results with those obtained from the finite element method, the accuracy and correctness of the present method are demonstrated. Finally, the effects of temperature, thickness, layer number, and materials on the displacement and stress distributions of the plate are discussed in detail.