3-D Elasticity Solutions of Layered Rectangular Plates Subjected to Thermo-Loads

Abstract

According to the exact three-dimensional (3D) thermoelasticity theory, the elasticity solution of the simply-supported layered rectangular plates subjected to steady temperature loads was studied. An analytical method was developed to solve the temperature, stress and displacement fields in the plate. Firstly, the general solutions of the temperature, displacements and stresses in a simply-supported isotropic layer were obtained by solving the 3-D heat conduction equation and the 3-D equations of elasticity respectively, which were expressed in the form of double Fourier series. Then, the temperature, displacement and stress relationships between the upper surface and the lower surface of the isotropic layer were derived. Based on the continuity of the temperature, the heat flux, the displacements and the stresses on the interface of two adjacent layers with different material properties, the recursive formulae of temperature, displacements and stresses between the bottom layer and the top layer of the layered plate were obtained by using the transfer matrix method. The unknown coefficients in the solutions for every layer were uniquely determined by the upper surface and lower surface conditions of the plate. The distributions of the temperature, displacements and stresses in the plate were given by substituting the unknown coefficients obtained back to the recurrence formulae and the solutions. The convergence of the solutions was checked with respect to the number of the terms of series. Comparing the results with those obtained from the finite element method, the correctness of the present method was verified. Finally, the effects of surface temperatures, plate thickness, layer number and material properties of each layer on the distributions of the temperature, displacements and stresses in the plates were discussed in detail.