Two-dimensional problem for a thick plate with axi-symmetric distribution in the theory of generalized thermoelastic diffusion

Abstract

In this work the problem of a thermoelastic thick plate that is of infinite extent and finite thickness with a permeating substance in contact with one of the bounding planes is considered in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The upper surface is taken to be traction free, subjected to a time-dependent thermal shock and the chemical potential, also assumed to be a known function of time. The lower surface of the plate is laid on a rigid foundation, which is thermally insulating. The Laplace and Hankel transform techniques are used. The analytical solution in the transform domain is obtained by using a direct approach. The inverse of the double transform is obtained by using a numerical method based on Fourier expansion techniques. The temperature, displacement, stress and concentration, as well as the chemical potential, are obtained. Numerical computations are carried out and represented graphically.