Nonlinear generalized thermoelasticity of an isotropic layer based on Lord-Shulman theory

TLDR: In this paper, two coupled partial differential equations, namely; the energy and equation of motion are established, which are then transformed into a dimensionless presentation and discretised via the generalized differential quadrature method.

Abstract: Thermoelastic analysis of an isotropic homogeneous layer within the framework of Lord-Shulman theory of generalized thermoelasticty is performed in this research. Two coupled partial differential equations, namely; the energy and equation of motion are established. The energy equation is kept in its original nonlinear form and the assumption made in previous investigations to linearize the energy equation is not established in the present work. The two coupled equations are presented in terms of axial displacement and temperature change. These equations are then transformed into a dimensionless presentation and discretised via the generalized differential quadrature method. The resulting equations are traced in time by means of the well-known β − Newmark time marching scheme and solved iteratively at each time step. After validating the proposed approach and solution method for the case of thermally linear, a set of parametric studies are carried out to explore the effects of thermal shock magnitude, relaxation time, and the coupling parameter. It is shown that thermally nonlinear theory governs when thermal shock is severe, relaxation time is large, or coupling parameter is large.