Abstract
This paper deals with a new mathematical model of three-dimensional generalized thermoelasticity which has been improved using Lord–Shulman theory. The governing equations on non-dimensional forms have been applied to a three-dimensional half-space subjected to a rectangular moving heat source and traction-free surface by using the Laplace and double Fourier transform techniques. The inverses of the double Fourier and Laplace transforms have been calculated numerically by applying the complex formula of inversion of the transform by of the Fourier expansion method. The numerical results of the temperature increment, strain, stress, and displacement distributions have been represented in graphs for various values of the heat source speed parameter to show its effect on the thermo-mechanical waves. The heat source speed parameter leads to significant effects on both the thermal and mechanical waves.
Highlights
The difficulty in applications and in solving problems by using the mode of the Fourier transform is how the boundary conditions will be transformed
Because of the intricacy of the determining relations, it is very difficult to gain the exact solutions of thermoelasticity, and the numerical approach has been preferred lately with the advances in the information processing system software incorporating the boundary and finite element methods (Mesquita, Coda [11])
Youssef studied many models of a thermoelastic material subjected to moving heat source in the context of different theorems of generalized thermoelasticity (Youssef [23, 24])
Summary
The difficulty in applications and in solving problems by using the mode of the Fourier transform is how the boundary conditions will be transformed. Temel got the solutions by applying the numerical method of Durbin using the Laplace transform inversions in the real space (Temel et al [19]).
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