2D problem for a half-space in the generalized theory of thermo-viscoelasticity

In this work, we consider a two-dimensional problem for a visco-elastic half-space. Laplace and exponential Fourier transforms are used to solve the problem. The solution in the transformed domain is obtained by a direct approach. The inverse Fourier transforms are obtained by using the inversion formula of the transform, while the inverse Laplace transforms are obtained using a numerical method. The temperature, displacement and stress distributions are computed and represented graphically.