Abstract
A new generalized thermoelasticity theory with time-delay is constructed. The Uniqueness theorem is proved and variational characterization of the solution is given, for a linear anisotropic and inhomogeneous thermoelastic solid. The governing coupled equations of this theory, with a kernel function that can be chosen freely according to the necessity of applications, are applied to one- dimensional problem of a half-space. The bounding surface is taken to be traction free and subjected to a time-dependent thermal shock. The Laplace transforms technique is utilized to obtain the general solution in a closed form. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusions about the new theory are given. The predictions of the theory are discussed and compared with the dynamic coupled theory.