Problem in generalized thermoelasticity for a half-space subject to smooth heating of its boundary

The distribution of temperature, stress, and displacement in a homogeneous, isotropic solid occupying the half-space, and subjected to a smooth, time-dependent heating effect only at its bounding surface, is investigated. The problem is formulated in the context of generalized thermoelasticity with one relaxation time. The Laplace transform with respect to time is used to obtain the solution. Inversion of the resulting expressions is carried out using small values of time approximation as well as numerical inversion formulas. Numerical results for a particular case are given.