Thermoelastodynamic disturbances in a half-space under the action of a buried thermal/mechanical line source

The transient dynamic coupled-thermoelasticity problem of a half-space under the action of a buried thermal/mechanical source is analyzed here. This situation aims primarily at modeling underground explosions and impulsively applied heat loadings near a boundary. Also, the present basic analysis may yield the necessary field quantities required to apply the Boundary Element Method in more complicated thermoelastodynamic problems involving half-plane domains. A material response for the half-space predicted by Blot's thermoelasticity theory is assumed in an effort to give a formulation of the problem as general as possible (within the confines of a linear theory). The loading consists of a concentrated thermal source and a concentrated force (mechanical source) having arbitrary direction with respect to the halfplane surface. Both thermal and mechanical line sources are situated at the same location ina fixed distance from the surface. Plane-strain conditions are assumed tb prevail. Our problem can be viewed as a generalization of the classical Nakano-Lapwood-Garvin problem and its recent versions due to Payton (1968) and Tsai and Ma (1991). The initial/boundary; value problem is attacked with one- and two-sided Laplace transforms to suppress, respectively, the time variable and the horizontal space variable. A 9 x 9 system of linear equations arises in the double transformed domain and its exact solution is obtained by employing a program of symbolic manipulations. From this solution the two-si;led Laplace transform inversion is then obtained exactly through contour integration. The one-sided Laplace transform inversion for the vertical displacement at the surface is obtained here asymptotically for long times and numerically for short times, (C) 1999 Elsevier Science Ltd. All rights reserved.