| A numerical procedure is developed to solve two dimensional nonsteady heat flow problems in an isotropic homogeneous medium. The general technique, known as the boundary integral method, is designed to deal with finite or infinite bodies of arbitrary shape for which general linear boundary conditions can be specified. The fundamental characteristic of the approach is the restriction of the unknown quantities to the boundary, so that from a numerical viewpoint the number of dimensions is effectively reduced by one.;The technique is extended by incorporating the calculation of the temperature induced stresses, strains and displacements into a general boundary integral framework. To ensure the satisfaction of mechanical boundary conditions, an isothermal elastic solution is superimposed, enabling the entire procedure to be used for the analysis of quasistatic thermoelastic effects in isotropic homogeneous solids. The methods are applied to some practical problems arising in the study of rock mechanics.;Several versions of the technique are implemented. These include direct and indirect formulations, using either an algorithm which treats time as an integral dimension, or one which proceeds in a sequential stepwise manner. The methods are validated on test problems for which exact solutions are available, and are evaluated according to their performance with respect to accuracy, stability and efficiency. An attempt is then made to identify the class of problems for which each is most suitable. |
