CV BEM for 2D transient thermo-(poro-) elastic problems concerning with blocky systems with singular points and lines of discontinuities

This paper presents a new method for solving transient 2D thermo-(poro-) elastic problems involving blocky systems with singular points and lines of discontinuity. The efficiency and accuracy of the method arise from using complex variables (CV) and solving a problem in two separate stages. In the first stage, CV-BEM is combined with the dual reciprocity method (DRM) for transient heat (liquid) flow to obtain, as a solution, the sum of (i) a “quasi-steady” part (which may account for discontinuities and singular points) and (ii) a smooth unsteady part which is a linear combination of smooth radial basis functions (RBF). These parts, found by integrating a system of ordinary differential equations, are stored in array, which contains values for each small integration step. From these arrays, data for selected time instances, which are of interest for thermo-(poro-) elastic analysis, are used in the second stage to find stresses and stress intensity factors (SIFs) at the instances of interest. The second stage solution employs CVH-BEM for blocky systems with discontinuities and singular points: a common code of the CVH-BEM is complemented with evaluation of two pairs of addends on the right hand side of the boundary integral equation solved; one of the addends is the sum of well-known terms for the “quasi-steady” part, while the other is a linear combination of particular solutions corresponding to a standard RBF. The particular solution needed is found for the Gaussian RBF in a simple analytical form by using the CV. The efficiency and accuracy of the method are illustrated by studying stresses and stress intensity factors in a square plate with a crack under thermal shock applied either to the plate sides, or to the crack surfaces. An interesting and not obvious effect is revealed: it appears that under thermal shock on the crack surfaces, the flux intensity factor is actually independent of the crack length for short time instances, which results in moderate stress intensity factors after the thermal shock.