ON SINGULAR INTEGRAL-EQUATIONS AND FUNDAMENTAL-SOLUTIONS OF POROELASTICITY

This paper presents a unified formulation of the various singular inte gral equations used in the boundary element methods (BEM) for the solu tion of linear, quasi-static, anisotropic poroelasticity. In particula r, a derivation is provided that connects the ''direct method'' with t he ''indirect methods''. The presentation begins with an alternative d erivative of the time and space dependent reciprocal integral. The Som igliana-type integral equations for the direct BEM are first construct ed. By summing integral equations representing an interior and an exte rior domain problem, the Somigliana (displacement discontinuity) and V olterra (stress discontinuity) type dislocation equations for indirect BEM are obtained. An extension to the edge dislocation method is disc ussed. These stress and displacement discontinuity equations are then combined to construct a symmetric Galerkin integral equation system. T hrough such construction, many intriguing connections among Green's fu nctions of fluid source, dipole, dilatation, fluid body force, total b ody force, and displacement discontinuity are revealed. Finally, a com plete compilation of fundamental solutions for the isotropic case is p rovided. (C) 1998 Elsevier Science Ltd. All rights reserved.