On singular integral equations and fundamental solutions of poroelasticity

This paper presents a uni_ed formulation of the various singular integral equations used in the boundary element methods "BEM# for the solution of linear\ quasi!static\ anisotropic poroelasticity[ In particular\ a derivation is provided that connects the {{direct method|| with the {{indirect methods||[ The presentation begins with an alternative derivative of the time and space dependent reciprocal integral[ The Somigliana!type integral equations for the direct BEM are _rst constructed[ By summing integral equations representing an interior and an exterior domain prob! lem\ the Somigliana "displacement discontinuity# and Volterra "stress discontinuity# type dislocation equations for indirect BEM are obtained[ An extension to the edge dislocation method is discussed[ These stress and displacement discontinuity equations are then combined to construct a symmetric Galerkin integral equation system[ Through such construction\ many intriguing connections among Green|s functions of ~uid source\ dipole\ dilatation\ ~uid body force\ total body force\ and dis! placement discontinuity are revealed[ Finally\ a complete compilation of fundamental solutions for the isotropic case is provided[ 0887 Elsevier Science Ltd[ All rights reserved[