An Integral Equation Formulation of~Three-Dimensional Inhomogeneity Problems

Abstract

A displacement integral equation formulation of three-dimensional infinite isotropic matrix with inhomogeneities of arbitrary shapes is derived based on the assumption that both the inhomogeneity and matrix have the same Poisson’s ratio. Compared to the conventional boundary integral equation formulation which requires both the tractions and displacements on the interface between the inhomogeneity and matrix, the present displacement integral formulation only contains the unknown interface displacements. Therefore, its numerical implementation can easily be carried out since the handling of corners in any irregular shaped inhomogeneity is avoided. Thus, through the interface discretization using quadrilateral boundary elements, the resulting system of equations can be formulated so that the interface displacements can be obtained. Stresses at any point of interest can also be obtained by using the corresponding stress integral equation formulation which contains only the inhomogeneity-matrix interface displacements. Numerical results from the present approach are in excellent agreement with existing ones.