Numerical solution for elastic inclusion problems by domain integral equation with integration by means of radial basis functions

The unknown strains in the inclusions are expressed in terms of a series of radial basis functions (RBF) and polynomials in global coordinates. Based on the radial integration method proposed by Gao [J. Appl. Mech., Trans. ASME 69 (2002) 154, Engng Anal. Bound. Elem. 26 (2002) 905], the volume integrals for the evaluation of strains can be transformed into contour integrals on the inclusion boundaries. As a result of this transformation, there is no need to discretize the inclusions into finite elements. For the determination of the strains, collocation points are distributed at the interior of the inclusions to form a system of linear equations. Numerical results are compared with available analytical solutions and those based on a finite element discretization of the volume integrals.