Application of the multipole method to the problem on two close holes

We consider the plane elasticity problem on the interaction of two close identical holes under biaxial loading conditions at infinity. We study the stress state in the region of mutual interaction of the holes and near their contours. We propose a method for solving this problem on the basis of the representation of the jump displacement function as a sum of multipoles. Special attention is paid to the dependence of stress concentration on the parameters of the system of holes and its orientation with respect to the applied load. The stress fields are obtained for various locations of the holes. We also present the dependences of the maximum stress attained on the contour and the point of maximum stress concentration on the orientation of the pair of holes with respect to the external load.