Application of the multipole expansion method to evaluation of the stress state of an infinite elastic plane containing several circular holes

The 2D-elasticity problem of several closely-spaced circular holes in an infinite plane under biaxial loading at infinity is considered. The solution of the problem is found using the method of multipole decomposition, which is based on the representation of the jump displacement function as a sum of multipoles. Different arrangements of holes and their configurations are considered. The stress state in the region of mutual interaction of holes and near their contours is obtained. Special attention is given to the stress concentration around the holes. The points and magnitudes of stress concentration are determined and compared with those obtained around a single hole under the same loading conditions.