Asymptotic analysis of stresses in an isotropic linear elastic plane or half-plane weakened by a finite number of holes

Abstract

The problem of an isotropic linear elastic plane or half-plane weakened by a finite number of small holes is considered. The analysis is based on the complex potential method of Muskhelishvili as well as on the theory of compound asymptotic expansions by Maz’ya. An asymptotic expansion of the solution in terms of the relative hole radii is constructed. This expansion is asymptotically valid in the whole domain, i.e. both in the vicinity of the holes and in the far-field. The approach leads to closed-form approximations of the field variables and does not require any numerical approximation. Several examples of the interaction between holes or holes and an edge are presented.