Stresses in an elastic plane with periodic system of closely located holes

Abstract

By the method of singular integral equations, we study a two-dimensional periodic problem of the theory of elasticity for a plane with infinite collection of closely located curvilinear holes. Special attention is given to the unified approach to the solution of the problems of stress concentration near holes with sharp or rounded vertices. In this way, we obtain the solutions of the problems of elastic interaction of elliptic, oval, and rhombic holes and physical flaws for arbitrary distances between the holes. By passing to the limit as the distance between the boundary contours tends to zero, we determine the stress concentration and stress intensity factors at the rounded and sharp tips of the corresponding bilateral notches in the elastic plane.