On the stresses in the neighbourhood of a circular hole in a strip under tension

Abstract

The problem of determining the stresses in a plate under tension when the material is pierced by one or more circular holes is one of both theoretical interest and practical importance. Provided that the plate may be regarded as infinitely extended in two dimensions, the solution for a single hole is easily found and is well known. The presence of the hole leads to the occurrence of stresses equal to three times the tension at infinity, these maximum stresses occurring at the edge of the hole and on the diameter perpendicular to the direction of the applied tension. More general stress systems, corresponding to the presence of tractions at the edge of the hole, may be studied by similar methods, not only when the plate is infinite but also when there is a second circular boundary concentric with the first. A number of special solutions for the infinite plate have recently been published by BICKLEY. The solution for a semi-infinite plate with one circular hole was obtained by JEFFREY, using bipolar co-ordinates,§ which may be applied also to the case of an infinite plate pierced by two holes