An Approximate Analysis of Stress Concentration around a Conical Hole in a Plate

Abstract

Elastic stresses of a thick plate under bi-axial uniform tension, weakened by a symmetrical conical hole, is considered. The solution consists of a linear combination of elastic solutions which satisfy always the boundary conditions on the upper and the lower surfaces of the plate. The coefficients of the linear combination are determined numerically to satisfy the boundary conditions on the surface of the conical hole by using the least square method repeatedly. By this method, the solution is obtained without solving a simultaneous equation. The circumferential stress on the conical surface is always tension and becomes maximum at the minimum diameter of the hole. This maximum stress varies in terms of the zenithal angle of the conical hole and the ratio of the minimum diameter of the hole to the thickness, but is always greater than the maximum stress of the plate with a circular hole.