Problems of the concentration of elastic stresses near a conical defect

Abstract

A method of reducing non-axisymmetric problems of the concentration of stresses near a conical crack or thin conical inclusion in the form of a conical shell to a system of one-dimensional integro-differential equations is proposed. For the case where there is torsion of the elastic medium, the exact solution of the corresponding integro-differential equation is obtained. A method of computing the quadratures (including singular quadratures) to which these problems reduce is given. There is a fundamental difference between this, method and those proposed in [1, 2], in which special cases are considered in an axisymmetric formulation.