Torsional traction on an open finite cylindrical cavity

Abstract

This paper deals with the stress analysis of an elastic half-space with an open cylindrical cavity of finite dimension subjected to torsional shear tractions. Within the classical theory of elasticity, the boundary value problem is formulated as a generalized Cauchy singular integral equation from which fractional-order singularities in the stress distribution near the bottom of the hole can be deduced. As an illustration, the fundamental solution corresponding to a torsional ring load acting on the sidewall of the cavity is presented. The resulting load-induced as well as shape-induced singularities in the response are examined.