Green’s function for general cracked ring problems

Abstract

The two-dimensional elasticity problem of a circular ring or a hollow cylinder with a radial crack and subjected to arbitrary loads is considered. Using Muskhelishvili’s complex variable method, the dislocation solution is expressed in closed form. Dislocation pile-up and singular integral equation techniques may use the dislocation solution as a Green’s function to tackle general cracked ring problems. The circular ring with an internal edge crack and an embedded crack is analyzed. As an example, a ring containing a radial crack subjected to point loads is studied. Numerical procedures for calculating the stress intensity factors are presented.