The Somigliana Ring Dislocation Revisited: 1. Papkovich potential solutions for dislocations in an infinite space

摘要

In this paper the Papkovich-Neuber potential function solutions are derived for circular Somigliana dislocations with Burgers vectors in the radial (edge dislocation) and axial (glide dislocation) directions. The solutions for each case are expressed in terms of a single harmonic function, given by a Lipschitz-Hankel type integral. The asymptotic behaviour of the stresses arising due to Somigliana dislocations in the vicinity of the dislocation line and a large distance away from it is derived. The advantages of the new technique compared with the original solution are discussed.