Forces, Dislocations and Cracks

Abstract

In this chapter, we shall discuss the applications of two solutions which are singular at an interior point of a body, and which can be combined to give the stress field due to a concentrated force (the Kelvin solution) and a dislocation. Both solutions involve a singularity in stress with exponent −1 and are therefore inadmissable according to the criterion of §11.2.1. However, like the Flamant solution considered in Chapter 12, they can be used as Green’s functions to describe distributions, resulting in convolution integrals in which the singularity is integrated out. The Kelvin solution is also useful for describing the far field (i.e. the field a long way away from the loaded region) due to a force distributed over a small region.