Theory of images in plane-layered axisymmetric elastostatics

A fundamental theorem which automatically transforms the solution due to the presence of an arbitrary axisymmetric singularity in an unbounded homogeneous isotropic elastic solid into the corresponding solution for two perfectly bonded isotropic semi-infinite elastic solids is systematically applied in a stepwise fashion to obtain the complete image system when an arbitrary axisymmetric singularity is operative in or near a thick elastic layer which separates two other dissimilar isotropic semi-infinite elastic solids. The solution is closed and well structured. As an illustration, the distant effect in the interface layer produced by an influencing normal point force is luminously revealed to be two-dimensional, consisting of a combination at the origin of a bending hot spot and an infinite line of centres of dilatation. We conclude the paper with a complete theory of images for a free elastic layer under the influence of both axisymmetric and asymmetric singularities. We find that if the influencing displacement field is the gradient of a harmonic function, then the calculation of the induced elastic field reduces to the operation of differentiation only.