LINE AND POINT LOADS ON A NON-HOMOGENEOUS INCOMPRESSIBLE ELASTIC HALF-SPACE

Abstract

Consider an elastic half-space which is made of an incompressible elastic material whose modulus is directly proportional to distance from the free surface. It is well known that when a quasi-static pressure, varying arbitrarily over the surface, is applied to the half-space, the normal component of displacement at the surface is everywhere directly proportional to the pressure: the half-space mimics a Winkler foundation. The aim of this paper is to explain this well-known result (and others, concerning the stress field within the half-space) by tackling the basic cases in which normal line and point loads are applied to the surface. The solutions turn out to be remarkably simple. All of the known results emerge from the study, together with a few new ones. In particular, we obtain a simple formula for the “Winkler stiffness” of the half-space when the material is anisotropic.