A Rigid Punch in Contact With a Nonhomogeneous Elastic Solid

Abstract

This paper treats the axisymmetric problem of a rigid punch in contact with a nonhomogeneous elastic isotropic solid whose modulus of rigidity is a continuous function of the depth while the other elastic parameter, Poisson’s ratio, is assumed to be constant. An integral transform solution is given which reduces the formulation of the problem to a Fredholm integral equation of the second kind which is amenable to numerical treatment. The physical quantities of interest are studied in detail and illustrative numerical results for several punch profiles are obtained and exhibited in tabulated and graphical form.