A Numerical Solution for an Axially Symmetric Contact Problem

Abstract

A numerical scheme for the axially symmetric contact problem of a plate pressed between two identical spheres is given. The axially symmetric contact stress distribution is represented by a finite set of pressure distributions linearly varying with the radius between values defined in a set of concentric circles. The normal displacements of the bodies in contact resulting from these pressure distributions are matched at every radius of the discrete set of radii of these circles. The integral equation for the unkown contact stress distribution is thus approximated by a set of linear algebraic equations whose solution yields the unknown pressure values of the approximate distribution. The contact radius, relative approach, and the maximum contact stress are then computed numerically from this solution and are presented in terms of the total load, the radius of the sphere, and the plate thickness.