The Surface Displacement of an Elastic Half-space Loaded in a Slender, Bounded, Curved Surface Region with Application to the Calculation of the Contact Pressure under a Roller

Abstract

An asymptotic approximation of the displacement on the entire surface of an elastic half-space loaded by normal and shearing tractions in a slender, bounded, curved surface region is found by the method of matched asymptotic expansions. The solution takes the form of an integral representation consisting of two one-dimensional integrals. The accuracy of the method is tested by comparing it with the displacement calculated directly from the two-dimensional Boussinesq-Cerrutti integrals. Finally, a numerical method for the calculation of the normal pressure under not necessarily cylindrical rollers is briefly described, and results are given for a crowned cylindrical and a crowned conical roller.