"THE ELASTIC CONTACT PROBLEM INVOLVING A BILATERALLY LOADED THIN STRIP "

Abstract

"For the solution of the elastic contact problem, it is generally assumed that the contacting solids can be assimilated to elastic half-spaces. This assumption is reasonable when the contact area is small compared to the dimensions of the contacting solids, and when the contact stresses are restricted to a small vicinity of the initial point of contact, without reaching the boundaries of the solids. These conditions are not met when a thin strip is bilaterally and symmetrically compressed between two punches, as the dimensions of the contact area might be of the same order of magnitude as the strip thickness. Moreover, the stresses induced in the strip will reach the boundary without a significant decay in intensity. Consequently, in this contact scenario, the classical solutions for a point force acting on the boundary of the half-space cannot be directly applied. The starting point for the problem solution is a modified Boussinesq-type solution for the thin elastic layer, expressing the displacement and stress fields induced in an elastic strip by two opposed normal forces perpendicular to the layer boundaries. To this end, supplementary displacements are added to the half-space solution to satisfy both geometric and loading symmetry, as well as the linear elasticity equations. Superposition principle is then applied, resulting in a contact model for an elastic strip compressed between two identical indenters with aligned axes. An algorithm for the contact of solids that can be assimilated to elastic half-spaces is modified and applied to the contact involving a thin strip. To this end, the required influence coefficients for displacements are derived. A calculation example involving a thin strip compressed between two spheres is presented, and a comparison with the half-space solution is performed. "