Periodic contact problems in plane elasticity

Abstract

Various methods for solving the partial contact of surfaces with regularly periodic profiles—which might arise in analyses of asperity level contact, serrated surfaces or even curved structures—have previously been employed for elastic materials. A new approach based upon the summation of evenly spaced Flamant solutions is presented here to analyze periodic contact problems in plane elasticity. The advantage is that solutions are derived in a straightforward manner without requiring extensive experience with advanced mathematical theory, which, as it will be shown, allows for the evaluation of new and more complicated problems. Much like the contact of a single indenter, the formulation produces coupled Cauchy singular integral equations of the second kind upon transforming variables. The integral equations of contact along with both the boundary and equilibrium conditions provide the necessary tools for calculating the surface tractions, often found in closed-form for regularly periodic surfaces. Various loading conditions are considered, such as frictionless contact, sliding contact, complete stick, and partial slip. Solutions for both elastically similar and dissimilar materials of the mating surfaces are evaluated assuming Coulomb friction.