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.
