On solving and optimizing contact problems with doubly connected domains taking the nonlinear law of roughness deformation into account

Abstract A detailed study of the real properties of contacting bodies stimulated the development of the theory of contact problems in the direction of considering these properties. As a result, contact problems for rough surfaces were formulated. In this paper, an indentation of a doubly connected punch into an elastic rough half-space is investigated taking into account a nonlinear law of change in the deformation of the surface roughness. With a power dependence of the displacement due to the deformations of microasperity on the pressure, the main integral equation is the Hammerstein equation. Two-dimensional integral equations are transformed into one-dimensional ones using the small parameter method and the obtained expansion of the potential of the simple layer at an internal point. The potential expansion is applied to reduce the problem of indenting a non-circular annular punch into an elastic rough half-space into the similar problems for the contact domain with the circular ring form. Successive approximations are used for the solution. The role of the minimizing functional is played by the root-mean-square deviation of the normal pressure distribution arising under the punch from a certain optimal distribution. The result of the solution is shown by examples for ring contact domain.