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Formulations of periodic contact problems for an elastic half-plane and an elastic half-space interacting with a rigid body, having regular microgeometry, and a method for their approximate solution based on the localization principle are proposed. General relations, connecting contact characteristics of the interface (contact pressure distribution and dependence of the real contact area on the nominal pressure) with a single asperity shape and the distance between them, are obtained. The examples, illustrating the use of the obtained approximate relations for the contact characteristics analysis in the case of wavy and wedged profiles, are presented. The comparison of the obtained results with the available exact solutions is carried out. It was established that the approximate dependences coincide with the exact solution up to high values of the nominal pressures. New approximate solutions of 2D contact problems for a periodic system of parabolic asperities with single and double contact segments within a period are derived. It is also shown that the ratio of the contact zone size to the distance between asperities, at which the interaction effect becomes significant, only slightly depends on asperities shape.

Analysis of Elastic Normal Contact of Surfaces With Regular Microgeometry Based on the Localization Principle