Abstract
Doubly periodic contact problems are considered for a layer with an unknown contact domain. One face of the layer is subjected to sliding support or rigidly fixed. The problems are reduced to integral equations the kernels of which do not contain integrals. For full contact of the other layer face with a two-dimensional sinusoidal rigid surface, the problems have exact solutions used to verify computer programs realizing the numerical method of Galanov nonlinear integral equations which allows us to determine the contact domain and the contact pressure simultaneously. Mechanical characteristics are calculated for indentation of the system of elliptic paraboloids, the passage from discrete to continuous contact zones is investigated.
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