The model of elastic interior contact between a rough rigid disk and an isotropic plate with thin coating on a smooth cylindrical hole was developed. These investigations allowed us to take into account plastic deformations of a layer of the hole and probability characteristics of surface roughness of a disk. The method of complex potentials (the potentials of Kolosov-Muskhelishvily) and the dependence of plastic deformations of the layer obtained by Alecseev for plain joints were used. The problem was reduced to an integral-differential equation with respect to normal contact stress.
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