Wear of a high pressure layered pipe by a rough rigid bush

The article describes the solution to the problem of linear wear of a high pressure elastic pipe with an elastic coating by rigid bush worn on the pipe so that there is no gap between them. It is assumed that both the thickness of the coating in undeformed state and the shape of the inner surface of the bush are variable and depend on the coordinate along the axis of pipe. In the case when indicated characteristics are described by complex rapidly changing functions, standard approaches to solving such a problem turn out to be ineffective. The article describes an approach based on the use of special representations and basic functions that take into account the presence of complex characteristics. In the expression for contact pressures, which is the result of solving the problem and allows us to further evaluate the resource and durability of such a connection, the functions that describe the surfaces shapes are highlighted in explicit form. This allows us to perform exact calculations in cases where the forms are described by complex functions.