On the stresses under a bush on a cylindrical pipe with a nonuniform coating of variable thickness

In this paper, the problem of contact between a rigid bush and a pipe with an external nonuniform coating of variable thickness under internal pressure is formulated, and an analytical solution of this problem is constructed. In practice, such coatings are required, for example, to protect the main supporting pipe from the aggressive influence of the environment, to create its electrical insulation, etc. By the production processes, the coating can be nonuniform and variably thick. It is important to take such properties into account to analyze the stress-strain state of a pipe bearing a bush since the stress values vary, and hence, the service life of such a connection also varies. The mathematical model of the problem described above is an integral equation containing both integral operators with constant limits of integration (Fredholm operators) and operators with variable limits of integration (Volterra operators). This equation contains functions that describe the elastic properties of the coating and its thickness, and, therefore, they can vary rapidly or even be discontinuous. The paper describes a special approach based on the use of a special representation and special basis functions which are constructed using the characteristic features of the equation. This allows one, in the expression for the contact pressure under the bush, to express the functions describing the properties and the profile of the coating in the form of separate terms and multipliers. Therefore, to achieve a high accuracy in real calculations, it is sufficient to consider only relatively few terms in the series.