Wear problem for tube with thin nonuniform inner coating and rigid insert with complex profile

The article describes the formulation of problem wear an elastic pipe with a nonuniform internal coating by rigid insert, diameter which is variable. For this problem, mathematical model built, mixed integral equation. resulting equation contains functions related to variable properties and shape insert. When constructing analytical solution, special approach was used, since standard methods do not allow taking into account presence rapidly changing in equation, can describe shapes materials. In describing profile insertion are separated separate terms. This allows you always get accurate results.