Contact problems for hollow cylinders made of a nonhomogeneous material

Contact problems for elastic hollow cylinders made of a nonhomogeneous materia are considered. The cylinders are subjected to uniformly distributed internal or external pressure and interact with a stiff shroud or finite-length insert. Poisson's ratio (Young's modulus) of the elastic material varies along the radial coordinate. The problem equations are reduced to integral equations with respect to contact pressures. A singular asymptotic method, which is fairly effective for contact regions of sufficiently large length, is applied to solve the problem.