Contact problem for a hollow cylinder

The axisymmetric contact problem of the interaction of a rigid annular sleeve with an infinite hollow elastic cylinder with an arbitrary wall thickness, which is subjected to the action of a constant internal pressure, is investigated. When the solution of Lame's problem for a hollow cylinder and the integral transformation method are used, the contact problem is reduced to an integral equation with a difference kernel relative to the unknown pressure in the contact area. To solve this equation in the case of relatively wide sleeves, a modification of the singular asymptotic method based on complication of the approximating function for the symbol function of the kernel when the cylinder walls are made thinner is proposed. Calculations are performed for a broad range of variation of the relative thickness of the cylinder walls with approach to values that are characteristic of the theory of cylindrical shells, in which the shell thickness usually amounts to no more than 2% of the radius of the middle surface. ©2017