Stress analytical solution for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform distributed pressure

Abstract

The stress state around circular openings, such as boreholes, shafts, and tunnels, is usually needed to be evaluated. Solutions for stresses, strains and ultimate bearing capacities of pressurized hollow cylinder are common cases. Stress analytical method for plane problem of a double-layered thick-walled cylinder subjected to a type of non-uniform pressure on the outer surface and uniform radial pressure on the inner surface is given. The power series method of complex function is used. The stress analytical solution is obtained with the assumption that two layers of a cylinder are fully contacted. The distributions of normal and tangential contact stress along the interface, tangential stress on the inner boundary and stresses in the radial direction at θ=0°, 45° and 90°, are obtained. An example indicates that, when the elastic modulus of the inner layer of a double-layered thick-walled cylinder is smaller than that of the outer layer, the tangential stress is smaller than that in the corresponding point for a traditional cylinder composed of homogeneous materials. In that way, stress concentration at the inner surface can be alleviated and the stress distribution is more uniform. This is a capable way to enhance the elastic ultimate bearing capacity of thick-walled cylinder.