Exact solutions of heterogeneous elastic hollow cylinders

Two different kinds of heterogeneous elastic hollow cylinders are studied herein. One is a cylinder with multi-layers and another is a cylinder with continuously graded properties. A simple and convenient method is obtained to find the exact solutions of a N-layered elastic hollow cylinder submitted to uniform pressures on the inner and outer surfaces. For the hollow cylinder with continuously graded properties, the displacement method is used. A hyper-geometric equation is derived and solved, and then the exact solutions are found. The results obtained in the present paper are compared with both the numerical solutions and other findings provided by some references and good agreements are found. At the end of the present paper, some inherent properties of these two different kinds of heterogeneous graded hollow cylinders are presented and discussed.