An alternative numerical solution of thick-walled cylinders and spheres made of functionally graded materials

In the problem of thick-walled cylinders of functionally graded materials (FGMs), this paper chooses the displacement function as unknown in the governing equation. The Young's modulus is arbitrary and constant Poisson's ratio is assumed. Two fundamental solutions are defined from a numerical solution under two particular initial boundary conditions. In addition, the transmission matrix M is defined for the single layer case. The matrix relates the values of radical stress and displacement at the initial point to those at the end point of the layer. By using the matrix, the boundary value problem can be solved as well. After considering the continuation condition along the layers, the method of transmission matrix can also be used to the multiply-layered cylinder. The method of transmission matrix can also be used to solve the problem of the thick-walled sphere. A lot of numerical examples are presented.