Transfer matrix method for solution of FGMs thick-walled cylinder with arbitrary inhomogeneous elastic response

This paper presents a numerical solution for the thick cylinders made of functionally graded materials (FGMs) with a constant Poisson\'s ratio and an arbitrary Young\'s modulus. We define two fundamental solutions which are derived from an ordinary differential equation under two particular initial boundary conditions. In addition, for the single layer case, we can define the transfer matrix N. The matrix gives a relation between the values of stress and displacement at the interior and exterior points. By using the assumed boundary condition and the transfer matrix, we can obtain the final solution. The transfer matrix method also provides an effective way for the solution of multiply layered cylinder. Finally, a lot of numerical examples are present.