Study of multiply-layered cylinders made of functionally graded materials using the transfer matrix method

This paper provides a general solution for a multiply-layered cylinder made of functionally graded ma-terials. The Young’s modulus is assumed to be an arbitrary function of r, and the Poisson’s ratio takes a constant value. The first step is to study the single-layer case (a < r < b). A transfer matrix is defined, relating the values of radial stress and displacement at the initial point (r = a) to those at the end point (r = b). The matrix is evaluated on the basis of two fundamental solutions, which are evaluated numerically. The final solution is obtained by using many transfer matrices for layers, continuation conditions between layers, and boundary conditions at inner and outer boundaries. Several numerical examples are provided. 1.