An approximate analytical solution based on the Mori–Tanaka method for functionally graded thick-walled tube subjected to internal pressure

In this work an approximate analytical solution based on the Mori–Tanaka method for functionally graded thick-walled tube subjected to internal pressure is given. We assume that the tube consists of two isotropic linear elastic constituents and the volume fraction for one phase is a power function varied in the radial direction. Based on the Mori–Tanaka method, this paper obtains the differential equation of the radial displacement, and then an approximate analytical solution is obtained that agrees well with the numerical results of the Mori–Tanaka method. Furthermore, this paper discusses the same problem with two other methods, the Voigt method that we have already presented in Xin et al. (2014) and the Reuss method. All these three different methods can avoid the assumption of the distribution regularities of unknown overall material parameters appeared in existing papers. Further, they are valid for the materials with different Poisson’s ratios rather than constant Poisson’s ratios usually used in the existing references to obtain the effective Young’s modulus.