A revisiting of the elasticity solution for a transversely isotropic functionally graded thick-walled tube based on the Mori–Tanaka method

Abstract

In this paper, we present the elastic solutions for the problem of an internal pressurized functionally graded thick-walled tube based on the Voigt method in Xin et al. (Int J Mech Sci 89:344–349, 2014); a transversely isotropic functionally graded thick-walled tube subjected to internal pressure is studied. It is assumed that the functionally graded tube is made up of two linear isotropic elastic materials; the matrix is reinforced by fibers with circular cross section all aligned in the circumferential direction. The volume fraction of the reinforced material is identical with our previous work (i.e., Xin et al. in Int J Mech Sci 89:344–349, 2014). By using the Mori–Tanaka method, this paper obtains the differential equation of the radial displacement and then the numerical results of the radial displacement and the stresses are deduced. The approximate analytical solutions are also derived which agree well with the numerical results on the basis of the Mori–Tanaka method. Further, both based on the Mori–Tanaka method, the results received by the present model are compared with those by a particle model for solving an isotropic inner-pressurized FGM tube problem. Finally, in the numerical part the influences of the volume fraction and the elastic moduli’s ratio on radial displacement and the stresses are discussed.