A Mori-Tanaka method based theoretical approximation for functionally graded thick wall tube under combined thermal and mechanical loads

In this work, a FGM thick wall tube under both thermal and mechanical loadings is studied by referring to the Mori-Tanaka method. The studied FGM tube is assumed to be made of two distinct linear elastically deformable materials equipped with unique volume fractions. Specially, its material parameters are firstly evaluated in the scheme of the Mori-Tanaka method which can more accurately depict the effective material properties of FGMs composites. Later, we derive the ordinary differential equation (ODE) of the displacement along radial direction, based on which we determine the approximate analytical results of displacement and later derive explicit forms of stress components along all the radial, axial and circumferential directions. After comparison, we found that the derived analytical results agree well with that obtained through numerical method. Moreover, for the same researching problem we found the Mori-Tanaka method could outperform the Voigt method. Further, the results are valid for materials with different Poisson's ratios rather than constant Poisson's ratios usually used in the existing references. Finally, parametric studies are also conducted by exploring the variations of the displacement and stress components affected by different volume fractions and distinct thermal conductivities and expansion coefficients.