An Approximate Thermo-Mechanical Solution of a Functionally Graded Cylinder Using Hybrid Integral Transform and Finite Element Method

This article introduces a novel mixed method that combines the Fast Fourier Transform technique and a conventional Finite Element Method for investigating thermo-mechanical behavior of a thick functionally graded cylinder under asymmetric loadings. Material properties are assumed to vary along the radial direction according to a power function. Thermo-elastic governing equations of the cylinder are derived using principle of virtual work in cylindrical coordinates. Plane strain assumption is considered for a long cylinder during the analysis. Fast Fourier Transform technique is utilized in circumferential direction to discretize equations and related boundary conditions. Finite element method is then applied to remaining equations. For convergence study, the results obtained from this method are compared with those extracted from exact and complete FE solutions. It is observed from the results that the method has a super algebraic convergence behavior in circumferential direction. Influence of the mesh refinement is also investigated in the radial direction. According to ability of the mixed FFT-FE method for asymmetric analyzing, two kinds of loadings are considered here and results are presented. In thermo-elastic analyzing of the long cylinder, it’s obvious that the present method benefits from some features such as fast convergence and low computational cost in comparison with FE solution.