Investigation of displacements and stresses in thick-walled FGM cylinder subjected to thermo-mechanical loadings

In this paper, analytical and numerical solutions are presented for computing mechanical displacements and stresses in a thick-walled cylindrical made of functionally graded materials (FGMs) under mechanical and thermal loadings. The elastic modulus and thermal conductivity are assumed to vary in the radial direction, and the Poisson's ratio is assumed constant. Navier's ordinary second-order differential equation derived from the mechanical equilibrium equation was solved to obtain the exact solution of the displacement and stress distributions. Furthermore and in order to validate the accuracy of the analytical solution, a numerical model was construct using the finite element method. Very good agreement has been found between the analytical formulation and the predictions of numerical simulation which confirms the accuracy of the model in the case of a thick-walled tube made of FGM under steady state temperature distribution and a mechanical loading. These results clarify the influence of the thermal field, non-homogeneity parameter and internal pressure on the thermo-elastic response of the functionally graded cylindrical vessel.