Analytical and numerical investigation of displacements and stresses in thick-walled FGM cylinder with exponentially-varying properties

Abstract

In this paper, analytical solutions are presented for computing mechanical displacements and stresses in a thick-walled cylindrical made of functionally graded materials (FGMs) under mechanical loading. The pressure vessel is subject to axisymmetric internal pressure. The analytical model of the pressurized vessel is constructed, where the radial continuous varying of elastic modulus along the thickness was assumed. It has been assumed that the elastic modulus is varying through thickness of the FGM material according to an exponential distribution along the thickness. Navier’s equation, which is a second-order ordinary differential equation, was derived from the mechanical equilibrium equation. The distributions of the displacement and stresses were determined by the exact solution to Navier’s equation. The effect of the inhomogeneity parameter and internal pressure on radial displacement, radial, tangential and axial stresses in a functionally graded cylinder is analyzed. Results obtained clarify the influence of the mechanical field, non-homogeneity parameter on the elastic response of the functionally graded cylindrical vessel. This is depicted graphically by using radial displacement and stresses in a pressurized functionally graded cylinder. Thus, these parameters have remarkable effects on the distributions of radial displacement and radial and circumferential stresses. The inhomogeneity constant, which includes continuously varying volume fraction of the constituents, is a useful parameter from a design point of view in that it can be tailored for specific applications to control the stress distribution.