Investigation of displacement and stress fields in pressurized thick-walled FGM cylinder under uniform magnetic field

Abstract

In this paper, an analytical solution is presented for computing mechanical displacements and stresses in a thick-walled cylindrical pressurized vessel made of functionally graded materials (FGM). The pressure vessel is subject to axisymmetric mechanical loading within a uniform magnetic field. The analytical model of the pressurized vessel was constructed, where the radial continuous varying of elastic modulus and permeability along the thickness was assumed. It has been assumed that the elastic modulus and permeability are varying through thickness of the FG material according to a nonlinear general distribution along the thickness. Navier’s equation, which is a second-order ordinary differential equation, was derived from the mechanical equilibrium equation with the consideration of the Lorentz force resulting from the magnetic field. The distributions of the displacement and stresses were determined by the exact solution to Navier’s equation. Numerical results clarify the influence of the magnetic field, non-homogeneity parameter and internal pressure on the magneto-elastic response of the functionally graded cylindrical vessel. Thus, these parameters have remarkable effects on the distributions of radial displacement and radial and circumferential stresses.