Revisiting the elastic solution for an inner-pressured functionally graded thick-walled tube within a uniform magnetic field

TL;DR

This study provides analytical solutions for the mechanical and magnetic responses of a functionally graded thick-walled cylinder under internal pressure and magnetic field, emphasizing the influence of material composition and Poisson's ratio.

Contribution

It introduces a novel approach by deriving material constants from volume fractions rather than assumed functions, extending previous models.

Findings

Poisson's ratio significantly affects mechanical behavior.

Material composition influences displacement, stress, and magnetic field responses.

Results can reduce to special cases in prior literature.

Abstract

In this paper, the mechanical responses of a thick-walled functionally graded hollow cylinder subjected to uniform magnetic field and inner-pressurized loads are studied. Rather than directly assuming the material constants into some certain function forms as displayed in previous researches, we firstly give the volume fractions of different constituents of the FGM cylinder and then determine the expressions of material constants. By the use of the Voigt method the corresponding analytical solutions of displacements in radical direction, the strain and stress components and the perturbation magnetic field vector are derived by the following. In numerical part, the influences of volume fraction on displacement, stain and stress components and the magnetic perturbation filed vector are investigated; indicated by the results, we can conclude that the Poisson's ratio has a significant effect on the FGM cylinder's mechanical behaviors. Moreover, by some appropriate choices of the material constants it can be found that the obtained results in this paper can reduce to some special cases given in previous literatures.