Two-dimensional analytical solution of micropolar magneto-thermoelasticity FGM hollow cylinder under asymmetric load (r, θ)

Abstract

This paper presents a two-dimensional analytical solution (r, θ) to study micropolar magneto-thermoelasticity for a hollow cylinder, made of FGMs, under steady-state conditions. The physical properties of materials are in the form of a power function and undergo changes in the direction of the radius. To solve the heat transfer equation and Navier equations, the complex Fourier series and the power-law functions are used. By solving the equations using the general thermal and mechanical asymmetric boundary conditions on the inner and outer surface of the cylinder, radial displacement, circumferential displacement, force stresses, coupling stresses, and micro-rotation are obtained. Numerical examples of Aluminum-epoxy composite are presented for the three theories of classical, micropolar, and micropolar magneto thermoelasticity. Results indicated that the inner and outer surface of the cylinder subject to asymmetric harmonic temperature and mechanical distribution show that the values of the micropolar magnet theory are less than those of the classical theory and more than the values of the micropolar theory. Where harmonic radial stresses are applied to the inner surface of the cylinder, the values of the classical theories correspond to those of the micropolar theory. The presence of a magnetic field makes differences between the values of the micropolar magnet theory and the values of the two classical and micropolar theories. The study was validated by examining an example of homogenous materials under ambient conditions.