Analytical solution for magneto-thermo-elastic responses of an annular functionally graded sandwich disk by considering internal heat generation and convective boundary condition

Abstract

In this paper, an exact solution for stress distribution of a rotating sandwich disk subjected to magnetic, thermal fields, and convection heat transfer with the consideration of internal heat generation is presented. The sandwich disk is composed of three different layers in which the central layer is made of functionally graded material, whereas the inner and outer layers are made from pure metal and ceramic materials, respectively. All mechanical and thermal properties of the central layer are assumed to obey a power-law form in the radial direction with different non-homogeneity constants. Axisymmetric temperature distributions in each layer are obtained by solving Fourier heat conduction equation. By substituting the constitutive equations in equilibrium equation, a second-order differential equation in terms of radial displacement for each layer is derived by considering centrifugal force and Lorentz magnetic force obtained from Maxwell’s relations. Thereafter, the governing equations are analytically solved and radial displacement, radial and circumferential stresses for the current disk are obtained. Numerical simulations reveal the effects of internal heat generation, convection heat transfer, magnetic field, material properties, and angular velocity on the magneto-thermo-elastic response of the functionally graded sandwich disk. Also, a comparison study between metal, functionally graded, ceramic, and functionally graded sandwich disks is performed.