Novel exact layerwise analytical solution for anisotropic multi-layer magneto-piezo-elastic hollow spheres under asymmetric magneto-electro-hygro-thermo-mechanical loads

Abstract

In the present article, a novel analytical layer-dependent closed-form solution is proposed for multilayer magneto-piezo-elastic hollow spheres with anisotropic layers under asymmetric 2D magneto-electro-hygro-thermo-mechanical loads. The sphere is assumed to be fabricated from piezomagnetic materials and encounters steady-state Fikean and Fourier moisture and heat diffusions. The proposed solution satisfies the layerwise continuity conditions of the stresses and especially, heat and moisture fluxes (derivatives of the main quantities) at the interfaces between layers, in addition to continuity of the main magneto-electro-thermo-elastic quantities. In contrast to the common wrong usage of the Lorentz body force concept in the static and creep analyses, the magneto-electric, hygro-electric, pyro-magnetic, and hygro-magnetic interactions are taken into consideration as well. The governing equations are derived based on the general magneto-electro-hygro-thermo-elasticity. The analytical solution contains new ideas as a special change of variables was used to enable solving the resulting system of equations Legendre series. The coefficients of the mentioned Legendre series are in turn, obtained by solving a system of Eulerian partial differential equations. Effects of various material and environmental factors on the 2D radial and circumferential distributions of the radial and circumferential deformations, stress components, and the induced electrical and magnetic fields are evaluated in the results section. From the accomplished parametric studies, it is found that due to the differences in the various material properties of the successive layers, the gradients of the variations of the responses are not only quite different within the distinct layers but also cannot be estimated without numerical derivations.