A comprehensive 3D fully coupled theory for thermo-magneto-electro-elastic multilayered plates and shells

Abstract

A three-dimensional (3D) multifield static analysis is developed for thermo-magneto-electro-elastic multilayered plates, cylinders, cylindrical shells, and spherical shells. The thermo-magneto-electro-elastic coupling is investigated through six second-order differential equations for spherical shells expressed in terms of displacements, magnetic potential, electric potential, and temperature increment. The six second-order differential equations governing spherical shells consist of the following: the 3D equilibrium equations of elasticity, the 3D divergence equation of magnetic induction, the 3D divergence equation of electric displacement, and the 3D Fourier heat-conduction equation. These equations are fully coupled and are solved in strong form by employing Navier harmonic expansions in the in-plane directions and the exponential matrix method along the thickness coordinate. The 3D thermo-magneto-electro-elastic governing equations are formulated within a mixed curvilinear orthogonal reference system, thereby enabling the analysis of spherical shells, plates, cylinders, and cylindrical panels through an appropriate selection of the two radii of curvature. The layer-wise description is implemented by enforcing interlaminar continuity conditions between adjacent layers. Such continuity conditions are imposed on displacements, magnetic potential, electric potential, temperature increments, transverse shear and normal stresses, transverse normal magnetic induction, transverse normal electric displacement, and transverse normal heat flux. The Results section presents preliminary benchmark cases in which the proposed model is assessed against other multifield formulations available in the literature for both flat and curved structures. In addition, four original case studies are introduced to investigate the fully coupled interaction among thermal, magnetic, electric, and elastic fields. These case studies consider four different geometries spanning a thickness-ratio range from thick to thin configurations. The resulting data provide insight into the influence of multifield loadings and couplings in smart structures and offer useful benchmark solutions for the verification of less refined multifield analytical and numerical 3D/2D models.