Three-dimensional static analysis of magneto-electro-elastic composite shells

The present paper is devoted to the investigation of the behavior of simply-supported multilayered smart shells embedding piezomagnetic and piezoelectric layers. A three-dimensional (3D) approach is taken into account considering the mixed curvilinear orthogonal reference system for spherical shells, cylindrical shells and cylinders. The 3D magneto-electro-elastic problem for shells is composed by a set of second order differential equations for spherical shells: the three 3D equilibrium equations, the 3D divergence equation for the magnetic induction and the 3D divergence equation for the electric displacement. The solution procedure involves the use of Navier harmonic forms in the in-plane directions and the exponential matrix method in the thickness direction. Both sensor and actuator configurations for simply supported structures can be analyzed thanks to proper load boundary impositions on external surfaces. A layer-wise approach is implemented because congruence conditions on displacements, magnetic and electric potentials and equilibrium conditions on transverse shear and transverse normal stresses, transverse normal magnetic induction and transverse normal electric displacement are imposed between two adjacent layers. In the results section, a first subsection for the validation of the present model is proposed considering comparisons with other results in literature. The proposed 3D model is more general than 3D models proposed in the literature because it uses a general formulation for several geometries, lamination schemes and load conditions. In the second subsection, new cases are shown. Tabular values and graphical trends along the thickness direction are given for different variables. These new cases can be used to investigate magneto-electro-elastic coupling, material layer and thickness layer effects on curved smart structures with different geometries and load boundary conditions. Moreover, these results can be used as references for those scientists interested in the validation of 2D/3D numerical models because the proposed 3D model is exact, layer wise and it correctly considers zigzag effects and interlaminar continuity conditions. An accurate 3D evaluation of all the elasto-electro-magnetic variables in smart structures allows a more effective design for both sensor and actuator configurations.