3D exact magneto-electro-elastic static analysis of multilayered plates

This study proposes a three-dimensional (3D) coupled magneto-electro-elastic problem for the static analysis of multilayered plates embedding piezomagnetic and piezoelectric layers by considering both sensor and actuator configurations. The 3D governing equations for the magneto-electro-elastic static behavior of plates are explicitly show that are made by the three 3D equilibrium equations, the 3D divergence equation for magnetic induction, and the 3D divergence equation for the electric displacement. The proposed solution involves the exponential matrix in the thickness direction and primary variables’ harmonic forms in the in-plane ones. A closed-form solution is performed considering simply-supported boundary conditions. Interlaminar continuity conditions are imposed for displacements, magnetic potential, electric potential, transverse shear/normal stresses, transverse normal magnetic induction and transverse normal electric displacement. Therefore, a layerwise approach is adopted. The results section is composed of an assessment part, where the present model is compared to past 3D electro-elastic or magneto-elastic formulations and a new benchmark part. Benchmarks consider sensor and actuator plate configurations for the fully coupled magneto-electro-elastic cases for different thickness ratios. Tabular and graphical results are presented for displacements, stresses, magnetic potential, electric potential, transverse normal magnetic induction and transverse normal electric displacement. For each presented benchmark, magneto-electro-elastic coupling and thickness and material layer effects are discussed in depth.