Geometrically nonlinear static FE-simulation of multilayered magneto-electro-elastic composite structures

A fully geometrically nonlinear finite rotation shell element for static analysis of layered magneto-electro-elastic (MEE) coupled composite structures is proposed. Reissner–Mindlin first-order shear deformation (FOSD) theory with full geometrically nonlinear strain–displacement relations and finite rotations is used to obtain the variational formulation. The scalar electric and magnetic fields are assumed along with the quasi-static behavior of MEE layers. Electric and magnetic potentials are assumed to vary quadratically in the transverse direction. Three linear constitutive relations are used describe the magneto-electro-elastic coupling. The magneto-electro-elastic composite four node shell element behavior is refined by embodying an assumed natural strain (ANS) method for transverse shear strains, and an enhanced assumed strain (EAS) method for in-plane bending strains. The developed finite element model is deployed for static analysis of layered MEE structures in sensor and actuator configurations, and results are compared with the available references. Additionally, several numerical examples are simulated to show the potentiality and predictive capabilities of the proposed finite element method.