Variable Kinematics models and finite elements for nonlinear analysis of multilayered smart plates

A variable kinematics approach for moderately large deflection analysis of smart magneto-electro-elastic multilayered plates is presented. The approach is based on the condensation of the electro-magnetic state into the plate kinematics, whose nonlinear strain–displacement relationships are expressed in the von Karman sense. This leads to models resulting in an effective mechanical plate, which takes the multifield coupling effects into account by the plate stiffness, inertia and loading characteristics, consistently defined as combinations of the layers material properties. By a unified approach, both equivalent single layer and layerwise models are developed formulating the associated isoparametric finite elements. Results are presented for different kinematics with through-the-thickness expansion up to the fourth order with the aim of validating the modeling strategy and showing its features for the investigation of smart plates geometrical nonlinear behaviour.