Multilayered plate elements with node-dependent kinematics for electro-mechanical problems

In the present work, a new class of finite elements (FEs) for the analysis of composite and sandwich plates embedding piezoelectric skins and patches is proposed. By making use of node-by-node variable plate theory assumptions, the new finite element allows for the simultaneous analysis of different subregions of the problem domain with different kinematics and accuracy, in a global/local sense. As a consequence, the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states, and their electro-mechanical coupling present a complex distribution. The primary advantage is that no ad-hoc techniques and mathematical artifices are required to mix the fields coming from two different and kinematically incompatible adjacent elements, because the plate structural theory varies within the finite element itself. In other words, the structural theory of the plate element is a property of the FE node in this present approach, and the continuity between two adjacent elements is ensured by adopting the same kinematics at the interface nodes. The finite element arrays of the generic plate element are formulated in terms of fundamental nuclei, which are invariants of the theory approximation order and the modeling technique (Equivalent-Single-Layer, Layer-Wise). In this work, the attention is focused on the use of Legendre polynomial expansions to describe the through-the-thickness unknowns to develop advanced plate theories. Several numerical investigations, such as composite and sandwich multilayered plates embedding piezoelectric skins and patches with various load, boundary conditions, and piezoelectric material polarizations, are carried out to validate and demonstrate the accuracy and efficiency of the present plate element, including comparison with various closed-form and FE solutions from the literature.