Mixed Elements for the Analysis of Anisotropic Multilayered Piezoelectric Plates

Abstract

Mixed plate elements for accurate evaluation of transverse mechanical stresses and electrical displacement are developed and compared in this work. Various forms of the Reissner mixed variational theorem are considered to a priori fulfill the interlaminar continuity of transverse electromechanical variables. Classical formulation based on the principle of virtual displacements are implemented for comparison purposes. 2D assumptions are introduced by means of the Carrera unified formulation (CUF). Layer-wise theories are developed by using Legendre type polynomials of various order in the plate-thickness expansion. The evaluation of the interlaminar continuity of transverse electric displacement and/or transverse stresses on the static response of piezoelectric actuated/sensing plate is provided and compared. Orthotropic and anisotropic simply supported plates are considered. Results are assessed by comparison with available 3D piezoelasticity solutions. The mixed formulations that a priori evaluate the transverse electric displacement appear of particular interest. These last, in fact, permit an easy, convenient and reliable calculation of the electric charge and make feasible the development of robust control algorithms.