Hierarchical Finite Element Analysis of Multilayered Plates Subjected to Mechanical, Thermal and Electrical Loadings

This paper addresses to static and dynamic problems of multilayered plate and also embedded piezoelectric layers by means of finite element methods (FEM). Formulation on the basis of Principle of Virtual Displacements (PVD) and Reissner Mixed Variational Theorem (RMVT) are considered. A series of hierarchic, two-dimensional plate elements are presented within the “Unified Formulation” recently introduced by the first author. Finite element matrices are derived for static and dynamic problems of piezoelectric laminates. Numerical solutions are compared to available ones to assess mixed and classical finite elements in both case of Layer-Wise (LW) and Equivalent-Single-Layer (ESL) variable description. The superiority of RMVT applications with respect to classical ones based on Principle of Virtual Displacements (PVD) has been confirmed by the conducted numerical investigation.