Hierarchic finite elements based on a unified formulation for the static analysis of shear actuated multilayered piezoelectric plates

Purpose - The purpose of this paper is to present several two-dimensional plate elements for the analysis of shear actuated laminate. Design/methodology/approach - The limitations of the classical formulations based on the principle of virtual displacements in depicting the peculiar behavior of the transverse and normal stresses of multilayered structures have been easily overcome by using the mixed variational theorem proposed by Reissner (Reissner mixed variational theorem). In the framework of a unified formulation (UF), the assumptions of the unknowns is made through a common expansion leading both to global and layerwise description of the assumed unknowns. In addition, the possibility to choose the order of the expansion between one and four allows to be derived and compared 22 different plate models. The performances of the proposed elements have tested on application for whom an exact solution is available in open literature. Findings - The obtained results complain quite well with the exact ones even if the need of advanced plate models come to evidence. Originality/value - This paper describes how the capabilities of the UF to accurately analyze multilayered structures exploiting the shear mode actuation have been tested and states that in order to extend the capabilities of the UF, further efforts should be made toward the assumptions of discontinuous electric fields (potential and normal displacement). The paper confirms the need for advanced higher order plate models in modeling of adaptive laminate.