Hierarchic multilayered plate elements for coupled multifield problems of piezoelectric adaptive structures: Formulation and numerical assessment

The paper presents a hierarchic model for the analysis of multifield problems related to multilayered plates subjected to mechanical, electric and thermal loads. In the framework of a unified formulation (UF), the finite element method has been used to derive a complete family of plate elements distinguished from one another by the variational statement and the laminate kinematic assumptions upon which each of them is based. Depending on the accuracy required by the analysis, the most appropriate element can be easily derived choosing the primary unknowns of the model by selecting between displacement or partially mixed formulations (Principle of Virtual Displacement, Reissner's mixed variational theorem). The complete derivation of fully coupled variational statements (classical and partially mixed) is also given for thermopiezoelastic analysis. The description of the unknowns can then be chosen between global (ESL) and layerwise (LW). Finally the order of the expansion can be set in the range from 1 to 4 thus selecting first order or higher order plate models. Then, results in form of tables and graphs are given in order to validate the proposed elements.