Abstract

This paper proposes mixed finite elements, FEs, with an a priori continuous transverse electric displacement component D_z. The Reissner Mixed Variational Theorem (RMVT) and the Unified Formulation (UF) are applied to the analysis of multilayered anisotropic plates with embedded piezoelectric layers. Two forms of RMVT are compared. In a first, partial, form (P-RMVT), the field variables are displacements u, electric potential Φ and transverse stresses σ_n. The second, full, form (F-RMVT) adds D_z as an independent variable. F-RMVT allows the a priori and complete fulfillment of interlaminar continuity of both mechanical and electrical variables.

We treat both equivalent single-layer models (ESLM), where the number of variables is kept independent of the number of layers, an layerwise models (LWM), in which the number of variables depends in each layer. According to the UF the order N of the expansions assumed for the u, φ, σ_n and D_z fields in the plate thickness direction z as well as the number of the element nodes N_n have been taken as free parameters.

In most cases the results of the classical formulation which are based on Principle of Virtual Displacements (PVD) are given for comparison purposes. The superiority of the F-RMVT results, with respect to the P-RMVT and to PVD ones, is shown by few examples for which three-dimensional solution is available. In particular, the F-RMVT results to be very effective for the evaluation of interlaminar continuous D_z fields.

Keywords

piezoelectric plates, finite elements, mixed method, transverse continuity, unified formulation

Authors