Vol. 2, No. 3, 2007

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Mixed piezoelectric plate elements with continuous transverse electric displacements

Erasmo Carrera and Christian Fagiano

Vol. 2 (2007), No. 3, 421–438

This paper proposes mixed finite elements, FEs, with an a priori continuous transverse electric displacement component Dz. 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 σn. The second, full, form (F-RMVT) adds Dz 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, σn and Dz fields in the plate thickness direction z as well as the number of the element nodes Nn 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 Dz fields.

piezoelectric plates, finite elements, mixed method, transverse continuity, unified formulation
Received: 9 October 2006
Accepted: 29 November 2006
Published: 1 May 2007
Erasmo Carrera
Dept. of Aeronautics and Aerospace Engineering
Politecnico di Torino
Corso Duca degli Abruzzi, 24
10129 Torino
Christian Fagiano
Dept. of Aeronautics and Aerospace Engineering
Politecnico di Torino
Corso Duca degli Abruzzi, 24
10129 Torino
Department of Mechanics, Aerospace Structures and Materials
Delft University of Technology
P.O. Box 5058
2600 GB Delft