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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 11
A Unified Formulation for Finite Element Analysis of Piezoelectric Adaptive Plates A. Robaldo+, E. Carrera+ and A. Benjeddou*
+Aerospace Department, Politecnico di Torino, Italy
Full Bibliographic Reference for this paper
A. Robaldo, E. Carrera, A. Benjeddou, "A Unified Formulation for Finite Element Analysis of Piezoelectric Adaptive Plates", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 11, 2004. doi:10.4203/ccp.79.11
Keywords: piezoelectric, multilayered plates, finite elements, higher-order theories, smart structures, vibration analysis, unified formulation.
Summary
As a result of potential applications, during the last decades, significant efforts have been devoted to the
research on the so-called smart structures. Such structures differ from the conventional ones by
the presence of elements able to perform as actuators and/or sensors, allowing the structures itself
to adapt and/or sense to the external environment. This capability leads to a wide range of
applications, in particular in the aerospace field such as vibration suppression, shape adaption of
aerodynamic surfaces, noise reduction, precision positioning of antennas, aeroelastic control of
lifting surfaces and shape control of optical devices. Even if a variety of different materials can
be utilized in smart structures, only piezoelectric materials have shown the capability to perform
effectively both as actuators and sensors elements. Another advantage of piezoelectric materials
is their simple integration within multilayered composite structures combining low density and
superior mechanical and thermal properties along with sensing, actuation and control. However,
multilayered structures embedding piezoelectric layers require appropriate electromechanical
modelling, see [1,2,3,4]. On the other hand, the solution of practical problems demand the use of
computational methods such as the finite element method.
This work presents some finite elements for the analysis of laminated plates embedding
piezoelectric layers based on the Principle of Virtual Displacements (PVD) and the unified
formulation introduced by Carrera [5,6]. One of the most interesting features of this element is
the use of the unified formulation for the description of the unknowns which allows to keep the
order of the expansion of the variables along the thickness direction as a parameter of the model
and at the same time to perform both Equivalent Single Layer (ESL) and Layer-Wise (LW)
descriptions of the state mechanical variables. The displacement unknowns are expanded up to
the fourth order through a set of functions The full coupling between the electric and mechanical fields is considered; thus, the electric potential is taken as a state variable of the problem. The governing equations have been derived substituting the constitutive relations expressed in terms of the displacements and electric potential into the PVD statement. The discretized governing equations have then been given in the form of matrices that can be easily assembled starting from simpler arrays whose dimensions are in general 3x3 called Fundamental Nuclei. Both four-noded and nine-noded quadrilateral isoparametric elements have been formulated. Results for the free vibration frequencies in the case for a single layer piezoelectric plate and of a hybrid sandwich plate have been reported for various finite elements. Simply-supported square plates have been considered, while the lamination angle have been limited to cross-ply in order to compare the finite element results with those obtained by a Navier-type solution based on the same formulation [2]. The proposed numerical solution has shown a very good agreement with the analytical one [2]. Higher order LW elements lead to results very close to the 3D exact solution. References
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