Nonlinear modeling of composite plates with piezoceramic layers using finite element analysis (original) (raw)
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Analytical and numerical modelling of laminated composites with piezoelectric layers
Journal de Physique IV (Proceedings), 2004
We propose an accurate and efficient approach to laminated piezoelectric plates based on a refinement of elastic displacement and electric potential through the plate thickness. More precisely, the model accounts for a shearing function and a layerwise approximation for the electric potential. The layerwise approach becomes a necessity in order to accommodate electric potential at the electrode interfaces. The equations of motion for the piezoelectric composite are deduced from a variational formulation incorporating the continuity conditions at the layer interfaces by using Lagrange multipliers. Different situations are investigated among them (i) bimorph and (ii) sandwich structures for two kinds of electromechanical loads applied (density of force and electric potential) and are compared to the finite element computations performed on the 3D model. The vibration problem is also presented and the frequencies for the axial and flexural modes are obtained. At last performance and effectiveness of the model are also discussed and applications to control of the structure shape and vibration are proposed.
Two-dimensional modelling of laminated piezoelectric composites: analysis and numerical results
Thin-Walled Structures, 2001
We propose a new approach to laminated piezoelectric plates based on a refinement of the electric potential as function of the thickness coordinate of the laminate and accounting for shear effects. Moreover, the variation of the electric potential as function of the thickness coordinate is modelled for each layer of the laminate. The equation for the laminated piezoelectric plate are then obtained by using a variational formulation involving mechanical surface loads or prescribed electric potential on the top and bottom faces of the plate. In addition to the equations for the generalized stress resultants (due to the shear effects), the equation of the electric charge conservation is also deduced for the 2D model. Particular attention is devoted to the single piezoelectric plate and bimorph structure and the through-thickness distribution of the displacements, electric potential as well as stresses are given for different kinds of electromechanical loads. The results thus obtained are compared to those provided by a finite element method performed for the full 3D model. A good agreement is observed for plates made of layers of PZT-4 piezoelectric material. The comparison ascertains the effectiveness of the present 2D approach to piezoelectric laminates.
Smart Materials and Structures, 2010
This paper presents a procedure to numerically analyze the coupled electro-structural response of laminated plates with orthotropic fiber reinforced layers and piezoelectric layers using the generalized finite element method (GFEM). The mechanical unknowns, the displacements, are modeled by a higher order shear deformation theory (HSDT) of the third order, involving seven generalized displacement functions. The electrical unknowns, the potentials, are modeled by a layerwise theory, utilizing piecewise linear functions along the thickness of the piezoelectric layers. All fields are enriched in the in-plane domain of the laminate, according to the GFEM, utilizing polynomial enrichment functions, defined in global coordinates, applied on a bilinear partition of unities defined on each element. The formulation is developed from an extended principle of Hamilton and results in a standard discrete algebraic linear motion equation. Numerical results are obtained for some static cases and are compared with several numerical and experimental results published in the literature. These comparisons show consistent and reliable responses from the formulation. In addition, the results show that GFEM meshes require the least number of elements and nodes possible for the distribution of piezoelectric patches and the enrichment provides more flexibility to reproduce the deformed shapes of adaptive laminated plates.
Classical and Advanced Computational Plate/Shell Models for Piezoelectric Laminated Structures
This lectures is devoted to advanced computational models for multilayered plate/shell structures embedding piezoelectric layers as sensor/actuators. The hierarchical modelling is obtained by referring to the Carrera Unified Formulation which permits the development of equivalent single-layer and layer-wise theories based on classical and mixed variational statements. The need of layer-wise analysis is pointed out as well as the convenience to refer to mixed variational statements to evaluate transverse mechanical and electrical variables without any post-processing. Mostly an overview of the recent work co-authored by the first author is given. The results have been obtained by running an in-house software recently named MUL2.
AIP Advances
Among many smart materials, piezoelectric materials have emerged as the most studied ones for practical applications. They owe their success to several factors, including low price, high bandwidth, availability in various formats, and ease of handling and implementation. The present study focused on the performance of piezoelectric laminated composite plate under various electromechanical loading conditions by utilizing the first-order shear deformation theory with the Newton–Raphson residual and iteration with Gauss integration point in Ansys. For the first time, the effects of electrical loading, circuit arrangement, voltage variation, and polynomial variable transverse loading are studied over piezoelectric composite plate (PCP). The effects of plate aspect ratio, thickness ratio, boundary conditions, ply orientations, nature of loading conditions, and voltage variation are presented. The study also utilized open and close circuit arrangements as sensors and actuators to gauge th...
Journal of Intelligent Material Systems and Structures, 2018
Laminated composite panels are extensively used in various engineering applications. Piezoelectric transducers can be integrated into such composite structures for a variety of vibration control and energy harvesting applications. Analyzing the structural dynamics of such electromechanical systems requires precise modeling tools which properly consider the coupling between the piezoelectric elements and the laminates. Although previous analytical models in the literature cover vibration analysis of laminated composite plates with fully covered piezoelectric layers, they do not provide a formulation for modeling the piezoelectric patches that partially cover the plate surface. In this study, a methodology for vibration analysis of laminated composite plates with surface-bonded piezo-patches is developed. Rayleigh–Ritz method is used for solving the modal analysis and obtaining the frequency response functions. The developed model includes mass and stiffness contribution of the piezo-...
Theoretical Analysis of Piezoelectric Hybrid Plates
2016
An analytical method is devlopteded to analyze piezoelectric hybrid laminated composite plates with arbitrary lamination and boundary conditions subjected to electromechanical loads. The method is based on separation of spatial variables of displacement field components. Within the displacement field of a first-order shear deformation plate theory and using the principle of minimum total potential energy, two systems of coupled ordinary differential equations with constant coefficients are obtained. These equations may be solved analytically with the help of state-space approach. Also a Levy-type solution is employed for verification the validity and accuracy of the proposed method. It is seen that the present results have close agreements with those obtained by Levy-type method.
Vibration Control Simulation of Laminated Composite Plates with Integrated Piezoelectrics
Journal of Sound and Vibration, 1999
A finite element formulation is presented to model the dynamic as well as static response of laminated composite plates containing integrated piezoelectric sensors and actuators subjected to both mechanical and electrical loadings. The formulation is based on the classical laminated plate theory and Hamilton's principle. In this formulation, the mass and stiffness of the piezo-layers have been taken into account. A four-node non-conforming rectangular plate bending element is implemented for the analysis. A simple negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to actively control the dynamic response of an integrated structure through a closed control loop. The model is validated by comparison with existing results documented in the literature. Several numerical examples are presented. The influence of stacking sequence and position of sensors/actuators on the response of the plate is evaluated.
Piezothermoelastic composite plate analysis using first-order shear deformation theory
Computers & Structures, 1994
The response of composite plates constructed of ~phite/epoxy laminae with an attached piezoelectric polyvinyl~dene fluoride layer subjected to mechanical, thermal and electric field loading is considered for various length-to-depth and aspect ratios. First-order shear deformation theory is extended to include the piezothermoelastic response of composite k'ate structures. Analytic results are obtained for a plate simply supported along all edges. A nine-node Lagrangian finite element formulation is established and results are presented for simply supported or fixed boundary conditions. Numerical results show that moderately thick piezothermoelastic composites are sensitive to shear deformation, but increasing plate aspect ratio reduces the shear deformation influence.