A unified formulation for finite element analysis of piezoelectric adaptive plates

Robaldo, Alessandro; Carrera, Erasmo; Benjeddou, Ayech

doi:10.1016/j.compstruc.2006.01.029

Cited by 100 publications

(27 citation statements)

References 20 publications

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“…It is based on Carrera's Unified Formulation (CUF), which has been developed by Carrera for multilayered structures [37]. Many works have been devoted to the extension of CUF to electromechanical problems, see [38][39][40][41]. Among others, Carrera [42] extends principle of virtual displacement (PVD) and RMVT variational statements to piezo-laminated plates, see also [43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches

Cinefra

Valvano

Carrera

2015

International Journal of Smart and Nano Materials

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The present article considers the free-vibration analysis of plate structures with piezoelectric patches by means of a plate finite element with variable through-the-thickness layer-wise kinematic. The refined models used are derived from Carrera's Unified Formulation (CUF) and they permit the vibration modes along the thickness to be accurately described. The finite-element method is employed and the plate element implemented has nine nodes, and the mixed interpolation of tensorial component (MITC) method is used to contrast the membrane and shear locking phenomenon. The related governing equations are derived from the principle of virtual displacement, extended to the analysis of electromechanical problems. An isotropic plate with piezoelectric patches is analyzed, with clamped-free boundary conditions and subjected to open-and short-circuit configurations. The results, obtained with different theories, are compared with the higher-order type solutions given in the literature. The conclusion is reached that the plate element based on the CUF is more suitable and efficient compared to the classical models in the study of multilayered structures embedding piezo-patches.

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Section: Introductionmentioning

confidence: 99%

A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches

Cinefra

Valvano

Carrera

2015

International Journal of Smart and Nano Materials

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“…Based on Eqs. (4), (6), (25), (27) and the nodal degrees of freedom, the electric potential, displacements, strain and electric field components may be expressed in the following matrices form:…”

Section: Finite Element Modelmentioning

confidence: 99%

A finite element model based on coupled refined high-order global-local theory for static analysis of electromechanical embedded shear-mode piezoelectric sandwich composite beams with various widths

Beheshti-Aval

Shahvaghar-Asl

Lezgy-Nazargah

et al. 2013

Thin-Walled Structures

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a b s t r a c tIn this study, a new theory for the accurate simulation of the shear-mode behaviour of thin or thick piezoelectric sandwich composite beams is developed. The effects of transverse normal stress and transverse flexibility of layers are considered in the development of the proposed formulation. In order to increase the computational accuracy, all kinematic and stress continuity conditions are satisfied at layer interfaces. Moreover, for the first time, both the electrically induced strain components and the transverse flexibility are taken into account in the proposed formulation. Despite the fact that the number of unknown mechanical parameters in this theory is only one degree higher than the first order shear deformation theory, the accuracy is surprisingly more pronounced for the thicker beams. (S.B. Beheshti-Aval).[10], Kogl and Bucalem [11,12] Chee et al. [13], Jiang and Li[14], Shu [15], Thornburgh and Chattopadhyay [16], Fukunaga et al. [17] and Mitchell and Reddy [18]used equivalent single layer theories (ESLT) for the analysis of extension-mode piezoelectric beams/plates structures. The idea of layer-wise theory (LWT) or discrete-layer theory was presented and developed by Heyliger and Saravanos [19], Saravanos and Heyliger [20], Saravanos et al.[21], Kusculuoglu et al. [22], Garcia Lage et al. [23,24] Robaldo et al. [25], and Tzou and Ye [26]. Beheshti-Aval and Lezgy-Nazargah[27,28] used a sinus zigzag (ZZ) model for analyzing and controlling of smart laminated piezoelectric beams. Kapuria [29], Kapuria et al. [30], and Kapuria and Alam [31] presented an efficient coupled ZZ theory for static and dynamic analysis of extension-mode piezoelectric laminated/sandwich beams based on third order ZZ approximations. introduced a computationally low cost FE model for the static analysis of extension-mode piezoelectric multilayered/sandwich beams based on global-local theory. For an overview on the modeling of extension-mode piezoelectric laminates, readers can refer to Benjeddou [33].The use of a shear-mode piezoelectric actuator was first proposed by Sun and Zhang [34]. In their work, they employed thickness-shear piezoelectric patches to create transverse deflection in sandwich beams. Moreover, they demonstrated that shear-mode actuators can offer many advantages over the extension-mode actuators. The analysis of this study was carried out using the ANSYS finite-element package. Furthermore, Zhang and Sun [35] developed an analytical model to predict the static, as well as the dynamic behavior of a sandwich beam which comprises of a core layer of shear-mode piezoelectric. The model relies on the assumptions that the face layers obey the Euler-Bernoulli theory, while the core piezoelectric layer follows the Timoshenko theory. Moreover, closed-form solutions of a static cantilever beam with shear-mode actuators were presented. Benjeddou et al. [36] proposed a finite element model of a sandwich beam with extension and shear piezoelectric segments. To verify their model, they compared their finite e...

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“…This expression of the electromechanical problem is at the starting point of either finite element formulations or mathematical questions in (linear) piezoelectricity (see [9] and [10] for example).…”

Section: P3d(ω)mentioning

confidence: 99%

Plates made of piezoelectric materials: When are they really piezoelectric?

Geymonat

Licht²,

Weller³

2011

Applied Mathematical Modelling

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This paper aims at presenting in a synthetic way mathematical results that have been rigorously and recently derived by the authors. These results deal with the simplified but accurate modeling of linearly piezoelectric thin plates. It is shown how mathematical tools lead to two different situations linked to either sensors or actuators devices. Moreover we enlighten the fact that for some piezoelectric crystal classes, the coupling between the electrical and the mechanical effects disappear in the plate. Finally, we furnish a detailled example of such models in the case of a plate constitued by a 222 symmetry class material.

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A unified formulation for finite element analysis of piezoelectric adaptive plates

Cited by 100 publications

References 20 publications

A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches

A layer-wise MITC9 finite element for the free-vibration analysis of plates with piezo-patches

A finite element model based on coupled refined high-order global-local theory for static analysis of electromechanical embedded shear-mode piezoelectric sandwich composite beams with various widths

Plates made of piezoelectric materials: When are they really piezoelectric?

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