A Piezoelectric Mixed Variational Theorem for Smart Multilayered Composites

Benjeddou, Ayech; Andrianarison, Orlando

doi:10.1080/15376490490491747

Cited by 25 publications

(20 citation statements)

References 24 publications

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“…Note that the negative sign before the electric field in the enlarged strain vector is introduced in order to get symmetric piezoelectric constitutive equations as can be seen from the matrix of their expression in terms of above enlarged vectors [9] …”

Section: Hamiltonian Variational Formulationmentioning

confidence: 99%

“…Following [9], let us introduce the so-called enlarged, or generalized, displacement U, strain S, stress T, and load G vectors…”

Section: Hamiltonian Variational Formulationmentioning

confidence: 99%

“…They differ by the retained electric variables: (i) by augmenting the electric potential and mechanical displacements with the transverse stresses as independent variables, a three-field partial mixed piezoelectric VF can be obtained [8] using a partial Legendre transformation; (ii) when the transverse electric displacement is added as an independent variable, this leads to the four-field partial mixed piezoelectric VF as obtained in [9] using Lagrange multipliers. The present work will show later that a four-field piezoelectric VF can also be obtained using the classical Hamiltonian formalism [10].…”

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confidence: 99%

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Hamiltonian partial mixed finite element-state space symplectic semi-analytical approach for the piezoelectric smart composites and FGM analysis

Andrianarison

Benjeddou

2012

Acta Mech

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A partial mixed finite element (FE)-state space method (SSM) semi-analytical approach is presented for the static analysis of piezoelectric smart laminate composite and functionally graded material (FGM) plates. Hence, using the Hamiltonian formalism, the three-dimensional piezoelectricity equations are first worked so that a partial mixed variational formulation, which retains the translational displacements, electric potential, transverse stresses, and transverse electric displacement as primary variables, is obtained; this allows, in particular, straightforward fulfillment of the electromechanical continuity constraints at the laminate interfaces. After an in-plane FE discretization only, the problem is first reduced, for a single layer, to a Hamiltonian eigenvalue problem that is solved using the symplectic approach; then, the multilayer solution is reached via the SSM propagator matrix. The proposed methodology is finally applied to the static analysis of piezoelectric-cross-ply hybrid laminated composite and FGM plates. In a comparison with open literature, available tabulated results show good agreements, thus validating the proposed approach.

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Section: Hamiltonian Variational Formulationmentioning

confidence: 99%

“…Following [9], let us introduce the so-called enlarged, or generalized, displacement U, strain S, stress T, and load G vectors…”

Section: Hamiltonian Variational Formulationmentioning

confidence: 99%

mentioning

confidence: 99%

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Hamiltonian partial mixed finite element-state space symplectic semi-analytical approach for the piezoelectric smart composites and FGM analysis

Andrianarison

Benjeddou

2012

Acta Mech

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“…RMVT application to thermoelastic multilayered composites has been assessed recently by Carrera [16,17] who has also exploited the RMVT concept for piezoelectric media [18,19]. Constraint of the electric field-potential relation has been proposed first by the authors [12,13] through their Piezoelectric Mixed Variational Theorem (PMVT) which can be seen as the analogue, for piezoelectric media, of RMVT for elastic media.…”

Section: Introductionmentioning

confidence: 99%

“…doi:10.1016/j.compstruc.2004.08.029 literature has been published on thermopiezoelectric smart structures and materials as attested by the latest assessment [8], review [9] and survey [10,11] papers. Careful analysis of the latter show that the use of mixed (hybrid) variational principles for analytical or modelling of piezoelectric-based smart structures has received great interest during the last half decade (see [12,13] for a review of this matter). However, to the authors knowledge, above thermopiezoelectric mixed variational principles have never been used.…”

Section: Introductionmentioning

confidence: 99%

A Thermopiezoelectric Mixed Variational Theorem for smart multilayered composites

Benjeddou

Andrianarison

2005

Computers & Structures

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Fabrication and Nanocompression Testing of Aligned Carbon‐Nanotube–Polymer Nanocomposites

et al. 2007

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The exceptional electronic, thermal, and mechanical properties of carbon nanotubes (CNTs) have motivated extensive research on their manufacturing and applications. At bulk scales, there is particular interest in property enhancements by adding CNTs to polymers to make composite materials. Most work on CNT-based composites presented in the literature to date has focused on dispersion of single-or multiwalled CNTs (SWNTs or MWNTs) in the matrix; however, bulk CNTs embedded in a polymeric matrix tend to form aggregates that are not only poorly adhered to the matrix but also concentrate stresses, compromising the effect of the CNTs as reinforcement.[1] On the other hand, establishing order and alignment among CNTs within a composite matrix offers significant further potential to harness the properties of individual CNTs at bulk scales by realizing the anisotropic properties of CNTs in desired directions, and by enabling packing and dispersion of CNTs at much higher volume fractions than in tangled configurations. In this work, CNT-polymer composites are manufactured by wetting as-grown arrays of vertically aligned CNTs rapidly and effectively (lack of voids) using off-the-shelf polymers. The wetting process not only preserves the alignment of the CNTs, but also allows the controlled manufacturing of nanocomposite test structures. Direct characterization of the mechanical properties of the nanocomposite structures is also presented in this work. The mechanical-reinforcement results support the feasibility of using these CNT arrays in large-scale hybrid advanced composite architectures reinforced with aligned CNTs. Such composites will also benefit from multifunctional property (e.g., electrical conductivity) enhancements owing to the aligned CNTs.The mechanical properties (e.g., Young's modulus, hardness) of thin films containing randomly oriented CNTs inside a polymer matrix have been assessed using various techniques, that is, analytical models, [2][3][4][5] standard tension and compression tests, [6][7][8][9][10] and nanoindentation techniques. [11][12][13][14][15] The composite modulus along the CNT axis (stiff axis) of well-aligned CNT-polymer composites has not been studied to date. In the most relevant related work, Fang et al. [16] usedBerkovich nanoindentation to determine the hardness of chemical vapor deposition (CVD)-grown aligned MWNTparylene nanocomposites, but did not report their modulus. Parylene is a gas-phase deposited polymer typically used for electrical isolation. Modulus characterization in the transverse direction (i.e., CNTs aligned perpendicular to the direction of modulus measurement) indirectly inferred from structural tests was reported, with a significant increase (by a factor of 20-30) over the assumed modulus of parylene. Modulus characterization using direct measurement methods, not dependent on structural models, is preferred when available. The present work is the first to characterize the mechanical properties of well-aligned CNT-epoxy nanocomposites along the CNT axis using direct...

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A Piezoelectric Mixed Variational Theorem for Smart Multilayered Composites

Cited by 25 publications

References 24 publications

Hamiltonian partial mixed finite element-state space symplectic semi-analytical approach for the piezoelectric smart composites and FGM analysis

Hamiltonian partial mixed finite element-state space symplectic semi-analytical approach for the piezoelectric smart composites and FGM analysis

A Thermopiezoelectric Mixed Variational Theorem for smart multilayered composites

Fabrication and Nanocompression Testing of Aligned Carbon‐Nanotube–Polymer Nanocomposites

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