An efficient coupled layerwise theory for dynamic analysis of piezoelectric composite beams

Kapuria, S.; Dumir, P.C.; Ahmed, A.

doi:10.1016/s0022-460x(02)01026-x

Cited by 33 publications

(14 citation statements)

References 26 publications

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“…cantilever beam with applied force or bending moment), to assess the validity of the present model in presence of boundary effects. • Proper introduction of the effect of transverse stresses on beam models more refined than the Euler-Bernoulli one, by revisiting the literature on equivalent single-layer Timoshenko models [15] and layerwise approaches [9] and by accounting also for influence of the bonding layers [27]. • Developing a corrected Euler-Bernoulli finite element for piezoelectric laminates and, after the previous point, also a generation of more accurate beam elements including the effect of transverse stresses.…”

Section: Discussionmentioning

confidence: 99%

“…In early works actuating [7] and sensing [8] functions of piezoelectric materials have been studied separately. The current trend is toward the formulation of completely coupled models taking into account the two-fold electromechanical coupling and introducing both electric and mechanical degrees of freedom [9][10][11][12][13][14]. Coupled electromechanical modelling is necessary for several reasons.…”

Section: Introductionmentioning

confidence: 99%

“…Many interesting and rigorous works have been dedicated to increase the model accuracy by introducing additional state variables to describe higher order effects with shareable and layerwise theories (see e.g. [9,23]). However, especially for vibration control applications [17,24,25], the basic induced strain Euler-Bernoulli model presented in [7] and its extensions for including the two-fold electromechanical coupling are still the most popular because of their simplicity.…”

Section: Introductionmentioning

confidence: 99%

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Extension of the Euler–Bernoulli model of piezoelectric laminates to include 3D effects via a mixed approach

Maurini

Pouget

Dell’Isola

2006

Computers & Structures

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In this paper a coupled Euler-Bernoulli model of laminated piezoelectric beams is proposed. It is characterized by accounting for the influence of 3D distribution of mechanical stresses and strains through corrected electromechanical constitutive equations. In particular, the hypothesis of vanishing transverse (width direction) normal stress typical of standard beam models is weakened by imposing vanishing stress resultants. This integral condition is enforced by adopting a mixed variational principle and Lagrange multiplier method. Explicit expressions for the beam constitutive coefficients are given and the sandwich and bimorph piezoelectric benders are studied in details. The model is assessed through comparisons with standard models and 3D finite element results, showing an important enhancement of standard beam theories.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extension of the Euler–Bernoulli model of piezoelectric laminates to include 3D effects via a mixed approach

Maurini

Pouget

Dell’Isola

2006

Computers & Structures

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“…Efficient zig-zag theories [11,12] have been presented by the authors for moderately thick hybrid beams in which the continuity of shear stress at layer interfaces is approximately satisfied by neglecting the explicit contribution of potential / to s zx . Subsequently, the authors presented [13] an improved version of this zig-zag theory in which the shear traction free conditions at the top and bottom and the transverse shear continuity conditions at layer interfaces are exactly satisfied, including the explicit contribution of / to s zx .…”

Section: Introductionmentioning

confidence: 99%

“…Smeared beam and discrete layer elastic beam models [2,7,10,17] have been used for hybrid beams by including the effect of induced strain of actuators. Uncoupled CLT, FSDT and TOT [3,4,8,15,22,25] and coupled CLT, FSDT, TOT [7,9,14,20,21,24,26] and coupled DLT [6,18] have been applied for the analysis of hybrid beams.Efficient zig-zag theories [11,12] have been presented by the authors for moderately thick hybrid beams in which the continuity of shear stress at layer interfaces is approximately satisfied by neglecting the explicit contribution of potential / to s zx . Subsequently, the authors presented [13] an improved version of this zig-zag theory in which the shear traction free conditions at the top and bottom and the transverse shear continuity conditions at layer interfaces are exactly satisfied, including the explicit contribution of / to s zx .…”

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confidence: 99%

Finite element model of efficient zig-zag theory for static analysis of hybrid piezoelectric beams

Kapuria

Dumir

Ahmed

et al. 2004

Computational Mechanics

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Finite element model is presented for the analysis of hybrid piezoelectric beams under static electromechanical load, using the one-dimensional (1D) coupled zig-zag theory developed recently by the authors. Two noded elements are used with cubic Hermite interpolation for deflection and electric potentials at the sub-layers and with linear interpolation for axial displacement and shear rotation. The expressions for the variationally consistent stiffness matrix and load vector are derived and evaluated in closed form using exact integration. The formulation is validated by comparison with the analytical solution for simply-supported beam. The finite element model is free of shear locking. The present zig-zag finite element results for cantilever beams are compared with the 2D finite element results using ABAQUS to establish the accuracy of the zig-zag theory for these boundary conditions. IntroductionHybrid piezoelectric laminates with embedded or surface bonded piezoelectric sensors and actuators to achieve desired control, form part of a new generation of adaptive structures. Robust coupled electromechanical models are needed to obtain accurate response of these structures. This work presents a finite element model of an efficient zig-zag theory for static analysis of hybrid beams. A review of 3D approaches, 2D theories for plates and shells, and 1D theories for beams, has been presented by Saravonas and Heyliger [19]. Analytical 2D solutions [16,23] for static response are available for simply-supported hybrid panels and beams. Finite element modelling of adaptive structural elements has been recently reviewed [1]. The normal to the mid-surface of thick and moderately thick beams gets distorted due to significant shear deformation and layerwise inhomogeniety. Classical lamination theory (CLT), first order shear deformation theory (FSDT) and third order shear deformation theory (TOT) use the same approximation for displacement across the thickness. Layer-wise approximations are used in discrete layer theories (DLT) with the number of unknowns dependent on the number of layers. The conditions of continuity of shear stress at the layer interfaces are violated in these theories. Zig-zag theories (ZIGT) are discrete layer theories in which the continuity conditions of shear stress at the layer interfaces and the shear traction-free conditions at the bottom and top of the beam are enforced to reduce the number of primary displacement unknowns whose number becomes independent of the number of layers. In coupled theories the electric variables are included as additional unknowns and the charge equations of equilibrium are included, whereas in uncoupled theories these are excluded. Smeared beam and discrete layer elastic beam models [2,7,10,17] have been used for hybrid beams by including the effect of induced strain of actuators. Uncoupled CLT, FSDT and TOT [3,4,8,15,22,25] and coupled CLT, FSDT, TOT [7,9,14,20,21,24,26] and coupled DLT [6,18] have been applied for the analysis of hybrid beams.Efficient zig-zag theories...

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Zhang

2020

Nonlinear Analysis of Thin-Walled Smart Structures

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An efficient coupled layerwise theory for dynamic analysis of piezoelectric composite beams

Cited by 33 publications

References 26 publications

Extension of the Euler–Bernoulli model of piezoelectric laminates to include 3D effects via a mixed approach

Extension of the Euler–Bernoulli model of piezoelectric laminates to include 3D effects via a mixed approach

Finite element model of efficient zig-zag theory for static analysis of hybrid piezoelectric beams

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