Bending analysis of functionally graded piezoelectric plates via quasi-3D trigonometric theory

Zenkour, Ashraf M.; Hafed, Zahra S.

doi:10.1080/15376494.2018.1516325

Cited by 37 publications

(7 citation statements)

References 46 publications

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“…The normal stresses � 11 and � 33 increase as /ℎ and increase. If we neglect the hygrothermal effect in Table 6 we will get the same results as those in Zenkour and Hafed (2019).…”

Section: Effect Of Gradient Indexmentioning

confidence: 70%

“…Also, the FGP plates consisted of Titanium/Zirconia are considered. The material properties are given by (Zidi et al 2014) Metal ( To verify the accuracy and validity of the present technique, results of EGP and FGP plates are compared with the solutions of several theories obtained by new hyperbolic shear deformation theory (HSDT) (Benyoucef et al 2010), sinusoidal shear deformation theory (SSDT) (Thai and Vo, 2013), a refined four-unknown plate theory RSPT (Al Khateeb and Zenkour 2014) and Q-3D (Zenkour and Hafed 2019). Tables 1-5 show the comparison of dimensionless deflection and stresses of Aluminum/Alumina EGP rectangular plate under sinusoidally load, while Table 6 illustrates the comparison of dimensionless deflection and stresses of Titanium/Zirconia FGP rectangular plate under sinusoidally load.…”

Section: Dimensionless Quantitiesmentioning

confidence: 99%

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Hygro-thermo-mechanical bending of FG piezoelectric plates using quasi-3D shear and normal deformations theory

Zenkour

Hafed

2019

Lat. Am. j. solids struct.

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A simple quasi-3D sinusoidal shear and normal deformations theory for the hygro-thermo-mechanical bending of functionally graded piezoelectric (FGP) plate is developed under simply-supported edge conditions. The governing equations are deduced based on the principle of virtual work. The exact solutions for FGP plate are obtained. The current study investigates the effect of some parameters, like piezoelectricity, hygrothermal parameter, gradient index and electric loading on the mechanical and electric displacements, electric potential and stresses. They are explored analytically and numerically presented and discussed in detail. The numerical results clearly show the effect of piezoelectric and hygrothermal parameter on the FGP plate.

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“…The normal stresses � 11 and � 33 increase as /ℎ and increase. If we neglect the hygrothermal effect in Table 6 we will get the same results as those in Zenkour and Hafed (2019).…”

Section: Effect Of Gradient Indexmentioning

confidence: 70%

Section: Dimensionless Quantitiesmentioning

confidence: 99%

Hygro-thermo-mechanical bending of FG piezoelectric plates using quasi-3D shear and normal deformations theory

Zenkour

Hafed

2019

Lat. Am. j. solids struct.

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“…Thus, a kinematically correct representation of the strain field in a discrete laminated layer is provided 45 . For more detailed information about these theories, the reader may consult 46‐52 …”

Section: Introductionmentioning

confidence: 99%

An efficient eight‐node quadrilateral element for free vibration analysis of multilayer sandwich plates

Belarbi

Zenkour

Tati

et al. 2021

Numerical Meth Engineering

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This article presents a free vibration analysis of laminated sandwich plates under various boundary conditions by using an efficient C0 eight‐node quadrilateral element. This new element is formulated based on the recently proposed layerwise model. The present model assumes an improved first‐order shear deformation theory for the face sheets while a higher‐order theory is assumed for the core maintaining an interlaminar displacement continuity. The advantage of this model relies on its number of variables is fixed, does not increase when increasing the number of lamina layers. This is a very important feature compared to the conventional layerwise models and facilitates significantly the engineering analysis. Indeed, the developed finite element is free of the shear locking phenomenon without requiring any shear correction factors. The governing equations of motion of the sandwich plate are derived via the classical Hamilton's principle. Several examples covering the various features such as the effect of modular ratio, aspect ratios, core‐to‐face thickness ratio, boundary conditions, skew angle, number of layers, geometry and ply orientations are solved for laminated composites and sandwich plates. The obtained results are compared with 3D, quasi‐3D, 2D analytical solutions, and those predicted by other advanced finite element models. The comparison studies indicate that the developed finite element model is of fast convergence to the reference and valid for both thick and thin laminated sandwich plates. Finally, it can be concluded that the present model is not only simple and accurate than the conventional ones, but also comparable with refined analytical solutions found in the literature.

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“…Ghayesh [11] studied the viscoelastic axially FG imperfect microbeam using couple stress theory. Zenkour and Hafed [12] investigated the bending analysis of the FG piezoelectric plates via quasi-3D trigonometric theory. Bouazza and Zenkour [13] investigated the buckling behavior of the laminated beam under a hygro-thermo-mechanical loading using hyperbolic refined shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

Mohammadi¹

2021

Preprint

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In this paper, the nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT is studied. Nonlocal elasticity theory is applied to consider the small scale effect. The nonlinear equations of motion are derived using Hamilton’s principle. First, a Galerkin-based numerical technique is applied to reduce the nonlinear governing equation into a set of Duffing-type time-dependent differential equations. Afterward, the analytical solutions are derived based on the method of multiple scales (MMS) and perturbation technique. All of the mechanical properties of the beam are temperature dependent. The impacts of the several variables are investigated on the nonlinear frequency ratio of the nanobeams. The results illustrate that when maximum deflection is smaller/ greater than 0.2, its impact on the nonlinear frequency ratio will decrease/increase.

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Bending analysis of functionally graded piezoelectric plates via quasi-3D trigonometric theory

Cited by 37 publications

References 46 publications

Hygro-thermo-mechanical bending of FG piezoelectric plates using quasi-3D shear and normal deformations theory

Hygro-thermo-mechanical bending of FG piezoelectric plates using quasi-3D shear and normal deformations theory

An efficient eight‐node quadrilateral element for free vibration analysis of multilayer sandwich plates

Nonlinear vibration analysis of the nanobeams subjected to magneto-electro-thermo loading based on a novel HSDT

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