Quasi-3D Refined Theory for Functionally Graded Porous Plates: Displacements and Stresses

Zenkour, Ashraf M.

doi:10.1134/s1029959920010051

Cited by 42 publications

(8 citation statements)

References 38 publications

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“…As quasi-3D theory includes both shear and normal deformations, various quasi-3D theories have been proposed in the literature. Some studies regarding the different responses of FG structures are reported in [33][34][35][36][37][38][39][40][41][42][43]. However, to the best of the author's knowledge, no prior studies have examined the buckling of FG porous plates with the consideration of the influence of the thickness stretching on the structure, which is essential for thick plate investigation.…”

Section: Introductionmentioning

confidence: 99%

Buckling Response of Functionally Graded Porous Plates Due to a Quasi-3D Refined Theory

Zenkour

Aljadani

2022

Mathematics

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A quasi-3D refined theory is used to investigate the buckling response of functionally graded (FG) porous plates. The present theory takes into consideration the effect of thickness stretching. Three models of FG porous plates are presented: an isotropic FG porous plate, FG skins with a homogenous core, and an FG core with homogenous skins. The FG porous material properties vary along with the thickness of the FG layer based on modified polynomial law. By using the principle of total potential energy, the equilibrium equations are obtained. The buckling response is determined for simply supported FG porous plates. Analytical investigations are verified to present the accuracy of the current quasi-3D refined theory in predicting the buckling response of FG porous plates. The effect of thickness stretching and several parameters such as porosity coefficients, mechanical loadings, geometric parameters, gradient indexes, and layer thickness ratios are discussed. It is observed that the current theory shows more accurate results for the buckling response of FG plates compared with other shear deformation theories.

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Section: Introductionmentioning

confidence: 99%

Buckling Response of Functionally Graded Porous Plates Due to a Quasi-3D Refined Theory

Zenkour

Aljadani

2022

Mathematics

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“…Hence, shear correction factors were introduced to correct this deficiency. To overcome the limitation of CLPT and FSDT, various HSDT (sinusoidal, exponential, hyperbolic, inverse‐hyperbolic, and third‐order shear deformation theory) were proposed for a better representation of transverse shear stresses without the use of correction factors 14‐22 . In the last decades, different types of higher‐order theories were proposed for multilayered plates and shells.…”

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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“…Zenkour and Hafed 27 examined the static investigation of the functionally graded plates according to shear deformation theory. Zenkour 28 examined the bending behavior of the functionally graded plates. Daikh and Zenkour 29 examined the dynamic and buckling analysis of porous sandwich plates according to a HSDT.…”

Section: Introductionmentioning

confidence: 99%

A novel nonlocal higher-order theory for the accurate vibration analysis of 2D FG nanoplates

Xie

Jin

Zhen

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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In this paper, vibration analysis of the 2 D-FG nanoplate is studied based on a novel higher-order shear deformation theory (HSDT). The proposed HSDT is a composition of trigonometric, exponential and polynomial functions which is one of the most accurate HSDTs. The mechanical properties of the nanoplate change along with the length and thickness directions, according to arbitrary functions. To model the displacement field, the impacts of both transverse shear and thickness stretching are considered. To consider the small-scale impact, nonlocal elasticity theory is applied. To obtain the equations of motion, Hamilton’s principle is applied. Navier method is used for a closed-form solution of the 2 D-FG nanoplates with simply-supported boundary conditions. The impact of different parameters including the small-scale parameter are studied on the natural frequency of the system. The results illustrate that when size effect parameter is smaller/greater than 0.5 nm, the impacts of the FG parameters on the frequency of the system increase/reduce.

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Quasi-3D Refined Theory for Functionally Graded Porous Plates: Displacements and Stresses

Cited by 42 publications

References 38 publications

Buckling Response of Functionally Graded Porous Plates Due to a Quasi-3D Refined Theory

Buckling Response of Functionally Graded Porous Plates Due to a Quasi-3D Refined Theory

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

A novel nonlocal higher-order theory for the accurate vibration analysis of 2D FG nanoplates

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