Third-order nonlocal elasticity in buckling and vibration of functionally graded nanoplates on Winkler-Pasternak media

Cutolo, A.; Mallardo, Vincenzo; Fraldi, Massimiliano; Ruocco, Eugenio

doi:10.1007/s12356-020-00059-3

Cited by 13 publications

(7 citation statements)

References 25 publications

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“…With the help of quasi-3D hyperbolic SDT and NSGT, Shahraki et al [53] carried out a buckling and vibration analysis of thick rectangular FG carbon nanotubes reinforced composite (FG-CNTRC) nanoplates resting upon a Kerr foundation. Cutolo et al [54] applied a Reddy’s HSDT for the buckling and free vibration analysis of FGM nanoplates resting on a Winkler-Pasternak foundation. By employing the Galerkin method and modified continuum NSGT, Daikh et al [55] proposed a new quasi-3D hyperbolic SDT to determine the deflection and stress distribution of sandwich FG nanoplates resting on a variable Winkler elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Belarbi

Houari

et al. 2022

Mathematics and Mechanics of Solids

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This work studies the size-dependent free vibration response of functionally graded (FG) nanoplates using a layerwise theory. The proposed model supposes not only a higher-order displacement field for the core but also the first-order displacement field for the two face sheets, thereby maintaining an interlaminar displacement continuity among layers. Unlike the conventional layerwise models, the number of variables is kept fixed and does not increase for an increased number of layers. This is a very important feature compared to conventional layerwise models and facilitates significantly the engineering analyses. The material properties of the FG nanoplate are graded continuously through the thickness direction in accordance with a power-law function. The Eringen’s nonlocal elasticity theory is here adopted to relax the continuum axiom required in classical continuum mechanics and hence hopeful to capture the small size effects of naturally discrete nanoplates. The equations of motion of the problem are obtained via a classical Hamilton’s principle. The present layerwise model is implemented with a computationally efficient C0- continuous isoparametric serendipity elements and applied to solve a large-scale discrete numerical problem. The robustness and reliability of the developed finite element model are demonstrated by a comparative evaluation of results against predictions from literature. The comparative studies show that the proposed finite element model is: (a) free of shear locking, (b) accurate with a fast rate convergence for both thin and thick FG nanoplates, and (c) excellent in terms of numerical stability. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanoplates to the aspect ratio, length-to-thickness ratio, nonlocal parameter, boundary conditions, power-law index, and modes shapes. Referential results are also reported, for the first time, for natural frequencies of FGM nanoplates which will serve as benchmarks for further computational investigations.

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Section: Introductionmentioning

confidence: 99%

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Belarbi

Houari

et al. 2022

Mathematics and Mechanics of Solids

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“…Despite the fact that attention was given to this question for functionally graded beams [30,[34][35][36], we did not find the determination of Z n in the literature. Here, we propose a simple argument and we suggest decomposing the full energy into:…”

Section: Position Of the Neutral Surfacementioning

confidence: 71%

Modeling the mechanics of growing epithelia with a bilayer plate theory

et al. 2021

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Epithelia, which consists of cell sheets lying on a substrate, are prevalent structures of multicellular organisms. The physical basis of epithelial morphogenesis has been intensely investigated in recent years. However, as 2D mechanics focused most attention, we still lack a rigorous description of how the mechanical interactions between the cell layer and its substrate can lead to 3D distortions. This work provides a complete description of epithelial mechanics using the most straightforward model of an epithelium: a thin elastic bilayer. We first provide experimental evidence in Drosophila tissues that localized alterations of the cell substrate (the extracellular matrix) can lead to profound 3D shape changes in epithelia. We then develop an analytical model modifying the Föppl-von Kármán equation with growth for bilayers. We provide a complete description of all contributions from biophysical characteristics of epithelia. We show how any localized inhomogeneity of stiffness or thickness drastically changes the bending process when the two layers grow differently. Comparison with finite element simulations and experiments performed on Drosophila wing imaginal discs validates this approach for thin epithelia Joseph Ackermann and Paul-Qiuyang Qu equally Contributed.

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“…Despite the fact that attention was given to this question for functionally graded beams [34,35,30,36], the determination of Z n has not been found in the literature. Here, we propose a simple argument and we suggest decomposing the full energy into:…”

Section: Position Of the Neutral Surfacementioning

confidence: 99%

Modeling the mechanics of growing epithelia with a bilayer plate theory

Ackermann

Paul-Qiuyang

Goff

et al. 2021

Preprint

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Epithelia, which consists of cell sheets lying on a substrate, are prevalent structures of multi-cellular organisms. The physical basis of epithelial morphogenesis has been intensely investigated in recent years. However, as 2D mechanics focused most attention, we still lack a rigorous description of how the mechanical interactions between the cell layer and its substrate can lead to 3D distortions. This work provides a complete description of epithelial mechanics using the most straightforward model of an epithelium: a thin elastic bilayer. We first provide experimental evidence in Drosophila tissues that localized alterations of the cell-substrate (the extracellular matrix) can lead to profound 3D shape changes in epithelia. We then develop an analytical model modifying the Foppl-von Karman equation with growth for bilayers. We provide a complete description of all contributions from biophysical characteristics of epithelia. We show how any localized inhomogeneity of stiffness or thickness drastically changes the bending process when the two layers grow differently. Comparison with finite-element simulations and experiments performed on Drosophila wing imaginal discs validate this approach for thin epithelia.

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Third-order nonlocal elasticity in buckling and vibration of functionally graded nanoplates on Winkler-Pasternak media

Cited by 13 publications

References 25 publications

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Modeling the mechanics of growing epithelia with a bilayer plate theory

Modeling the mechanics of growing epithelia with a bilayer plate theory

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