Buckling and vibration analysis of FG-CNT-reinforced composite rectangular thick nanoplates resting on Kerr foundation based on nonlocal strain gradient theory

Shahraki, Hosein; Riahi, Hossein Tajmir; Izadinia, Mohsen; Talaeitaba, Sayed Behzad

doi:10.1177/1077546319878976

Cited by 23 publications

(10 citation statements)

References 28 publications

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“…Lu et al [52] developed a novel size-dependent model based on the NSGT in conjunction with the Gurtin-Murdoch surface elasticity theory to study the vibration behavior of FG cylindrical shells. 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.…”

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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“…where k s , k u , k l , refer to the shear layer, upper, and lower spring layers, respectively [39].…”

Section: Hamilton's Principle and Governing Equationsmentioning

confidence: 99%

Theoretical and Numerical Solution for the Bending and Frequency Response of Graphene Reinforced Nanocomposite Rectangular Plates

et al. 2021

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In this work, we study the vibration and bending response of functionally graded graphene platelets reinforced composite (FG-GPLRC) rectangular plates embedded on different substrates and thermal conditions. The governing equations of the problem along with boundary conditions are determined by employing the minimum total potential energy and Hamilton’s principle, within a higher-order shear deformation theoretical setting. The problem is solved both theoretically and numerically by means of a Navier-type exact solution and a generalized differential quadrature (GDQ) method, respectively, whose results are successfully validated against the finite element predictions performed in the commercial COMSOL code, and similar outcomes available in the literature. A large parametric study is developed to check for the sensitivity of the response to different foundation properties, graphene platelets (GPL) distribution patterns, volume fractions of the reinforcing phase, as well as the surrounding environment and boundary conditions, with very interesting insights from a scientific and design standpoint.

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“…From their study, it can be observed that the buckling behavior of clamped FGM nanoplates was very sensitive to various parameters such as aspect and side-to-thickness ratios, material graduation, thermal condition, etc. The study of the influence of small-scale parameters on the vibration and buckling behavior of CNT-reinforced FGM plates was done by Shahraki et al [ 31 ]. The CNT-based FGM nanoplate was considered to rest on a Kerr elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Axial and Shear Buckling Analysis of Multiscale FGM Carbon Nanotube Plates Using the MTSDT Model: A Numerical Approach

Kumar

Szafraniec

et al. 2022

Materials

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The present paper investigates the axial and shear buckling analysis of a carbon nanotube (CNT)-reinforced multiscale functionally graded material (FGM) plate. Modified third-order deformation theory (MTSDT) with transverse displacement variation is used. CNT materials are assumed to be uniformly distributed, and ceramic fibers are graded according to a power-law distribution of the volume fraction of the constituents. The effective material properties are obtained using the Halpin–Tsai equation and Voigt rule of the mixture approach. A MATLAB code is developed using nine noded iso-parametric elements containing 13 nodal unknowns at each node. The shear correction factor is eliminated in the present model, and top and bottom transverse shear stresses are imposed null to derive higher-order unknowns. Comparisons of the present results with those available in the literature confirm the accuracy of the existing model. The effects of material components, plate sizes, loading types, and boundary conditions on the critical buckling load are investigated. For the first time, the critical buckling loads of CNT-reinforced multiscale FGM rectangular plates with diverse boundary conditions are given, and they can be used as future references.

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Buckling and vibration analysis of FG-CNT-reinforced composite rectangular thick nanoplates resting on Kerr foundation based on nonlocal strain gradient theory

Cited by 23 publications

References 28 publications

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Theoretical and Numerical Solution for the Bending and Frequency Response of Graphene Reinforced Nanocomposite Rectangular Plates

Axial and Shear Buckling Analysis of Multiscale FGM Carbon Nanotube Plates Using the MTSDT Model: A Numerical Approach

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