Nonlinear bending analysis of bilayer orthotropic graphene sheets resting on Winkler–Pasternak elastic foundation based on non-local continuum mechanics

Dastjerdi, Shahriar; Jabbarzadeh, Mehrdad

doi:10.1016/j.compositesb.2015.10.018

Cited by 32 publications

(7 citation statements)

References 33 publications

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“…Dastjerdi and colleagues 14,15 investigated the static behavior of monolayer annular/circular and double-layered rectangular nanographene plate. They received this conclusion that the maximum deflection declines along with the increasing small-scale effects.…”

Section: Introductionmentioning

confidence: 99%

Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force

Dastjerdi

Malikan

2020

Proceedings of the Institution of Mechanical Engineers, Part N:

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In this article, we have tried to simulate nonlinear bending analysis of a double-layered graphene sheet which contains a geometrical imperfection based on an eccentric hole. The first-order shear deformation theory is considered to obtain the governing equations. Also, the nonlinear von Kármán strain field has been assumed in order to obtain large deformations. Whereas the double-layered graphene sheet has been considered, the effect of van der Waals forces has been taken into account in the analysis. In order to implement the nanoscale impact, the nonlocal elasticity theory has been employed. The solution methodology, which is here based on the semi-analytical polynomial method solving technique presented previously by the authors, has been applied and again its efficiency has been demonstrated due to its highly accurate results. Due to the fact that this research has been done for the first time and there is no validation available, the results of the local single layer sheet are compared with ABAQUS software. The effects of some other parameters on the results have been studied such as the value of eccentricity, van der Waals interaction, and nonlocal parameter.

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Section: Introductionmentioning

confidence: 99%

Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force

Dastjerdi

Malikan

2020

Proceedings of the Institution of Mechanical Engineers, Part N:

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“…The nonlinear bending behavior of a bilayer rectangular graphene sheet subjected to a transverse uniform load in thermal environments was studied by Xu et al [68], in which the bilayer graphene sheet (BLGS) is modeled as a nonlocal double-layered plate containing a small scale effect and van der Waals interaction forces. Dastjerdi et al [69] investigated the nonlinear bending behavior of bilayer orthotropic rectangular graphene sheets resting on a two-parameter elastic foundation subjected to uniform transverse loads by using the nonlocal elasticity theory and solved the obtained nonlinear algebraic equations system by adopting the Newton-Raphson iterative scheme. The postbuckling behavior of both uniaxially and biaxially loaded GSs in a polymer environment was investigated by Naderi et al [70] by using a nonlocal plate model, in which the van der Waals interaction force between the graphene sheets and the polymer medium is considered as a nonlinear function of the graphene's deflection.…”

Section: Large Deformationmentioning

confidence: 99%

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

Liew

Zhang

2017

Journal of Modeling in Mechanics and Materials

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Abstract:This paper presents a literature review of recent research studies on the applications of nonlocal elasticity theory in the modeling and simulation of graphene sheets (GSs). The history, development and excellent properties of GSs are introduced. The details of nonlocal elasticity theory are also presented. A systematic introduction to the application of nonlocal elasticity on linear modeling and nonlinear modeling for single-layer graphene sheets (SLGSs) and multilayered graphene sheets (MLGSs) is also provided. The necessity of determining mechanical parameters and nonlocal parameters is discussed. Recommendations for future work are particularly presented. This work is intended to review the development of GSs, give an introduction to the research studies on nonlocal elasticity theory in the modeling of GSs, and provide recommendations for future research.

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“…A primary guess (

and

) was required for results in this approach. We can express the first iteration as [ 44 ].

where J denotes the Jacobian matrix 2 × 2 and A is a vector 2 × 1.…”

Section: Solution Approachmentioning

confidence: 99%

“…A primary guess (U 0 and W 0 ) was required for results in this approach. We can express the first iteration as [44].…”

Section: Solution Approachmentioning

confidence: 99%

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

Malikan

Eremeyev

2020

Nanomaterials

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Among various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In this article, we develop a model of a simultaneously coupled piezomagnetic–flexomagnetic nanosized Euler–Bernoulli beam and solve the corresponding problems. In order to evaluate the FM on the nanoscale, the well-known nonlocal model of strain gradient (NSGT) is implemented, by which the nanosize beam can be transferred into a continuum framework. To access the equations of nonlinear bending, we use the variational formulation. Converting the nonlinear system of differential equations into algebraic ones makes the solution simpler. This is performed by the Galerkin weighted residual method (GWRM) for three conditions of ends, that is to say clamp, free, and pinned (simply supported). Then, the system of nonlinear algebraic equations is solved on the basis of the Newton–Raphson iteration technique (NRT) which brings about numerical values of nonlinear deflections. We discovered that the FM effect causes the reduction in deflections in the piezo-flexomagnetic nanobeam.

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Nonlinear bending analysis of bilayer orthotropic graphene sheets resting on Winkler–Pasternak elastic foundation based on non-local continuum mechanics

Cited by 32 publications

References 33 publications

Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force

Mechanical analysis of eccentric defected bilayer graphene sheets considering the van der Waals force

Nonlocal elasticity theory for graphene modeling and simulation: prospects and challenges

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

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