Variational Principles for Nonlocal Continuum Model of Orthotropic Graphene Sheets Embedded in An Elastic Medium

Adali, Sarp

doi:10.1016/s0252-9602(12)60020-4

Cited by 24 publications

(11 citation statements)

References 55 publications

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“…The latter form of nonlocal elasticity theory has drawn more attention due to its simplicity. Eringen’s nonlocal elasticity theory also has been widely used to study the vibration behavior of CNT (Alibeigloo and Shaban, 2013; Ansari et al., 2012; Aydogdu, 2015; Karami and Farid, 2015), graphene sheets (Adali, 2012; Alibeigloo, 2013), nanosensors (Lee et al., 2010; Lee and Chang, 2012; Wang and Wang, 2014), etc.…”

Section: Introductionmentioning

confidence: 99%

Free vibration characteristics of nanoscaled beams based on nonlocal integral elasticity theory

Naghinejad

Ovesy

2017

Journal of Vibration and Control

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In the present article, the total potential energy principle and the nonlocal integral elasticity theory have been used to develop a novel finite element method for studying the free vibration behavior of nano-scaled beams. The formulations are based on Euler-Bernoulli beam theory and this method is able to properly analyze the free vibration of beams with various boundary conditions. By implementing the variational statements, the eigenvalue problem of the free vibration is obtained. The validation investigation is pursued by comparing the results of the current study with those available in the literature. The effects of nonlocal parameter, geometry parameters and boundary conditions on the free vibration of the Euler-Bernoulli beam are then studied.

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Section: Introductionmentioning

confidence: 99%

Free vibration characteristics of nanoscaled beams based on nonlocal integral elasticity theory

Naghinejad

Ovesy

2017

Journal of Vibration and Control

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“…The same methodology has been used earlier in the modelling of instability problems in the case of embedded carbon nanotubes 7 8 . Moreover, the Winkler's approach has also been used to study vibrations 9 , buckling 10 and wave propagation 11 of embedded single layer graphene sheets, the vibrational 12 and the wave propagation 13 characteristics of embedded double and multi- layer 14 graphene sheets using nonlocal elasticity theory.…”

mentioning

confidence: 99%

Failure Processes in Embedded Monolayer Graphene under Axial Compression

Androulidakis

Koukaras

Frank

et al. 2014

Sci Rep

101

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Exfoliated monolayer graphene flakes were embedded in a polymer matrix and loaded under axial compression. By monitoring the shifts of the 2D Raman phonons of rectangular flakes of various sizes under load, the critical strain to failure was determined. Prior to loading care was taken for the examined area of the flake to be free of residual stresses. The critical strain values for first failure were found to be independent of flake size at a mean value of –0.60% corresponding to a yield stress up to -6 GPa. By combining Euler mechanics with a Winkler approach, we show that unlike buckling in air, the presence of the polymer constraint results in graphene buckling at a fixed value of strain with an estimated wrinkle wavelength of the order of 1–2 nm. These results were compared with DFT computations performed on analogue coronene/PMMA oligomers and a reasonable agreement was obtained.

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“…It is worth noting that the nonlocal effect does not affect the bending strain energy. The kinetic energy is different from the one given by Adali [52,53]:…”

Section: Fourth-order Phenomenological Model: Nonlocal Eringen's Theorymentioning

confidence: 91%

Comparison of nonlocal continualization schemes for lattice beams and plates

et al. 2017

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International audienceThis paper investigates both stability and vibration of nonlocal beams or plates in the presence of compressive forces. Various nonlocal structural models have been proposed to capture the inherent scale effects of lattice-based beams or plates. These nonlocal models are either based on continualization of the difference equations of the original lattice problem (labeled as continualized nonlocal models), or developed from phenomenological nonlocal approaches such as Eringen's type nonlocality. Considered herein are several continualization schemes that lead to either fourth or sixth order spatial governing differential or partial differential equation. Even if the new continualized nonlocal plate models differ in their mathematical description, they appear to furnish very close macroscopic results as shown from asymptotic expansion arguments. The continualized nonlocal beam and plate models and the phenomenological approaches are also introduced from variational arguments. The key role of boundary conditions is shown especially for Eringen's nonlocal model that is not necessarily variationally based. For each of them, the buckling load and the natural frequencies are determined for simply supported beams and plates and compared to their counterparts obtained from the lattice model. The small length scale coefficient of the nonlocal beam or plate models is intrinsically constant and problem independent for the continualized approaches, whereas it is calibrated for the phenomenological models based on the equivalence with the reference microstructured model and consequently, depends on the load, the buckling or vibration mode or the aspect ratio. It is found that the nonlocal continualized approaches are more efficient than the nonlocal phenomenological ones. For beam problems, continualized nonlocal and phenomenological approaches such as Eringen's nonlocal theory can become the same. However, for plate problems, phenomenological approaches may differ significantly from continualized nonlocal ones; thereby offering one the opportunity to have a new class of two-dimensional nonlocal models

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Variational Principles for Nonlocal Continuum Model of Orthotropic Graphene Sheets Embedded in An Elastic Medium

Cited by 24 publications

References 55 publications

Free vibration characteristics of nanoscaled beams based on nonlocal integral elasticity theory

Free vibration characteristics of nanoscaled beams based on nonlocal integral elasticity theory

Failure Processes in Embedded Monolayer Graphene under Axial Compression

Comparison of nonlocal continualization schemes for lattice beams and plates

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