Variational principles for multi-walled carbon nanotubes undergoing buckling based on nonlocal elasticity theory

Adali, Sarp

doi:10.1016/j.physleta.2008.07.003

Cited by 108 publications

(40 citation statements)

References 32 publications

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“…Based on the nonlocal theory of Eringen, a number of studies have been published trying to develop nonlocal continuum models and apply them to analyze the general behavior of nanostructures [37][38][39][40][41][42][43][44][45][46][47][48]. Also the nonlocal continuum mechanics have been used by many researchers in the study of the buckling of nanotubes [49][50][51][52][53][54][55][56], nanobeams [57,58], and graphene sheets [59][60][61].…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Rahmani

Jandaghian

2015

Appl. Phys. A

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In this paper, a general third-order beam theory that accounts for nanostructure-dependent size effects and two-constituent material variation through the nanobeam thickness, i.e., functionally graded material (FGM) beam is presented. The material properties of FG nanobeams are assumed to vary through the thickness according to the power law. A detailed derivation of the equations of motion based on Eringen nonlocal theory using Hamilton's principle is presented, and a closedform solution is derived for buckling behavior of the new model with various boundary conditions. The nonlocal elasticity theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The proposed model is efficient in predicting the shear effect in FG nanobeams by applying third-order shear deformation theory. The proposed approach is validated by comparing the obtained results with benchmark results available in the literature. In the following, a parametric study is conducted to investigate the influences of the length scale parameter, gradient index, and length-to-thickness ratio on the buckling of FG nanobeams and the improvement on nonlocal third-order shear deformation theory comparing with the classical (local) beam model has been shown. It is found out that length scale parameter is crucial in studying the stability behavior of the nanobeams.

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Section: Introductionmentioning

confidence: 99%

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Rahmani

Jandaghian

2015

Appl. Phys. A

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“…Recently, the nonlocal continuum theory, which assumes that the stress tensor at any point is dependent on the whole strain field of the continuum, is widely used to characterize the small-scale effects of CNTs. This theory was firstly proposed by Eringen (1972) and was successfully used in solving the vibration (De Rosa and Lippiello 2017;Deng and Yang 2014;Ebrahimi and Nasirzadeh 2015;Hu et al 2012;Kiani 2013a, b;Xia and Wang 2010;Zhen et al 2011), wave propagation (Aydogdu 2014;Huang et al 2013;Narendar and Gopalakrishnan 2010;Narendar et al 2012;Wang et al 2006Wang et al , 2013Wang et al , 2015, and buckling (Adali 2008;Amara et al 2010;Khademolhosseini et al 2010;Robinson and Adali 2016;Setoodeh et al 2011) problems of CNTs. Several different nonlocal continuum theories, such as the nonlocal Euler-Bernoulli beam (Setoodeh et al 2011;Wang et al 2015;Zhen et al 2011), nonlocal Timoshenko beam (De Rosa and Lippiello 2017;Narendar and Gopalakrishnan 2010;Xia and Wang 2010), and nonlocal shell (Khademolhosseini et al 2010) theory, were adopted to study the mechanical behaviors of CNTs, in particular, because the CNT comprises a sheet of carbon atoms, which makes it perfect a candidate for nanocontainers to store gases and for nanotubes to convey fluids (Ansari et al 2016;Bahaadini and Hosseini 2016;SafarPour and Ghadiri 2017).…”

Section: Introductionmentioning

confidence: 99%

Flexural wave propagation in fluid-conveying carbon nanotubes with system uncertainties

Liu

2017

Microfluid Nanofluid

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Many studies have reported that the material properties of carbon nanotubes (CNTs) show a wide range and exhibit a great of uncertainties. The uncertainty, in turn, will affect the physical behaviors of CNTs. In this paper, an iterative algorithm-based interval analysis method is proposed to deal with the flexural wave propagation characteristics of fluid-conveying CNTs with system uncertainties. To make the conclusion more objective, the properties of the material and fluid are all considered as uncertain-but-bounded parameters, which can effectively describe the uncertainties where few data are available to perform the probabilistic analysis. The upper and lower bounds of the wave dispersion curves are predicted to clarify the influences of the uncertain material and fluid properties on the wave propagation behaviors of fluidconveying CNTs. It is demonstrated that the widths of the wave frequency and phase velocity behave different at different wavelengths. Besides, the bounds predicted by the probabilistic model are given to verify the present model, and the present model is also validated by comparing with the Monte Carlo simulation. The present model provides some useful guides for using CNTs to convey fluid flows.

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“…In the nonlocal elasticity theory proposed by Eringen [1], to account for scale effect it is assumed that the stress at a point is a function of strains at all points in the continuum. A large number of studies related with static [5,6], buckling [7][8][9][10][11][12] and vibration [13][14][15][16][17][18][19][20] analysis of nanostructures using Eringen's nonlocal elasticity theory can be found in literature.…”

Section: Introductionmentioning

confidence: 99%

Yerel Olmayan Şekil Değiştirme Gradyanı Teorisi Kullanılarak Elastik Zemine Gömülü Nano Çubuğun Eksenel Titreşim Analizi

Şi̇mşek¹

2016

Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi

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Size-dependent axial vibration of a nanorod embedded in elastic medium is studied for the first time in this paper within the framework of the nonlocal strain gradient theory. The governing equation of motion of the problem is derived using the equilibrium condition and it is solved analytically to obtain the exact expression of vibration frequency for a fixed-fixed nanorod. The influences of the nonlocal parameter, the material length scale parameter and the elastic medium coefficient on the free vibration frequencies are investigated in detail. The results show that free vibration frequencies are significantly dependent on the size effects, and the size effects gain more importance at higher modes. Therefore, the classical continuum theory is inappropriate to investigate the mechanical behavior of nanostructures.Keywords: Nanotechnology, Vibration, Nonlocal elasticity theory, Strain gradient theory, Nanorod Yerel Olmayan Şekil Değiştirme Gradyanı Teorisi Kullanılarak Elastik Zemine Gömülü Nano Çubuğun Eksenel Titreşim Analizi ÖzetElastik zemine gömülü bir nano çubuğun boyut etkisine bağlı eksenel titreşimi yerel olmayan şekil değiştirme gradyanı teorisi çerçevesinde ilk olarak bu çalışmada incelenmiştir. Probleme ait yönetici hareket denklemi denge şartı kullanılarak çıkarılmış, iki ucu ankastre nano çubuğun serbest titreşim frekansına ait kesin ifadeyi elde etmek için yönetici denklem analitik olarak çözülmüştür. Yerel olmayan parametre, malzeme uzunluk ölçek parametresi ve elastik zemin parametresinin serbest titreşim frekansları üzerindeki etkisi detaylı olarak incelenmiştir. Elde edilen sayısal sonuçlar göstermiştir ki; serbest titreşim frekansları boyut etkisine önemli derecede bağlıdır ve boyut etkisi yüksek modlarda daha çok önem kazanmaktadır. Bu nedenlerden dolayı, klasik sürekli ortamlar mekaniği nano ölçekteki yapıların analizi için uygun değildir.

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Variational principles for multi-walled carbon nanotubes undergoing buckling based on nonlocal elasticity theory

Cited by 108 publications

References 32 publications

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Flexural wave propagation in fluid-conveying carbon nanotubes with system uncertainties

Yerel Olmayan Şekil Değiştirme Gradyanı Teorisi Kullanılarak Elastik Zemine Gömülü Nano Çubuğun Eksenel Titreşim Analizi

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