Stability analysis of carbon nanotubes based on a novel beam model and its comparison with Sanders shell model and molecular dynamics simulations

Hosseini-Ara, Reza; Mirdamadi, Hamid Reza; Khademyzadeh, Hassan; Mostolizadeh, R.

doi:10.1590/s1678-58782012000200004

Cited by 4 publications

(5 citation statements)

References 21 publications

(17 reference statements)

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“…HosseiniAra@pnu.ac.ir For this end, Peddieson et al [8] for the first time developed a nonlocal Euler-Bernoulli beam model to study the nonlocal effects on the static behavior of micro-and nanobeams. Then, many researchers investigated small-length scale effects on buckling analysis of nano-beams using nonlocal theory [2,[9][10][11][12][13]. Also, Sudak [14] and Zhang et al [15] investigated the small-length scale effects on buckling of multi-walled carbon nanotubes (MWCNT).…”

Section: And Reza Hosseini-aramentioning

confidence: 99%

See 1 more Smart Citation

Nano-scale effects on nonlocal boundary conditions for exact buckling analysis of nano-beams with different end conditions

Hosseini-Ara

2018

J Braz. Soc. Mech. Sci. Eng.

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This paper presents a mathematical approach for applying the nano-scale effects on higher-order nonlocal boundary conditions for exact buckling strains of nano-beams based on a modified nonlocal Timoshenko beam theory (MNTBT) for various end conditions. Researchers usually neglect these higher-order boundary conditions in their analysis. Hence, the strain gradient approach and variational method are implemented in MNTBT for deriving these higher-order boundary conditions and exact closed-form critical buckling strains for different end conditions. On this basis, exact numerical results are presented for buckling analysis of single-walled carbon nanotubes (SWCNTs). It is investigated that nonlocal boundary conditions have the effect of reducing the critical buckling strains. This effect is the most significant for doubly clamped nano-beams and the least significant for cantilever nano-beams. Furthermore, it is shown that presented model based on higher-order nonlocal boundary conditions can capture correctly the length-dependent buckling strains of SWCNTs as compared with the other nonlocal beam theories. Finally, the results are compared with molecular dynamics simulations and the Eringen's nonlocal coefficient (e 0) is calibrated for buckling problems of SWCNTs with good accuracy as compared with literatures. Keywords Nonlocal boundary conditions Á Nano-scale effect Á Buckling Á Nano-beams Á Single-walled carbon nanotubes

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Section: And Reza Hosseini-aramentioning

confidence: 99%

“…Substituting the nonlocal shear force and bending moment defined in Eqs. (9) and (10) into the governing Eqs. (25) and (28) and eliminating / from these two equations, the transverse equilibrium equation in terms of lateral displacement for an axially loaded beam using a nonlocal strain gradient theory is obtained as…”

Section: Governing Equationsmentioning

confidence: 99%

Nano-scale effects on nonlocal boundary conditions for exact buckling analysis of nano-beams with different end conditions

Hosseini-Ara

2018

J Braz. Soc. Mech. Sci. Eng.

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“…Evidently, when the scale parameter is set equal to zero in Equations the well‐known relations in the classical theory are obtained. Also, it can be seen from Equations that in DM the effect of the scale parameter in the axial and shear stresses is different while in the strain gradient theory the scale parameter is the same for both the axial and shear stresses …”

Section: Bending Of Timoshenko Nanobeamsmentioning

confidence: 99%

Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

2018

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By taking the effect of the scale parameter explicitly into account, bending behavior of Euler‐Bernoulli and Timoshenko nanobeams is studied using doublet mechanics. In addition, the effect of chirality on the softening or hardening behavior of an Euler‐Bernoulli nanobeam in bending is studied by taking the effect of the chiral angle explicitly into account. For the bending of the Timoshenko nanobeam the effect of the scale parameter and chirality on the axial and shear stresses is studied and the results are compared with the gradient and Eringen‐like models. It is shown that as the chiral angle increases, a simply supported Timoshenko nanobeam under a uniform loading changes from a softening to a hardening nanobeam indicating that chirality has a pronounced effect on the bending response of the nanobeams.

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“…Recently, nanotechnology has presented a new field of applied sciences which deals with the mechanical analysis of the micro-and nanolength scale structures [1][2][3][4][5][6][7][8][9]. Among these, nanotubes and nanorings are the most applicable nanostructures which can play an important role for different applications [10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Lateral buckling analysis of nanotubes and nanorings under uniform external pressure: a closed-form nonlocal solution

Hosseini-Ara

Kashi

Toghraie

2021

J Braz. Soc. Mech. Sci. Eng.

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This study presents a modified cylindrical shell theory to predict the critical lateral buckling of both nanotubes and nanorings under uniform external pressure. To this end, nonlocal elasticity theory is incorporated into Donnell's cylindrical shell model and closed-form critical lateral buckling solutions for different nanotubes and nanorings are derived from the coupled displacement equations. In this regard, a novel method is presented for decoupling the displacement equations to facilitate the derivation of the equations and results. Also, the effects of nonlocal parameter, aspect ratio, and mode numbers are investigated for lateral buckling of short and long nanotubes as well as nanorings. Results show that increasing the nonlocal effects, aspect ratio, and mode numbers of the nanotubes can reduce the value of the critical lateral pressure. Finally, the numerical results are compared with existing literature and show good agreement. The results of the new model are more accurate to capture the size effects for nanotubes and nanorings. These findings are useful for designing nanoscale devices.

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Stability analysis of carbon nanotubes based on a novel beam model and its comparison with Sanders shell model and molecular dynamics simulations

Cited by 4 publications

References 21 publications

Nano-scale effects on nonlocal boundary conditions for exact buckling analysis of nano-beams with different end conditions

Nano-scale effects on nonlocal boundary conditions for exact buckling analysis of nano-beams with different end conditions

Doublet mechanical analysis of bending of Euler‐Bernoulli and Timoshenko nanobeams

Lateral buckling analysis of nanotubes and nanorings under uniform external pressure: a closed-form nonlocal solution

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