Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

Malikan, Mohammad; Eremeyev, Victor A.

doi:10.1088/2053-1591/ab691c

Cited by 32 publications

(10 citation statements)

References 79 publications

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“…(23) based on the A zd A and substituting Eqs. (2) and 4into the obtained relation, the static moment stress resultants in the nonlocal state are found to be [50][51][52][53][54][55][56][57][58][59]…”

Section: Vdw Interactionmentioning

confidence: 64%

Buckling analysis of a non-concentric double-walled carbon nanotube

2020

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On the basis of a theoretical study, this research incorporates an eccentricity into a system of compressed double-walled carbon nanotubes (DWCNTs). In order to formulate the stability equations, a kinematic displacement with reference to the classical beam hypothesis is utilized. Furthermore, the influence of nanoscale size is taken into account with regard to the nonlocal approach of strain gradient, and the van der Waals interaction for both inner and outer tubes is also considered based on the Lennard–Jones model. Galerkin decomposition is employed to numerically deal with the governing equations. It is evidently demonstrated that the geometrical eccentricity remarkably affects the stability threshold and its impact is to increase the static stability of DWCNTs.

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Section: Vdw Interactionmentioning

confidence: 64%

Buckling analysis of a non-concentric double-walled carbon nanotube

2020

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“…Inserting Equation (27) into Equation (35), the moment stress resultant in nanoscale is developed as [57][58][59][60][61][62]…”

Section: Size-dependent Modelmentioning

confidence: 99%

On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

Malikan

Eremeyev

2020

Symmetry

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The fundamental motivation of this research is to investigate the effect of flexoelectricity on a piezoelectric nanobeam for the first time involving internal viscoelasticity. To date, the effect of flexoelectricity on the mechanical behavior of nanobeams has been investigated extensively under various physical and environmental conditions. However, this effect as an internal property of materials has not been studied when the nanobeams include an internal damping feature. To this end, a closed-circuit condition is considered taking converse piezo–flexoelectric behavior. The kinematic displacement of the classical beam using Lagrangian strains, also applying Hamilton’s principle, creates the needed frequency equation. The natural frequencies are measured in nanoscale by the available nonlocal strain gradient elasticity model. The linear Kelvin–Voigt viscoelastic model here defines the inner viscoelastic coupling. An analytical solution technique determines the values of the numerical frequencies. The best findings show that the viscoelastic coupling can directly affect the flexoelectricity property of the material.

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“…In [ 26 ], the second strain gradient of Mindlin merged successfully with the nonlocal theory of Eringen. This model (NSGT) was incorporated in a lot of research performed on the nanoparticles in recent years—see e.g., [ 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ] and many others—and can be a proper item at the nanoscale.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Due to being the nanobeam a size-dependent particle, the scale-dependent property should be substituted in Equations (33) and (34). In [26], the second strain gradient of Mindlin merged successfully with the nonlocal theory of Eringen.…”

Section: Mathematical Modelmentioning

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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Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method

Cited by 32 publications

References 79 publications

Buckling analysis of a non-concentric double-walled carbon nanotube

Buckling analysis of a non-concentric double-walled carbon nanotube

On the Dynamics of a Visco–Piezo–Flexoelectric Nanobeam

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

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