Buckling of double-walled carbon nanotubes modeled by solid shell elements

Wang, Chen; Q, Y.; Zhang, Yingyan; Ang, Kok Keng

doi:10.1063/1.2202108

Cited by 35 publications

(34 citation statements)

References 40 publications

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“…Such factors include thermal effects [25,[32][33][34], the defects of CNTs [25][26][27]32], the initial stresses [31] and the constraints on the two ends of CNTs [29][30]31]. Interesting phenomena have been observed, such as the negative Poisson ratio of defective single wall CNTs (SWCNTs) [26] and the variation of buckling modes due to the switch of the end constraints on multiwall CNTs (MWCNTs) [30].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, the interest of the mechanics of CNTs has been transferred from their fundamental behaviours to the effect of internal and external factors on the elastic properties [24][25][26], buckling [27][28][29][30] and vibration [31] of CNTs. Such factors include thermal effects [25,[32][33][34], the defects of CNTs [25][26][27]32], the initial stresses [31] and the constraints on the two ends of CNTs [29][30]31].…”

Section: Introductionmentioning

confidence: 99%

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Low frequency vibration of multiwall carbon nanotubes with heterogeneous boundaries

Chowdhury¹,

Wang²,

Adhikari³

2010

J. Phys. D: Appl. Phys.

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Heterogeneous end constraints are imposed on multiwall carbon nanotubes (MWCNTs) by sequentially clamping one end of their originally simply supported constituent tubes. The finite element method is employed to study the vibration of such MWCNTs with an emphasis on the effect of the mixed boundary conditions. The results show that the clamping process constantly enhances the dynamic stiffness of MWCNTs, which leads to substantial frequency increase up to 50% and in some cases, the transformation of the fundamental vibration mode. In particular, the vibration frequency is always found to be most sensitive to fixing the outermost tubes, showing the critical role of this individual tube in determining the structural stiffness of the whole MWCNTs as a coupled system.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Low frequency vibration of multiwall carbon nanotubes with heterogeneous boundaries

Chowdhury¹,

Wang²,

Adhikari³

2010

J. Phys. D: Appl. Phys.

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“…The behaviors and material properties of CNTs using either or continuum mechanics modeling or atomistic modeling have been conducted in Wang et al [8]. For the analysis of CNTs, when compared to continuum mechanics modeling, atomistic modeling is an easy approach and relatively inexpensive.…”

Section: Introductionmentioning

confidence: 99%

Vibrational Behavior of Single-Walled Carbon Nanotubes Based on Donnell Shell Theory Using Wave Propagation Approach

Hussain¹

2018

Novel Nanomaterials - Synthesis and Applications

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This chapter is concerned with the vibration analysis of single-walled carbon nanotubes (SWCNTs). This analysis is based on the Donnell thin shell theory. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in SWCNTs. The axial modal dependence is measured by the complex exponential functions implicating the axial modal numbers. Vibration frequency spectra are gained and evaluated for physical parameter like length-to-diameter ratios. The dimensionless frequency is also investigated in armchair and zigzag SWCNTs with in-plane rigidity and mass density per unit lateral area for armchair and zigzag SWCNTs. These frequencies of the SWCNTs are computed with the aid of the computer software MATLAB. These results are compared with those obtained using molecular dynamics (MD) simulation and the results are somewhat in agreement.

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“…For a short MWNT, the above relation is applicable for the outmost layer of the tube because the inter-layer interaction of MWNTs is very small. 200 It has also been investigated by atomic-scale finite element method, 188,189,190,198 molecular dynamics method, 40,192,193,194,199 and nanoindent experiment. 201,202 It is found that the tube displays indeed the shell-like buckling behavior as the right-handed side of Eq.…”

mentioning

confidence: 99%

“…The value of α depends on the boundary conditions of the carbon nanotube. This relation has been investigated by atomicscale finite element method 188,189,190 and molecular dynamics method or ab initio calculations. 191,192,193,194,195 The basic numerical result is that the tube exhibits rod-like buckling behavior as the right-handed side of Eq.…”

mentioning

confidence: 99%

Elastic Theory of Low-Dimensional Continua and Its Applications in Bio- and Nano-Structures

Tu¹,

Ouyang²

2008

Jnl of Comp & Theo Nano

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This review presents the elastic theory of low-dimensional (one-and two-dimensional) continua and its applications in bio-and nano-structures.First, the curve and surface theory, as the geometric representation of the low-dimensional continua, is briefly described through Cartan moving frame method. The elastic theory of Kirchhoff rod, Helfrich rod, bending-soften rod, fluid membrane, and solid shell is revisited. The free energy density of the continua, is constructed on the basis of the symmetry argument. The fundamental equations can be derived from two kinds of viewpoints: the bottom-up and the top-down standpoints. In the former case, the force and moment balance equations are obtained from Newton's laws and then some constitute relations are complemented in terms of the free energy density. In the latter case, the fundamental equations are derived directly from the variation of the free energy. Although the fundamental equations have different forms obtained from these two viewpoints, several examples reveal that they are, in fact, equivalent to each other.Secondly, the application and availability of the elastic theory of low-dimensional continua in bio-structures, including short DNA rings, lipid membranes, and cell membranes, are discussed. The kink stability of short DNA rings is addressed by using the theory of Kirchhoff rod, Helfrich rod, and bending-soften rod. The lipid membranes obey the theory of fluid membrane. The shape equation and the stability of closed lipid vesicles, the shape equation and boundary conditions of open lipid vesicles with free edges as well as vesicles with lipid domains, and the adhesions between a vesicle and a substrate or another vesicle are fully investigated. A cell membrane is simplified as a composite shell of lipid bilayer and membrane skeleton, which is a little similar to the solid shell. The equations to describe the in-plane strains and shapes of cell membranes are obtained. It is found that the membrane skeleton enhances highly the mechanical stability of cell membranes.Thirdly, the application and availability of the elastic theory of low-dimensional continua in nanostructures, including graphene and carbon nanotubes, are discussed. A revised Lenosky lattice model is proposed based on the local density approximation. Its continuum form up to the second order terms of curvatures and strains is the same as the free energy of 2D solid shells. The intrinsic roughening of graphene and several typical mechanical properties of carbon nanotubes are revisited and investigated based on this continuum form. It is possible to avoid introducing the controversial concepts, the Young's modulus and thickness of graphene and single-walled carbon nanotubes, with this continuum form.

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Buckling of double-walled carbon nanotubes modeled by solid shell elements

Cited by 35 publications

References 40 publications

Low frequency vibration of multiwall carbon nanotubes with heterogeneous boundaries

Low frequency vibration of multiwall carbon nanotubes with heterogeneous boundaries

Vibrational Behavior of Single-Walled Carbon Nanotubes Based on Donnell Shell Theory Using Wave Propagation Approach

Elastic Theory of Low-Dimensional Continua and Its Applications in Bio- and Nano-Structures

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