Scale Coefficient, Length, Mode and Radius Effect on Critical Axial Compressed Buckling Load of Carbon Nanotubes via Nonlocal Continuum Model

2012 ◽  
Vol 629 ◽  
pp. 296-301
Author(s):  
Hong Liang Tian
Keyword(s):  
Carbon Nanotubes ◽  
Continuum Model ◽  
Elastic Shell ◽  
Elastic Beam ◽  
Analytic Solutions ◽  
Buckling Load ◽  
Beam Model ◽  
Mechanical Behaviors ◽  
Nonlocal Beam ◽  
Scale Coefficient

Some exact concise analytic solutions of critical axial compressed buckling load for carbon nanotubes are derived via nonlocal beam. Scale coefficient, length, mode and radius effect on nonlocal critical axial compressed buckling load of CNTs is established and can be analyzed in terms of the general solutions. Radius effect on nonlocal critical axial compressed buckling load is only found through nonlocal elastic shell model but not derived via nonlocal elastic beam model. Numerical calculations of CNTs show that local critical axial compressed buckling load through local elastic theory is overestimated. Scale coefficient, length, mode and radius effect should be taken into account in predicting more accurate results for mechanical behaviors of CNTs via continuum model.

Critical Buckling Load of Triple-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory

2020 ◽  
Vol 62 ◽  
pp. 108-119
Author(s):  
Tayeb Bensattalah ◽  
Ahmed Hamidi ◽  
Khaled Bouakkaz ◽  
Mohamed Zidour ◽  
Tahar Hassaine Daouadji
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Axial Compression ◽  
Buckling Load ◽  
Small Scale ◽  
Beam Model ◽  
Buckling Loads ◽  
Critical Buckling Load ◽  
Nonlocal Continuum Theory ◽  
Walled Carbon Nanotubes

The present paper investigates the nonlocal buckling of Zigzag Triple-walled carbon nanotubes (TWCNTs) under axial compression with both chirality and small scale effects. Based on the nonlocal continuum theory and the Timoshenko beam model, the governing equations are derived and the critical buckling loads under axial compression are obtained. The TWCNTs are considered as three nanotube shells coupled through the van der Waals interaction between them. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, a significant dependence of the critical buckling loads on the chirality of zigzag carbon nanotube is confirmed, and these are then compared with: A single-walled carbon nanotubes (SWCNTs); and Double-walled carbon nanotubes (DWCNTs). These findings are important in mechanical design considerations and reinforcement of devices that use carbon nanotubes.

EFFECT OF THE VAN DER WAALS INTERACTION ON ANALYSIS OF DOUBLE-WALLED CARBON NANOTUBES

2005 ◽  
Vol 05 (03) ◽  
pp. 457-474 ◽  
Author(s):  
Q. WANG
Keyword(s):  
Carbon Nanotubes ◽  
Van Der Waals ◽  
Elastic Beam ◽  
Beam Model ◽  
Mechanical Models ◽  
Parametric Studies ◽  
Kink Instability ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Vdw Interaction

This paper presents the research on the analysis of the van der Waals (vdW) interaction on double-walled carbon nanotubes (DWNTs) via an elastic beam model. The parametric studies on the size of DWNTs are conducted to show the effect of vdW interaction on the analysis of both a cantilever DWNT subjected to force at the free tip and a DWNT subjected to pure bending. In addition, the kink instability for the cantilever DWNT is analyzed based on the proposed beam model. It is hoped that the research will provide mechanical models for the analysis of both single-walled nanotubes (SWNTs) and multi-walled nanotubes (MWNTs), as well as for kink instability analysis of carbon nanotubes (CNTs).

Nonlocal Flügge Shell Model for Vibrations of Double-Walled Carbon Nanotubes With Different Boundary Conditions

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
R. Ansari ◽  
B. Arash
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Shell Model ◽  
Scale Effects ◽  
Elastic Shell ◽  
Small Scale ◽  
Geometrical Parameters ◽  
Beam Model ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

In this paper, the vibrational behavior of double-walled carbon nanotubes (DWCNTs) is studied by a nonlocal elastic shell model. The nonlocal continuum model accounting for the small scale effects encompasses its classical continuum counterpart as a particular case. Based upon the constitutive equations of nonlocal elasticity, the displacement field equations coupled by van der Waals forces are derived. The set of governing equations of motion are then numerically solved by a novel method emerged from incorporating the radial point interpolation approximation within the framework of the generalized differential quadrature method. The present analysis provides the possibility of considering different combinations of layerwise boundary conditions. The influences of small scale factor, layerwise boundary conditions and geometrical parameters on the mechanical behavior of DWCNTs are fully investigated. Explicit expressions for the nonlocal frequencies of DWCNTs with all edges simply supported are also analytically obtained by a nonlocal elastic beam model. Some new intertube resonant frequencies and the corresponding noncoaxial vibrational modes are identified due to incorporating circumferential modes into the shell model. A shift in noncoaxial mode numbers, not predictable by the beam model, is also observed when the radius of DWCNTs is varied. The results generated also provide valuable information concerning the applicability of the beam model and new noncoaxial modes affecting the physical properties of nested nanotubes.

CONTINUUM MODEL FOR STABILITY ANALYSIS OF CARBON NANOTUBES UNDER INITIAL BEND

2005 ◽  
Vol 05 (04) ◽  
pp. 579-595 ◽  
Author(s):  
Q. WANG ◽  
F. XU ◽  
G. Y. ZHOU
Keyword(s):  
Carbon Nanotubes ◽  
Stability Analysis ◽  
Theoretical Analysis ◽  
Current Model ◽  
Local Buckling ◽  
Elastic Beam ◽  
Beam Model ◽  
Kink Instability ◽  
Critical Axial Force ◽  
Double Wall

Stability analysis of carbon nanotubes (CNT) under initial bend is conducted using continuum elastic beam models for both single wall nanotube (SWNT) and double wall nanotube (DWNT). A discrete beam model is proposed for simulating the mechanism of kink instability, a local buckling phenomenon, of CNTs. Theoretical analysis of the critical axial load for kink instability is carried out with the elastic beam model. Based on the theoretical analysis, the size effect of CNTs on the critical axial force is studied. By setting the initial bend to be zero, the current model can be used to predict the buckling load of a straight CNT as well.

Nonlocal beam model for axial buckling of carbon nanotubes with surface effect

2012 ◽  
Vol 99 (5) ◽  
pp. 56007 ◽  
Author(s):  
Yu-Gang Sun ◽  
Xiao-Hu Yao ◽  
Ying-Jing Liang ◽  
Qiang Han
Keyword(s):  
Carbon Nanotubes ◽  
Surface Effect ◽  
Beam Model ◽  
Axial Buckling ◽  
Nonlocal Beam

Dynamical Stability Behaviors of Fluid-Conveyed Double-Walled Carbon Nanotubes

2011 ◽  
Vol 268-270 ◽  
pp. 138-142
Author(s):  
Yan Yan ◽  
Wen Quan Wang
Keyword(s):  
Carbon Nanotubes ◽  
Flow Velocity ◽  
Critical Role ◽  
Elastic Beam ◽  
Model Potential ◽  
Dynamical Stability ◽  
Beam Model ◽  
Time Histories ◽  
Double Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Based on an elastic beam model, potential flow theory and N-mode Galerkin discretization technique, the dynamical stability behaviors of fluid-conveyed double-walled carbon nanotubes (DWCNTs) considering geometry nonlinearity relating to the time as variation of the flow velocity are studied. The results show that the bifurcations happen in turn of pitchfork and Hopf types as the flow velocity increases. The vdW forces do not change the bifurcation types but make the critical velocities increase sharply. Furthermore, the vdW forces play a critical role in keeping the synchronization of the time histories of the amplitudes or the velocities of different layers of the CNTs-fluid system.

Dynamic Deflection of a Single-Walled Carbon Nanotube Under Ballistic Impact Loading

2011 ◽  
Vol 2 (4) ◽  
Author(s):  
Demetris Pentaras ◽  
Isaac Elishakoff
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Elastic Beam ◽  
Single Walled Carbon Nanotubes ◽  
Ballistic Impact ◽  
Beam Model ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Walled Carbon Nanotubes ◽  
The Relationship

The dynamic deflections of geometrically different single-walled carbon nanotubes are determined under various high-velocity impacts and for different positions at which ballistic impact is applied. Elastic beam model is applied to study the dynamic deflection of single-walled carbon nanotubes for two cases of boundary conditions, namely to clamped–clamped and clamped-free single-walled carbon nanotubes. Moreover, we examine the relationship between the single-walled carbon nanotube radius, the relative position at which the ballistic impact takes place, the speed of the object (e.g., bullet) that strikes the nanotube, and the deflection of the nanotube for a specific bullet size and shape as was used by recent study in the literature.

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