Thermal Buckling Analysis of Multi-Walled Carbon Nanotubes Through a Nonlocal Shell Theory Incorporating Interatomic Potentials

2013 ◽  
Vol 36 (1) ◽  
pp. 56-70 ◽  
Author(s):  
R. Ansari ◽  
A. Shahabodini ◽  
H. Rouhi ◽  
A. Alipour
Keyword(s):  
Carbon Nanotubes ◽  
Shell Theory ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Interatomic Potentials ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

Thermal Buckling of Multi-Walled Carbon Nanotubes by Nonlocal Elasticity

2006 ◽  
Vol 74 (3) ◽  
pp. 399-405 ◽  
Author(s):  
Renfu Li ◽  
George A. Kardomateas
Keyword(s):  
Carbon Nanotubes ◽  
Thermal Loading ◽  
Scale Effects ◽  
Elastic Shell ◽  
Thermal Buckling ◽  
Small Scale ◽  
Internal Length ◽  
Internal Characteristic ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes

The small internal length scales of nanomaterials/nano-devices may call the direct application of classical continuum models into question. In this research, a nonlocal elastic shell model, which takes the small scale effects into account, is developed to study the thermal buckling behavior of multi-walled carbon nanotubes. The multi-walled carbon nanotubes are considered as concentric thin shells coupled with the van der Waals forces between adjacent nanotubes. Closed form solutions are formulated for two types of thermal buckling of a double-walled carbon nanotube: Radial thermal buckling (as in a shell under external pressure) and axial thermal buckling. The effects of small scale effects are demonstrated, and a significant influence of internal characteristic parameters such as the length of the C‐C bond has been found on the thermal buckling critical temperature. The study interestingly shows that the axial buckling is not likely to happen, while the “radial” buckling may often take place when the carbon nano-tubes are subjected to thermal loading. Furthermore, a convenient method to determine the material constant, “e0” and the internal characteristic parameter, “a,” is suggested.

Beam equations for multi-walled carbon nanotubes derived from Flügge shell theory

2009 ◽  
Vol 465 (2104) ◽  
pp. 1199-1226 ◽  
Author(s):  
Tsuneo Usuki ◽  
Kiyoshi Yogo
Keyword(s):  
Carbon Nanotubes ◽  
Shell Theory ◽  
Beam Theory ◽  
Velocity Curve ◽  
Radial Coordinate ◽  
Surrounding Matrix ◽  
Longitudinal Coordinate ◽  
Multi Walled Carbon Nanotubes ◽  
Walled Carbon Nanotubes ◽  
Non Locality

The Flügge shell theory is frequently used for the analysis of carbon nanotubes (CNTs) due to the relatively accurate results it provides in spite of its theoretical simplicity. Based on the Flügge shell theory, a tubular beam theory was established by considering non-locality. In order to convert a cylindrical shell theory for a curved plate per unit width into a tubular beam theory by contour integration, the longitudinal coordinate that passes through the centre of the circular contour was defined, and, based on this, the radial coordinate was defined. In this way, a generalized beam theory (GBT) was obtained as a further refined form of the Flügge theory. This GBT coincides with the Flügge theory, if the refined form and the non-locality are ignored. After obtaining the phase-velocity curve and the group-velocity curve with respect to single- to triple-walled CNTs, the influences of multiplicity, reduction of the plate-bending stiffness and the stiffness of the surrounding matrix were investigated.

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