Axial buckling of multiwall carbon nanotubes with heterogeneous boundaries

Abstract

The finite element method has been employed to study the effects of different boundary conditions on the axial buckling of multiwall carbon nanotubes ͑MWCNTs͒. Unlike previous works, both homogeneous and heterogeneous end constraints are considered for the constituent tubes of various MWCNTs comprising shell-type ͑i.e., the length-to-diameter ratio L / D Ͻ 10͒, beam-type ͑i.e., L / D Ͼ 10͒, and the two different types of constituent tubes. The results show that clamping the individual tubes of simply supported or free MWCNTs exerts a variety of influences on their buckling behaviors depending on the type of the MWCNTs, the position, and the number of the clamped tubes. Clamping the outermost tube can enhance the critical buckling strain up to four times of its original value and can shift the buckling modes of those MWCNTs consisting both shelland beam-type tubes. In contrast, little difference can be observed when simply supported ends of MWCNTs are replaced by free ends or vice versa. Explicit buckling mode shapes obtained using the finite element method for various physically realistic cases have been shown in the paper.

Buckling of a Clamped-Free Double-Walled Carbon Nanotube by the Bubnov-Galerkin Method

“…Nonlocal elasticity theory was utilized by several investigators, namely by Sudak [7], Adali [8], Kumar et al [9] and Artan and Tepe [10]. Other pertinent works include those by Waters et al [11], Sears and Batra [12], Aydogdu and Ece [13], Hu et al [14], Yang et al [15], Lu et al [16], Tong et al [17], Wang et al [18], Zhang et al [19], and others. Literature reviews on the buckling of carbon nanotubes were written by Wang et al [20], and Wang et al [21].…”

Low frequency vibration of multiwall carbon nanotubes with heterogeneous boundaries

“…The end constraint on CNTs has been identified as a major external factor that exerts strong effects on the buckling of CNTs [29,30]. This issue is of practical interest because surrounding media will inevitably enforce a variety of constraints on the two ends of CNTs.…”

“…As a typical example, while the outer tube of a double wall CNT is clamped the inner tube may still be free or simply supported. To our best knowledge, such heterogeneous constraints were not considered for MWCNTs until our recent buckling analysis of MWCNTs [30]. Specifically, the vibration analysis of the MWCNTs with mixed boundary conditions still remains absent in the literature.…”

“…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].…”

“…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].…”