Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction

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On the modeling of carbon nanotubes: A critical review (2014, neutral): “[108] 2005 – Continuum cylindrical shell – – – – Establishing an algorithm for buckling”
Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model (2012, background): “c is the vdW-interaction coefficient between the inner and outer nanotubes, which can be estimated from the Lennard–Jones potential [24]:”
On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: equilibrium, governing equation and static deflection (2010, methodology): “The most common atomic modelling method is the molecular dynamics (MD) method [ 4-6 ] .A s the MD method considers each individual molecule and its multiple mechanical or chemical web-interactions, its use requires extremely fast computing facilities and thence it is largely confined to relatively r”
Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes (2008, positive): “…pk on tube k is given as follows: p1 ¼ c12ðo1 o2Þ and p2 ¼ c21ðo2 o1Þ, (4) where cij (i, j ¼ 1, 2) is the vdW interaction coefficient, which is estimated as (He et al., 2005) cij ¼ 1001p s12 3a4 E13ij 1120p s6 9a4 E7ij Rj, (5) where Emij ¼ ðRj þ RiÞ m Z p=2 0 dy ½1 Kij cos2 y m=2 (6) and Kij ¼…”