Buckling behavior of SWCNTs and MWCNTs resting on elastic foundations using an optimization technique
This paper aims to investigate the buckling behavior of multi walled carbon nanotubes (MWCNTs) and single walled carbon nanotubes (SWCNTs) embedded in an elastic medium using the nonlocal cylindrical shell theory. The SWCNT is treated as a cylindrical shell and MWCNT is considered as multiple SWCNTs nested inside one another, they interact with each other via van der Waals interactions. The interaction between the matrix and the outer wall is modeled as a foundation using Winkler, Pasternak, and Kerr models. An optimization technique is developed to estimate the nonlocal critical buckling load of SWCNT and MWCNT. Furthermore, analytical formulas are proposed to describe the buckling behavior of SWCNTs embedded in an elastic medium without taking into account the effects of the nonlocal parameter. In the proposed formulas, van der Waals interactions between adjacent tubes and the effect of terms involving tube radii differences are taken into account, although they are generally neglected in expressions published in the literature. The effects of the number of layers, the nonlocal parameter, and the elastic foundation parameters are investigated. Moreover, the effects of different parameters on the stability behavior of the carbon nanotubes are also discussed.