Nanoscale vibration and buckling of single-walled carbon nanotubes using the meshless local Petrov–Galerkin method

Abstract

The meshless local Petrov–Galerkin (MLPG) method is implemented to analyze the free vibration and axial buckling characteristics of single-walled carbon nanotubes (SWCNTs) with different boundary conditions. To this end, a nonlocal shell model accounting for the small scale effect is used. In the theoretical formulations, a variational form of the Donnell shell equations is constructed over a local sub-domain which leads to derivation of the mass, stiffness and geometrical stiffness matrices. Comprehensive results for the resonant frequencies and critical axial buckling loads of SWCNTs are presented. The influences of boundary conditions, nonlocal parameter and geometrical parameters on the mechanical behavior of SWCNTs are fully investigated. The results obtained from the present numerical scheme are shown to be in good agreement with those from exact solution for simply-supported SWCNTs and those of molecular dynamics simulations. It is shown that the natural frequencies and critical axial buckling loads of SWCNTs are strongly dependent on the small scale effect and geometrical parameters.