A mesh-free computational framework for predicting buckling behaviors of single-walled carbon nanocones under axial compression based on the moving Kriging interpolation

Abstract

This paper employs a higher-order gradient continuum theory for studying mechanical properties of single-walled carbon nanocones (SWCNCs). The SWCNC is constructed by rolling up a fan-shaped graphite sheet and connecting their two sides to form a conical structure. A mesh-free computational framework based on the moving Kriging (MK) interpolation is developed to study the buckling behaviors of SWCNCs under axial compression. Mechanical behaviors of SWCNCs with five different apex angles, i.e. 19.2°, 38.9°, 60°, 84.6° and 112.9°, are studied. Critical strains are predicted with the SWCNC subjects to uniform axial compression on the two ends. Computational results demonstrate that the apex angle has an increasing effect on the critical strain but a decreasing effect on the elastic properties (such as axial Young’s modulus) of SWCNCs. The corresponding buckling patterns reveal that a larger apex angle developed more fins on the side surface of the CNC at critical strain. For some of the CNCs, it is found that the elastic property slightly increases as the cutting tip’s length increases. Besides, a sharp-decrease of the critical strain with an increase number of fins, which approach to ripples, indicates that the CNC becomes unstable.