Stability of single-walled carbon nanotubes and single-walled carbon nanocones under self-weight and an axial tip force

Poorly designed structures buckle under the action of an unbearable axial force, self-weight or a combination of different axial forces. The increasing exploration of nanostructures for future devices dictates that the buckling of uniform single-walled carbon nanotubes (SWCNTs) and single-walled carbon nanocones (SWCNCs) should be well studied. Therefore in this paper, the investigation of the boundary value problems associated with the buckling of the SWCNTs and SWCNCs is carried out. The theoretical formulation of the mathematical model for these nanostructures is premised on the newly advanced nonlocal continuum theory. Predictions of the nN range critical loads of SWCNT and SWCNT under self-weight and an axial tip force are carried out with an optimized variant of the Galerkin method. The analysis reveals the degree of influence of the nonlocal parameter on the critical loads of the SWCNTs and the SWCNCs under different boundary conditions. A non-monotonically increasing trend is observed between the critical load values and increasing aspect ratio of the SWCNT. In the case of the SWCNC, the analysis reveals a positive linear relationship between the critical loads and the apex angles of the SWCNC. The apex angle also acts as a counterbalance to the small-scale coefficient.