INVESTIGATING THE SURFACE ELASTICITY AND TENSION EFFECTS ON CRITICAL BUCKLING BEHAVIOUR OF NANOTUBES BASED ON DIFFERENTIAL TRANSFORMATION METHOD

Abstract

By considering the coupled effects of surface and nonlocal elasticity theory, the critical buckling load response of silicon/aluminium nanotubes is investigated in this paper. The nonlocal Eringen theory takes into account the effect of small scale size while the Gurtin-Murdoch model is used to incorporate the surface effects. Governing equations are derived through Hamilton’s principle. The differential transformation method (DTM) as an efficient and accurate numerical tool is employed to solve the governing equations of nanotubes subjected to different boundary conditions. The output results are compared favourably with available published works. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the nonlocal parameter, surface effect, aspect ratio, mode number and beam size on critical buckling loads of the nanotube in detail. The results show that increasing the nonlocal parameter increase the buckling ratio of the nanotubes.