Spatial buckling analysis of current-carrying nanowires in the presence of a longitudinal magnetic field accounting for both surface and nonlocal effects

In this paper, three-dimensional buckling behavior of nanowires was investigated based on Eringen's Nonlocal Elasticity Theory. The electric current-carrying nanowires were affected by a longitudinal magnetic field based upon the Lorentz force. The nanowires (NWs) were modeled based on Timoshenko beam theory and the Gurtin-Murdoch's surface elasticity theory. Generalized Differential Quadrature (GDQ) method was used to solve the governing equations of the NWs. Two sets of boundary conditions namely simple-simple and clamped-clamped were applied and the obtained results were discussed. Results demonstrated the effect of electric current, magnetic field, small-scale parameter, slenderness ratio, and nanowires diameter on the critical compressive buckling load of nanowires. As a key result, increasing the small-scale parameter decreased the critical load. By the same token, increasing the electric current, magnetic field, and slenderness ratio resulted in a decrease in the critical load. As the slenderness ratio increased, the effect of nonlocal theory decreased. In contrast, by expanding the NWs diameter, the nonlocal effect increased. Moreover, in the present article, the critical values of the magnetic field of strength and slenderness ratio were revealed, and the roles of the magnetic field, slenderness ratio, and NWs diameter on higher buckling loads were discussed.