Column buckling of doubly parallel slender nanowires carrying electric current acted upon by a magnetic field

Axial buckling of current-carrying double-nanowire-systems immersed in a longitudinal magnetic field is aimed to be explored. Each nanowire is affected by the magnetic forces resulted from the externally exerted magnetic field plus the magnetic field resulted from the passage of electric current through the adjacent nanowire. To study the problem, these forces are appropriately evaluated in terms of transverse displacements. Subsequently, the governing equations of the nanosystem are constructed using Euler–Bernoulli beam theory in conjunction with the surface elasticity theory of Gurtin and Murdoch. Using a meshless technique and assumed mode method, the critical compressive buckling load of the nanosystem is determined. In a special case, the obtained results by these two numerical methods are successfully checked. The roles of the slenderness ratio, electric current, magnetic field strength, and interwire distance on the axial buckling load and stability behavior of the nanosystem are displayed and discussed in some detail.