RETRACTED: Surface and shear effects on spatial buckling of initially twisted nanowires

Abstract

The buckling behavior of nanowires (NWs) has been of focus of attention of the applied mechanics community during the past decade; however, their spatial buckling under the action of both axial force and twisting moment has not been methodically formulated yet. To bridge this scientific gap, the authors eagerly investigate the problem accounting for surface energy based on the Euler–Bernoulli and Timoshenko beam theories. By exploiting these inclusive models, the governing equations are established and solved by the reproducing kernel particle method (RKPM). For simply supported NWs, an exact solution and assumed modes approach (AMA) are also developed. Expectantly, a reasonably good match between the results attained by the RKPM and those of the AMA is achieved. The unstable conditions of the NW under severe axial forces and twisting moments are identified both analytically and numerically for the first time. The influences of the length and radius of the NW on the buckling behavior of the nanostructure are then discussed, and the critical roles of shear deformation and surface energy are methodically displayed and discussed.