Spatially nonlocal instability modeling of torsionaly loaded nanobeams

Abstract

Various aspects of buckling of nanobeams have been explored; nevertheless, instability and spatial buckling of these tiny elements under the concurrent action of longitudinal load and torsional moment have not yet been displayed using nonlocal continuum mechanics. To fill this crucial research gap, herein, we are interested in methodically examining this critical phenomenon. Aiming at this goal, suitable nonlocal beam models are established and the deformation equations are constructed accounting for the nonlocality. In order to assess the critical buckling response, a Galerkin-based meshless approach is developed and spatially nonlocal buckling behavior of torsionally loaded nanobeams is inclusively addressed. The nonlocal unstable regions associated with the spatially buckled nanobeam for various nonlocality and geometry data are specified for the first time and the critical roles of nonlocality and shear deformation on them are carefully revealed and discussed. In the presence of applied torsional moments, the concept of the critical lateral and longitudinal dimensions of the nanostructure is also introduced.