Nonlocal and shear effects on column buckling of single-layered membranes from stocky single-walled carbon nanotubes

Axial buckling behavior of single-layered membranes from vertically aligned single-walled carbon nanotubes is studied in the context of the nonlocal continuum theory of Eringen. To this end, useful discrete models based on the nonlocal Rayleigh, Timoshenko, and higher-order beam theories are developed to evaluate critical buckling loads associated with both in-plane and out-of-plane buckling modes. In discrete models, the size of the eigenvalue equations to be solved drastically magnifies for highly populated membranes. Thereby, development of models whose computational efforts do not affected by the population of the membrane is of great advantageous. To bridge this scientific gap, appropriate nonlocal continuous models are established based on the developed discrete models. The accuracy of the proposed discrete and continuous models is checked and remarkable results are achieved. Subsequently, the roles of the influential factors on both in-plane and out-of-plane axial buckling loads are addressed. The obtained results can be regarded as a basic step in examining of axial buckling mechanisms of more complex systems consist of multi-layered membranes from parallel or even orthogonal single-walled carbon nanotubes.