Nonlocal Stress Theory for Buckling Instability of Nanotubes: New Predictions on Stiffness Strengthening Effects of Nanoscales

Applying the nonlocal elasticity theory, this paper derives new, exact nonlocal governing equations and solutions for buckling instability of thin nanotubes. The analysis predicts new nanoscale influence which strengthens the stiffness of nanotubes. Based on the fundamentals of variational energy principle, new higher-order governing differential equations are formulated and the corresponding higher-order boundary conditions first realized. The critical instability buckling loads for various types of end constraints are presented and discussed in detail. The predicted results show surprising effects of nonlocal nanoscale parameter on critical buckling loads which provides new insights into the physics of nanoscale on buckling of nanotubes based on nonlocal stress field theory. It is demonstrated that the commonly accepted equilibrium equation is not a true state of equilibrium and it could be made perfect should the nonlocal bending moment be replaced by a newly defined effective nonlocal bending moment. Qualitative comparisons with other non-nonlocal approaches including molecular dynamics simulation, strain gradients model, couple stress model and experiments justify that the stiffness enhancement conclusion as predicted by the new nonlocal stress model. Subsequently, the physical interpretation of the new effects and phenomenon of nanoscale is discussed.