Comments on nonlocal effects in nano-cantilever beams

In nonlocal elasticity theory, it is still unclear that whether the nonlocal effect exists or not in the bending of a nano-cantilever beam subjected to a concentrated force at the free end, and whether the equivalent stiffness of nanostructures weakens or strengthens than that predicted by classical theory. Based on the two-dimensional differential constitutive relations of nonlocal elasticity in the plane-stress state, this work derived the governing equation of nanobeams by introducing certain simplifying assumptions. The equation was then applied to the nano-cantilever beam subjected to several typical external forces, and the nonlocal effect on the bending behavior was thus revealed. Moreover, a different solution methodology was proposed in Appendix A to further verify the two-dimensional analyses in the text. It is shown that while nonlocal effect does not show up in the nano-cantilever beam subjected to a concentrated force only, the bending of the beam subjected to general transverse distributed loads is significantly influenced by the nonlocal scale effect factor. It is also demonstrated that the equivalent stiffness of a nanostructure predicted by the nonlocal theory may be larger or smaller than that by the classical theory, depending on the category of applied loads. Results reported in this study could be useful for designing or optimizing nano-electro-mechanical systems (NEMS) where the nano-cantilever beam acts as a basic component.