Small-scale effects in nanorods

The Eringen model of nonlocal elasticity provides an effective theoretical tool to assess small-scale effects in carbon nanotubes (CNTs). A variational formulation of the nonlocal elastostatic problem is proposed in this paper. The merit of the variational treatment, over standard ones based on integration of a second-order differential equation, consists in revealing a simple basic analogy. According to this analogy, the nonlocality effect is simulated by prescribing an axial distortion linearly depending on the first derivative of the axial load intensity. The nonlocal elastostatic problem can then be solved by standard tools of structural analysis with prescription of equivalent imposed distortions. Examples of nanorods with one fixed and one free end and with fixed ends are explicitly carried out.