Impact of the Curvature of Planar Beam on its Deformation Induced by the Nano Effect

Nanostructures are increasingly used in micro- and nanoscale devices and systems, driving intensive investigation into nanoscale mechanical effects. Among the theoretical frameworks developed to describe these phenomena, the Eringen’s nonlocal elasticity theory has emerged as the most widely adopted due to its clear physical foundation and tractable mathematical formulation. On this basis, the present study develops an extended constitutive model for the bending behavior of curved beams within the nonlocal elasticity framework and proposes a new approach for characterizing nanoscale bending deformation. Particular emphasis is placed on elucidating how geometric curvature regulates the manifestation of nonlocal (nano) effects. Using a combination of theoretical derivations and numerical calculations, the proposed model is rigorously validated, and the bending responses of curved nanobeams subjected to various loading conditions are systematically examined. The findings demonstrate that curvature plays a decisive role in shaping nanoscale effects and that these effects on structural behavior can be effectively modulated by strategically designing the beam curvature across different geometric configurations and loading scenarios.