Closed-form expression for geometrically nonlinear large deformation of nano-beams subjected to end force

. In this paper, exact analytical solutions are developed to describe size-dependent nonlinear bending behavior of cantilever nano-beams subjected to end force. To obtain large deformation of the nano-beam, geometric and equilibrium equations of the deformed element are used in conjunction with the nonlocal differential constitutive relation. The governing equations are obtained by considering the assumption of inextensibility and the Euler-Bernoulli hypothesis. Some numerical examples have been solved to demonstrate the applicability and accuracy of the present formulations. Furthermore, by using the present closed-form solutions, the deformed configurations of the nano-beams are determined for different loading conditions. Our results reveal that the nano-beam exhibits softening or hardening behaviors when nonlocality is increasing, depending on the applied loading conditions.