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Surface Effect and Nonlocal Effect on Nanowires Bent by a Point Force at an Arbitrary Axial Position

Under different boundary conditions, the nanowires bent by a point force at an arbitrary axial position are studied analytically by considering the surface effect and the nonlocal effect. The surface effect is modeled to be the superposition of the forces induced from residual surface tension and surface elasticities. For the purpose of modeling the residual surface tension, the generalized Young–Laplace equation is introduced into the Euler–Bernoulli beam equation. The surface elasticities are taken into account via a core-shell model. An additional term is added in the bending moment equation in order to describe the nonlocal effect. Closed-form analytical solutions are obtained, indicating that both the surface effect and the nonlocal effect, as well as the boundary conditions and the force position, may influence the force–displacement curves of the bending nanowires. The solutions are compared with previous research studies. This work suggests that the applied force position and the boundary conditions may influence the experimentally measured Young's moduli of bending nanowires.