Study of Large Deflection in Nano-Beams Using the Nonlocal Elasticity Theory

A nonlocal elastic beam model is developed by incorporating Eringen's nonlocal constitutive equation into the large deflection beam theory for a nano-cantilever Euler–Bernoulli beam. The equilibrium equations are solved in an iterative manner using the shooting method. Deformed configurations of beam for different values of nonlocal parameter are plotted, and the final length of the beam after deflection is obtained. It is demonstrated that the beam scale has a significant impact on its flexural behavior under the large deflection, such that the nano-beam deflection can be either larger or smaller than the classical theory, depending on the loading level.