A Finite Element Approach for Modeling of Nano-Beams Incorporated with Nonlocal Elasticity

Abstract

In recent years, nonlocal elasticity has been used to properly model nano-beam, -plate and -shell due to their small length scale. When the internal characteristic length and time scale are large enough compared to external length, the classical elastic theory fails. In this paper, a finite element method for modelling of nonlocal nano-beams is presented based on nonlocal elasticity theory. Differential constitutive equation of Eringen has been developed to describe the nonlocal elastic behaviour of nano-beams. The Galerkin’s method has been used for finite element formulation. Firstly, the governing differential equation of nonlocal elasticity theory has been converted to a weak form, and then the final form of finite element method has been exploited for Euler-Bernoulli nano-beams by attention to the boundary conditions and the interpolation functions.