A Nonlocal Finite Element Approach to Nanobeams

Abstract

This paper presents a consistent derivation of a new nonlocal finite element procedure in the framework of continuum mechanics and nonlocal thermodynamics for the analysis of bending of nanobeams under transverse loads. This approach is able to provide the overall performance and the influence of specific parameters in the behavior of nanobeams and it is also able to deal with nanomechanical systems by solving a reduced number of algebraic equations. An example shows that the proposed nonlocal finite element procedure, using a mesh composed by only four elements of equal size, provides the exact values in terms of transversal displacement and bending of the nanobeam.