Stability analysis of a gradient elastic beam using nite element method

Abstract

Gradient elasticity models have been proposed in recent years in order to describe phenomena that cannot be described by classical elasticity models. In this contribution, the finite element model is conducted within the context of non-classical continuum mechanics, by introducing a material length scale parameter. The finite element method for the Euler-Bernoulli beam model is applied for the buckling analyzes of micro/nanobeams with the additional boundary conditions. Gradient elasticity stiffness and stability matrices are calculated to solve beam buckling problems. A qualitative discussion is given on this calculation process. The study contains two major parts, namely, finite element modeling of gradient elastic beams with the additional boundary conditions and gradient elasticity theory based approach for predicting buckling behavior of nanostructures. The gradient elasticity solutions are compared with their classical counterparts. The results illustrate the small length-scale effect in the stability expression or the surprisingly stiffening effect against buckling for some classes of beam buckling problems. The aim of this paper is to introduce some scale effects to derive relevant structural models which applies to nanostructures. Key words: Carbon nanotubes, gradient elasticity, finite element method, additional boundary conditions, nanobeams.