Postbuckling analysis of microscale beams based on a strain gradient finite element approach

Abstract

The postbuckling problem of Euler–Bernoulli (EB) microbeams under different boundary conditions is addressed in this paper using a non-classical finite element (FE) approach with a novel beam element. The proposed element is capable of considering the strain gradient effects and hence is appropriate to use at microscale. First, based on Mindlin’s strain gradient theory (SGT), a size-dependent EB beam model including strain gradient effects is developed. Then, by a FE approach, the non-classical beam element is constructed which needs two additional degrees of freedom per node as compared to the classical EB beam element. The new element is based upon Mindlin’s SGT, and can be easily reduced to that based on various higher-order elasticity theories such as the modified versions of strain gradient and couple stress theories. Selected numerical results are presented to show the reliability of the developed FE formulation, and also to study the small scale influences on the bifurcation diagrams of microbeams. © 2016, Springer Science+Business Media Dordrecht.