Postbuckling scrutiny of highly deformable nanobeams: A novel exact nonlocal-surface energy-based model

Abstract

This paper deals with analytical postbuckling analysis of elastic slender beam-like nanostructures by considering both surface energy and nonlocality effects. Using Euler-Bernoulli beam theory, the continuum-based governing equation is established for axially compressed nanobeams with large displacements. To capture the postbuckling behavior of the nanostructure more accurately, an exact solution is proposed on the basis of elastica approach. The explicit expressions of postbuckling load and maximum displacements are obtained for nanobeams with various ends. The predicted results are successfully checked with those of a Galerkin-modal-based approach. The postbuckled shapes of nanobeams are then presented based on the classical elasticity theory and the newly developed size-dependent models to show the roles of the nonlocality and surface energy. The effects of both nanobeam's length and diameter on the nonlinear trends of load-displacement are displayed. The present work can be regarded as a benchmark for further numerical/analytical studies on postbuckling of nonlocal-surface energetic ensembles of vertically aligned nanostructures.