Some New Approximate Solutions in Closed-Form to Problems of Nanobars

Abstract

Following recent technological advancements, a great attention has been paid to the mechanical behaviour of structural elements of nanosize. In this study, some solutions to mechanical problems of bars of nanosize are examined using Eringen's two-phase nonlocal elasticity. Assuming the fraction coefficient of nonlocal part of the material is small, a perturbation expansion with respect to it is performed. With this procedure, the original nonlocal problem is broken into a set of local elasticity problems. Solutions to some example problems of nanobars are provided in closed-form for the first time, and commented on. The new solutions provided herein may well serve for benchmark studies, as well as identification of material parameters of nano-sized structural elements, such as carbon nanotubes.