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

Abstract

Following recent technological advancements, a great attention has been paid to mechanical behaviour of structural elements of nanosize. In this study, some solutions to mechanical problems of bars of nanosize is 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.

Keywords

• nanobars
• nonlocal elasticity
• nanomechanics
• closed-form solutions
• approximate methods

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