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S. P. Xu [1,2] and M. R. Xu [3] and C. M. Wang [2]

Academic Editor: Jyh Horng Chou

, 1, , College of Engineering, , Ocean University of China, , Qingdao 266100, , China, , ouc.edu.cn,

, 2, , Department of Civil and Environmental Engineering, , National University of Singapore, , Singapore, , 117576, , nus.edu.sg,

, 3, , School of Mathematics, , University of Jinan, , Jinan 250022, , China, , ujn.edu.cn,

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

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1. Introduction

The discovery of carbon nanotubes ushers a new era in the nano world [1]. The enhanced features of nanomaterial in mechanical, electrical, optical, and chemical properties over traditional ones open up many application opportunities in cutting-edge fields that range from sensing, and communications to energy harvesting. However, when the size of the structure scales down to nanodomains, an issue of considerable importance, namely, the size effect, arises and becomes prominent [2]. The size effect may greatly alter the macroscopic properties, and moreover, it calls the applicability of classical continuum models into question. Various modified continuum theories (such as couple stress theory, strain gradient elasticity theory, and modified couple stress theory) have thus been proposed to account for the size effect in the micro/nanoscale structures. Among them, the nonlocal elasticity theory, pioneered by Eringen [3], has been widely accepted and attracted an ever growing attention in recent years. This is because Eringen’s nonlocal continuum-based models are mathematically easy to tackle and physically reasonable from the atomistic viewpoint of lattice dynamics and molecular dynamics simulations [4]. This theory abandons the classical assumption of locality and admits that the stress state depends not only on the strain at that point but on the strains of every point in the body. In this way, information concerning about the long-range forces between atoms is incorporated into the theory, and consequently, the internal size scale is represented in the constitutive equations simply as a material parameter.

So far, there have been considerable studies on size effects in problems of bending, vibration, buckling, and wave propagation...

   

         

       

   

               

 

       

                                                     

       

 

   

           

         

                                                 

 

                   

                                                   

   

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