文献类型：期刊文献

英文题名：Exact solutions for the bending of Timoshenko beams using Eringen's two-phase nonlocal model

作者：Wang, Yuanbin[1];Huang, Kai[2];Zhu, Xiaowu[2];Lou, Zhimei[3]

机构：[1]ShaoXing Univ, Dept Math, Shaoxing, Zhejiang, Peoples R China;[2]Zhongnan Univ Econ & Law, Sch Math & Stat, Wuhan 430073, Hubei, Peoples R China;[3]ShaoXing Univ, Dept Phys, Shaoxing, Zhejiang, Peoples R China

年份：2019

卷号：24

期号：3

起止页码：559

外文期刊名：MATHEMATICS AND MECHANICS OF SOLIDS

收录：SCI-EXPANDED(收录号：WOS:000463620600003)、、EI(收录号：20181404981399)、Scopus(收录号：2-s2.0-85044787872)、WOS

基金：Xiaowu Zhu was supported by the Natural Science Foundation of China (Project No. 61503415). Yuanbin Wang was supported by a grant from the Natural Science Foundation of China (Project No. 11472177).

语种：英文

外文关键词：Eringen's nonlocal elasticity; differential equation; Timoshenko beam theory; bending; asymptotics

外文摘要：Eringen's nonlocal differential model has been widely used in the literature to predict the size effect in nanostructures. However, this model often gives rise to paradoxes, such as the cantilever beam under end-point loading. Recent studies of the nonlocal integral models based on Euler-Bernoulli beam theory overcome the aforementioned inconsistency. In this paper, we carry out an analytical study of the bending problem based on Eringen's two-phase nonlocal model and Timoshenko beam theory, which accounts for a better representation of the bending behavior of short, stubby nanobeams where the nonlocal effect and transverse shear deformation are significant. The governing equations are established by the principal of virtual work, which turns out to be a system of integro-differential equations. With the help of a reduction method, the complicated system is reduced to a system of differential equations with mixed boundary conditions. After some detailed calculations, exact analytical solutions are obtained explicitly for four types of boundary conditions. Asymptotic analysis of the exact solutions reveals clearly that the nonlocal parameter has the effect of increasing the deflections. In addition, as compared with nonlocal Euler-Bernoulli beam, the shear effect is evident, and an additional scale effect is captured, indicating the importance of applying higher-order beam theories in the analysis of nanostructures.