文献类型：期刊文献

英文题名：Exact solutions for the static bending of Euler-Bernoulli beams using Eringen's two-phase local/nonlocal model

作者：Wang, Y. B.[1];Zhu, X. W.[2];Dai, H. H.[3]

机构：[1]ShaoXing Univ, Dept Math, 900 ChengNan Ave, Shaoxing 312000, Zhejiang, Peoples R China;[2]Zhongnan Univ Econ & Law, Sch Math & Stat, Wuhan 430073, Peoples R China;[3]City Univ Hong Kong, Dept Math, 83 Tat Chee Ave, Kowloon Tong, Hong Kong, Peoples R China

年份：2016

卷号：6

期号：8

外文期刊名：AIP ADVANCES

收录：SCI-EXPANDED(收录号：WOS:000383909100036)、、EI(收录号：20163502762882)、Scopus(收录号：2-s2.0-84983642493)、WOS

基金：This work was supported by a grant from Zhongnan University of Economics and Law (Project No.: 31541411205), a GRF grant (Project No.: CityU11303015) from the Research Grant Council of HongKong SAR, China and a grant from the National Nature Science Foundation of China (Project No.: 11572272). Y.B. Wang also thanks the support of a grant from the National Nature Science Foundation of China (Project No.: 11472147) and a grant from ShaoXing University (Project No.: 20145002).

语种：英文

外文关键词：Asymptotic analysis - Boundary conditions

外文摘要：Though widely used in modelling nano-and micro-structures, Eringen's differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen's two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).