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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 341232, 12 pages
http://dx.doi.org/10.1155/2013/341232
Research Article

Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection

1College of Engineering, Ocean University of China, Qingdao 266100, China
2Department of Civil and Environmental Engineering, National University of Singapore, Singapore 117576
3School of Mathematics, University of Jinan, Jinan 250022, China

Received 13 September 2012; Accepted 20 January 2013

Academic Editor: Jyh Horng Chou

Copyright © 2013 S. P. Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Investigated herein is the postbuckling behavior of an initially imperfect nonlocal elastic column, which is simply supported at one end and subjected to an axial force at the other movable end. The governing nonlinear differential equation of the axially loaded nonlocal elastic column experiencing large deflection is first established within the framework of Eringen's nonlocal elasticity theory in order to embrace the size effect. Its semianalytical solutions by the virtue of homotopy perturbation method, as well as the successive approximation algorithm, are determined in an explicit form, through which the postbuckling equilibrium loads in terms of the end rotation angle and the deformed configuration of the column at this end rotation are predicted. By comparing the degenerated results with the exact solutions available in the literature, the validity and accuracy of the proposed methods are numerically substantiated. The size effect, as well as the initial imperfection, on the buckled configuration and the postbuckling equilibrium path is also thoroughly discussed through parametric studies.