Stability Analysis of Nonlocal Elastic Columns with Initial Imperfection

• Published in: Mathematical problems in engineering Vol. 2013; no. 2013; pp. 1 - 12
• Main Authors: Xu, S. P., Wang, C. M., Xu, Meirong
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2013; Hindawi Limited
• Subjects: Applied mathematics; Approximation; Archives & records; Carbon; Columns (structural); Configurations; Defects; Deformation; Differential equations; Elasticity; Engineering; Exact solutions; Mathematical analysis; Mathematical models; Mathematical problems; Mechanics; Nanotechnology; Nonlinear differential equations; Nonlocal elasticity; Numerical methods; Perturbation methods; Postbuckling; Size effects; Stability analysis; Studies; China
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2013/341232

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.