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Applied Computational Intelligence and Soft Computing
Volume 2012 (2012), Article ID 683483, 6 pages
Research Article

A Hybrid Power Series Artificial Bee Colony Algorithm to Obtain a Solution for Buckling of Multiwall Carbon Nanotube Cantilevers Near Small Layers of Graphite Sheets

1Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz 6135743337, Iran
2Engineering Part of Iman Madar Naslaha Co. (IMEN), Ahvaz, Iran

Received 24 April 2012; Revised 13 June 2012; Accepted 17 June 2012

Academic Editor: Erich Klement

Copyright © 2012 Aminreza Noghrehabadi 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.


A hybrid power series and artificial bee colony algorithm (PS-ABC) method is applied to solve a system of nonlinear differential equations arising from the distributed parameter model of multiwalled carbon nanotube (MWCNT) cantilevers in the vicinity of thin and thick graphite sheets subject to intermolecular forces. The intermolecular forces are modeled using van der Waals forces. A trial solution of the differential equation is defined as sum of two polynomial parts. The first part satisfies the boundary conditions and does contain two adjustable parameters. The second part is constructed as not to affect the boundary conditions, which involves adjustable parameters. The ABC method is applied to find adjustable parameters of trial solution (in first and second part). The obtained results are compared with numerical results as well as analytical solutions those reported in the literature. The results of the presented method represent a remarkable accuracy in comparison with numerical results. The minimum initial gap and the detachment length of the actuator that does not stick to the substrate due to the intermolecular forces, as important parameters in pull-in instability of MWCNT actuator, are evaluated by obtained power series.