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Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 591532, 9 pages
http://dx.doi.org/10.1155/2014/591532
Research Article

Variational Principles for Buckling of Microtubules Modeled as Nonlocal Orthotropic Shells

Discipline of Mechanical Engineering, University of KwaZulu-Natal, Durban 4041, South Africa

Received 15 April 2014; Revised 19 June 2014; Accepted 20 June 2014; Published 5 August 2014

Academic Editor: Chung-Min Liao

Copyright © 2014 Sarp Adali. 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

A variational principle for microtubules subject to a buckling load is derived by semi-inverse method. The microtubule is modeled as an orthotropic shell with the constitutive equations based on nonlocal elastic theory and the effect of filament network taken into account as an elastic surrounding. Microtubules can carry large compressive forces by virtue of the mechanical coupling between the microtubules and the surrounding elastic filament network. The equations governing the buckling of the microtubule are given by a system of three partial differential equations. The problem studied in the present work involves the derivation of the variational formulation for microtubule buckling. The Rayleigh quotient for the buckling load as well as the natural and geometric boundary conditions of the problem is obtained from this variational formulation. It is observed that the boundary conditions are coupled as a result of nonlocal formulation. It is noted that the analytic solution of the buckling problem for microtubules is usually a difficult task. The variational formulation of the problem provides the basis for a number of approximate and numerical methods of solutions and furthermore variational principles can provide physical insight into the problem.