A Homotopy Perturbation-Based Method for Large Deflection of a Cantilever Beam Under a Terminal Follower Force

Abstract

The large deflection problem of a uniform cantilever beam subjected to a terminal concentrated follower force is investigated. The governing equations, which characterize a two-point boundary value problem, are transformed into an initial-value problem. A new algorithm based on the homotopy perturbation method is proposed and applied to the resulting problem and the characteristics of load versus displacement are obtained analytically. The convergence of this method is discussed and the details of load-deflection curves are present. Compared with other existing methods, the present scheme is shown to be highly accurate, while only lower order perturbation is required.

Keywords:

• Large deflection
• Cantilever beam
• Follower force
• Homotopy perturbation method

Acknowledgments

The authors are grateful for the critical and helpful comments of the anonymous referees. This work was supported by Chinese Universities Scientific Fund (Grant No. 2011js048).