Multiple Scales Solution for a Beam with a Small Bending Stiffness
Publication: Journal of Engineering Mechanics
Volume 136, Issue 1
Abstract
This paper considers the problem of a beam with a small bending stiffness, within the framework of a nonlinear beam model that includes both the classical cable and the linear beam as limiting cases. This problem, treated as a perturbation of the catenary solution, is solved with the multiple scales method. The resulting expressions of the beam deflection and of the internal forces, as well as those obtained with the more commonly applied matched asymptotics method, are compared with numerical results. This comparison indicates that a better accuracy can be achieved with the multiple scales approach, for a similar computational effort. These results also suggest that application of the multiple scales method to the solution of beam problems involving boundary layers extend the range of values of the small parameter, for which accurate analytical solutions can be obtained by a perturbation technique.
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Acknowledgments
The theory presented in this paper has been developed during an invited stay of V. Denoël at the Commonwealth Scientific and Industrial Research Organization (CSIRO, Perth, Australia), under the agreement of the Belgian Fund for Scientific Research and the University of Liège (Belgium). These institutions are therefore warmly acknowledged. The writers also acknowledge the benefits of fruitful discussions with Dr. Thomas Richard (CSIRO).
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Published In
Journal of Engineering Mechanics
Volume 136 • Issue 1 • January 2010
Pages: 69 - 77
Copyright
© 2010 ASCE.
History
Received: Aug 5, 2008
Accepted: May 12, 2009
Published online: May 15, 2009
Published in print: Jan 2010
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