Patching Asymptotics Solution of a Cable with a Small Bending Stiffness
Publication: Journal of Structural Engineering
Volume 139, Issue 2
Abstract
The analysis of a cable with a small bending stiffness is a problem encountered in many engineering applications such as the fatigue assessment of stay cables, the modeling of pipeline laying operation, or the determination of bending stresses in drillpipe assemblies. Because this phenomenon is modeled by a singularly perturbed equation, standard numerical techniques fail to solve these problems efficiently. As an alternative, provided the complexity of the analytical developments does not preclude their application, these problems may be tackled with appealing analytical procedures such as matching asymptotics or multiple scales. Otherwise, advanced numerical simulations combining patching asymptotics within a numerical framework are the only possible approach for problems where the governing equations are too complex. Patching asymptotics also feature a number of merits such as the possibility of using a boundary layer with a finite extent. Aiming at a better understanding of this latter technique, the purpose of this paper was to determine the solution of a cable with a small bending stiffness. Interesting details about patchability conditions and about how to restore higher derivative continuity are included. The accuracy of the patching asymptotics approach is also compared with that of matched asymptotics.
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Acknowledgments
The idea of considering a patching asymptotics approach for the solution of that problem emerged during a stay of V. Denoël at the Commonwealth Scientific and Industrial Research Organization (Perth, Australia). The authors thank Professor E. Detournay for interesting discussions and interactions.
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© 2013 American Society of Civil Engineers.
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Received: Jan 6, 2012
Accepted: Apr 24, 2012
Published online: Apr 26, 2012
Published in print: Feb 1, 2013
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