Symmetric Catenary of a Uniform Elastic Cable of Neo-Hookean Material
Publication: Journal of Engineering Mechanics
Volume 132, Issue 7
Abstract
The Cartesian equations of the symmetric catenary of a uniform nonlinear elastic cable of neo-Hookean material are determined in parametric form. The catenary is plotted here in nondimensional terms for a number of values of the two constants on which it depends: One being that of an inextensible catenary and the other specifying the thermoelastic properties of the neo-Hookean material. The resolution of the equations to find these values from the geometrical and material data requires much more sophisticated numerical algorithms than do the inextensible catenary and the elastic one based on Hooke’s law, but this drawback is circumvented by adjusting an accurate analytical approximation that evens the difficulty of the two problems and allows the symmetric catenary of a neo-Hookean cable to be determined and drawn by using any graphing program endowed with numerical algorithms for basic calculus. A closed form of the Cartesian equations of the catenary is also provided on the basis of this analytical approximation.
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Acknowledgments
This investigation was performed within a research project (MAT0201422) sponsored by the Ministerio de Ciencia y Tecnología of Spain. The writer wishes to express particular gratitude to his colleague Professor Mariano Soler for his valuable assistance.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 132 • Issue 7 • July 2006
Pages: 747 - 753
Copyright
© 2006 ASCE.
History
Received: Jun 21, 2005
Accepted: Nov 10, 2005
Published online: Jul 1, 2006
Published in print: Jul 2006
Notes
Note. Associate Editor: Bojan B. Guzina
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