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5.—Qualitative Aspects of the Spatial Deformation of Non-linearly Elastic Rods.§

Published online by Cambridge University Press:  14 February 2012

Stuart S. Antman  and
Kathleen B. Jordan
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Extract

In this article we examine the qualitative behaviour of non-planar equilibrium states ofnon-linearly elastic rods subject to terminal loads. In our geometrically exact theory, a rod is endowed with enough geometric structure for it to undergo flexure, torsion, axial extension, and shear. The constitutive equations give appropriate stress resultants and couples as non-linear functions of appropriate strains. These constitutive relations must meet minimal conditions ensuring that they be physically reasonable. It turns out that the equilibrium states of such a rod are governed by a boundary value problem for a quasilinear fifteenth-order system of ordinary differential equations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 73 , 1975 , pp. 85 - 105
Copyright
Copyright © Royal Society of Edinburgh 1975

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