The stability of an inextensible unshearable elastic rod with quadratic strain energy density subject to end loads is considered. We study the second variation of the corresponding rod-energy, making a distinction between in-plane and out-of-plane perturbations and isotropic and anisotropic cross-sections, respectively. In all cases, we demonstrate that the naturally straight state is a local energy minimizer in parameter regimes specified by material constants. These stability results are also accompanied by instability results in parameter regimes defined in terms of material constants. © 2012 Springer Science+Business Media B.V.
|Original language||English (US)|
|Number of pages||19|
|Journal||Journal of Elasticity|
|State||Published - Mar 1 2012|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). AG is a Wolfson Royal Society Merit Holder. AM is also supported by an EPSRC Career Acceleration Fellowship EP/J001686/1. We also would like to thank John Maddocks for comments on an earlier version of this manuscript, and bringing to our attention important references.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.