Abstract
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.
Original language | English |
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Pages (from-to) | 75-93 |
Number of pages | 19 |
Journal | Journal of Elasticity |
Volume | 109 |
Issue number | 1 |
Early online date | 1 Mar 2012 |
DOIs | |
Publication status | Published - 30 Sept 2012 |
Keywords
- elastic rod
- stability of straight axis solution
- variational criterion