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 |
|---|---|
| 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