Stability Estimates for a Twisted Rod Under Terminal Loads: A Three-dimensional Study |
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Authors: | Apala Majumdar Christopher Prior Alain Goriely |
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Institution: | 1. OCCAM, Mathematical Institute, Oxford University, 24 - 29 St Giles??, Oxford, England, OX1 3LB
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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. |
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