The Mathematical Institute, University of Oxford, Eprints Archive

Static and dynamic stability results for a class of three-dimensional configurations of Kirchhoff elastic rods

Majumdar, A. and Goriely, A. (2012) Static and dynamic stability results for a class of three-dimensional configurations of Kirchhoff elastic rods. Physica D . (Submitted)

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Abstract

We analyze the dynamical stability of a naturally straight, inextensible and unshearable elastic rod, under tension and controlled end rotation, within the Kirchhoff model in three
dimensions. The cases of clamped boundary conditions and isoperimetric constraints are treated separately. We obtain explicit criteria for the static stability of arbitrary extrema of a general quadratic strain energy. We exploit the equivalence between the total energy and a suitably defined norm to prove that local minimizers of the strain energy, under explicit hypotheses, are stable in the dynamic sense due to Liapounov. We also extend our analysis
to damped systems to show that static equilibria are dynamically stable in the Liapounov sense, in the presence of a suitably defined local drag force.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1593
Deposited By:Peter Hudston
Deposited On:01 Sep 2012 08:40
Last Modified:01 Sep 2012 08:40

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