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

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 loc...

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A. Majumdar More by this author
A. Goriely More by this author
Publication date:
2012
URN:
uuid:5ce5110d-1ed9-45cd-9f9d-87f704f9b41d
Local pid:
oai:eprints.maths.ox.ac.uk:1593

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