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

Apala Majumdar, Alain Goriely

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)91-101
Number of pages11
JournalPhysica D: Nonlinear Phenomena
Volume253
DOIs
Publication statusPublished - 15 Jun 2013

Keywords

  • elastic rods
  • static stability
  • dynamic stability
  • Euler buckling
  • energy minimizers
  • local drag models

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