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Journal of Elasticity

, Volume 109, Issue 1, pp 75–93 | Cite as

Stability Estimates for a Twisted Rod Under Terminal Loads: A Three-dimensional Study

  • Apala Majumdar
  • Christopher Prior
  • Alain Goriely
Article

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.

Keywords

Cosserat rods Stability of straight axis solution Variational criterion 

Mathematics Subject Classification (2000)

74B20 49K40 

Notes

Acknowledgements

This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). AG is a Wolfson Royal Society Merit Holder. AM is also supported by an EPSRC Career Acceleration Fellowship EP/J001686/1. We also would like to thank John Maddocks for comments on an earlier version of this manuscript, and bringing to our attention important references.

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Apala Majumdar
    • 1
  • Christopher Prior
    • 1
  • Alain Goriely
    • 1
  1. 1.OCCAM, Mathematical InstituteOxford UniversityOxfordEngland

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