### Abstract

This paper reformulates the governing equations of an extensible elastic rod by reference to a given spatial curve. This Eulerian formulation is motivated by the need to solve efficiently the constrained elastica problem encountered in many medical and engineering applications, in which a thin rod is inserted in a tortuous conduit. The Eulerian reformulation of the equations hinges on the restatement of the rod local equilibrium in terms of derivatives with respect to the curvilinear coordinate associated with the reference curve and the description of the rod deflection as a perturbation of this curve. The originality of the proposed formulation lays in the axially unconstrained character of the resulting system such that the determination of the rod configuration between two fixed points reduces to the resolution of a classical boundary value problem.

Original language | English (US) |
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Title of host publication | Research and Applications in Structural Engineering, Mechanics and Computation - Proceedings of the 5th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2013 |

Publisher | Taylor and Francis - Balkema |

Pages | 865-870 |

Number of pages | 6 |

ISBN (Print) | 9781138000612 |

DOIs | |

State | Published - 2013 |

Event | 5th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2013 - Cape Town, South Africa Duration: Sep 2 2013 → Sep 4 2013 |

### Publication series

Name | Research and Applications in Structural Engineering, Mechanics and Computation - Proceedings of the 5th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2013 |
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### Other

Other | 5th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2013 |
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Country | South Africa |

City | Cape Town |

Period | 9/2/13 → 9/4/13 |

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## Cite this

*Research and Applications in Structural Engineering, Mechanics and Computation - Proceedings of the 5th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2013*(pp. 865-870). (Research and Applications in Structural Engineering, Mechanics and Computation - Proceedings of the 5th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2013). Taylor and Francis - Balkema. https://doi.org/10.1201/b15963-158