Eulerian formulation for an extensible elastic rod

A. Huynen, E. Detournay, V. Denoël

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

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 languageEnglish (US)
Title of host publicationResearch and Applications in Structural Engineering, Mechanics and Computation - Proceedings of the 5th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2013
PublisherTaylor and Francis - Balkema
Pages865-870
Number of pages6
ISBN (Print)9781138000612
DOIs
StatePublished - 2013
Event5th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2013 - Cape Town, South Africa
Duration: Sep 2 2013Sep 4 2013

Publication series

NameResearch and Applications in Structural Engineering, Mechanics and Computation - Proceedings of the 5th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2013

Other

Other5th International Conference on Structural Engineering, Mechanics and Computation, SEMC 2013
CountrySouth Africa
CityCape Town
Period9/2/139/4/13

Fingerprint Dive into the research topics of 'Eulerian formulation for an extensible elastic rod'. Together they form a unique fingerprint.

  • Cite this

    Huynen, A., Detournay, E., & Denoël, V. (2013). Eulerian formulation for an extensible elastic rod. In 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