Spatially complex localisation in twisted elastic rods constrained to a cylinder

John Michael Tutill Thompson, G. H. M. Van Der Heijden, A. R. Champneys

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

We consider the problem of a long thin weightless rod constrained to lie on a cylinder awhile being held by end tension and twisting moment. Applications of this problem are found. Cor instance. in the buckling of drill strings inside a cylindrical hole. In a previous paper the general geometrically exact formulation was given and the case of a rod of isotropic cross-section analysed in detail. It was shown that in that case the static equilibrium equations are completely integrable and can be reduced to those of a one-degree-of-freedom oscillator whose non-trivial fixed points correspond to helical solutions of the rod. A critical load was Found where the rod coils up into a helix.

Here the anisotropic case is studied. It is shown that the equations are no longer integrable and give rise to spatial chaos with infinitely many multi-loop localised solutions. Helices become slightly modulated. We study the bifurcations of the simplest single-loop Solution and a representative multi-loop as the aspect ratio of the rod Is cross-section is varied. It is shown how the anisotropy unfolds the 'coiling bifurcation'. The resulting post-buckling behaviour is of the softening-hardening-softening type typically seen in the cellular buckling of long structures. and can be interpreted in terms of a so-called Maxwell effective failure load. (C) 2002 Elsevier Science Ltd. All rights reserved.

Original languageEnglish
Pages (from-to)1863-1883
Number of pages20
JournalInternational Journal of Solids and Structures
Volume39
Issue number7
DOIs
Publication statusPublished - Apr 2002

Keywords

  • elastic rod
  • anisotropy
  • cylindrical constraint
  • localised solutions
  • multi-pulse homoclinic orbits
  • softening-hardening-softening response
  • Maxwell failure load
  • helical collapse
  • drill string
  • DEFORMATION
  • ORBITS
  • LIE

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