Helical post-buckling of a rod in a cylinder: with applications to drill-strings

J. M. T. Thompson, M. Silveira, G. H. M. van der Heijden, M. Wiercigroch

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)


The helical buckling and post-buckling of an elastic rod within a cylindrical casing arises in many disciplines, but is particularly important in the petroleum industry. Here, a drill-string, subjected to an end twisting moment combined with axial tension or compression, is particularly prone to buckling within its bore-hole—with potentially serious results. In this paper, we make a detailed theoretical study of this type of instability, deriving precise new results for the advanced post-buckling stage when the rod is in continuous contact with the cylinder. Results, including rigorous stability analyses and contact pressure assessments, are presented as equilibrium surfaces to facilitate comparisons with experimental results. Two approximate solutions give insight, universal graphs and parameters, for the practically relevant case of small angles, and highlight the existence of a critical cylinder diameter. Excellent agreement with experiments is achieved.
Original languageEnglish
Pages (from-to)1591-1614
Number of pages24
JournalProceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences
Issue number2142
Early online date22 Feb 2012
Publication statusPublished - 8 Jun 2012


  • rod mechanics
  • drill-strings
  • post-buckling
  • helical buckling


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