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.
|Number of pages||24|
|Journal||Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences|
|Early online date||22 Feb 2012|
|Publication status||Published - 8 Jun 2012|
- rod mechanics
- helical buckling
Thompson, J. M. T., Silveira, M., van der Heijden, G. H. M., & Wiercigroch, M. (2012). Helical post-buckling of a rod in a cylinder: with applications to drill-strings. Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences, 468(2142), 1591-1614. https://doi.org/10.1098/rspa.2011.0558