Journal of Engineering Mathematics

, Volume 38, Issue 1, pp 13-31

First online:

Matched asymptotic expansions for bent and twisted rods: applications for cable and pipeline laying

  • D.M. StumpAffiliated withDepartment of Mathematics, The University of Queensland
  • , G.H.M. van der HEIJDENAffiliated withDepartment of Mathematics, The University of Queensland

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The geometrically exact theory of linear elastic rods is used to formulate the general three-dimensional problem of a twisted, clamped rod hanging under gravity and subject to buoyancy forces from a fluid. The resulting boundary-value problem is solved by the method of matched asymptotic expansions. The truncated analytical solution is compared with results obtained from a numerical scheme and shows good agreement. The method is used to consider the near-catenary application of a clamped pipeline.

Key words:  rod theory, matched asymptotic expansions, boundary layers, catenary, heavy cables, pipelines, buoyancy forces