Journal of Engineering Mathematics

, Volume 38, Issue 1, pp 13–31

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

• D.M. Stump
• G.H.M. van der HEIJDEN
Article

## Abstract

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

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## Authors and Affiliations

• D.M. Stump
• 1
• G.H.M. van der HEIJDEN
• 2
1. 1.Department of MathematicsThe University of QueenslandSt. LuciaAustralia
2. 2.Department of MathematicsThe University of QueenslandSt. LuciaAustralia