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

D.M. Stump & G.H.M. van der Heijden

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.

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

J. Eng. Math. 38, 13-31 (2000).