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