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

The geometrically exact theory of linear elastic rods is used to formulate the general three-dimensional problem of a twisted, clamped rod hanging und er gravity and subject to buoyancy forces from a fluid. The resulting bound ary-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.