Matched asymptotic expansions for bent and twisted rods: Applications for cable and pipeline laying. (English) Zbl 0958.74032
Summary: 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. We use this method to consider the near-catenary application of a clamped pipeline.
MSC:
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74G10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
