Implicit and Explicit Implementation of the Dynamic Relaxation Method for the Definition of Initial Equilibrium Configurations of Flexible Lines

Recent activities in the offshore oil exploitation industry require new structural concepts employing flexible lines (both mooring lines and risers). Such systems present increasingly complex configurations, with dynamic nonlinear behaviour; therefore, the use of efficient numerical solution procedures, based on the Finite Element Method, becomes mandatory for their analysis. The usual analysis procedure for flexible lines by the FEM is based in the calculation of an initial, stable static equilibrium configuration in order to define the finite element mesh. Usually this configuration is obtained by the classic catenary equations. However, in more complex problems these equations cannot be applied. Therefore, the objective of this work is to present the use of a more general finite element approximation, associated to dynamic relaxation algorithms. Such algorithms can be started from arbitrary configurations, not necessarily in equilibrium. The resulting procedure is accurate, robust, and avoids numerical problems such as the ill-conditioning of the tangent stiffness matrix, allowing the static equilibrium configuration to be obtained in an efficient way.