Static Non-linear Three-dimensional Analysis of a Riser Bundle by a Substructuring and Incremental Finite Element Algorithm

The problem of static, non-linear, large three-dimensional deformation of riser bundles used in offshore oil and gas production is studied within the limits of small strain theory. The mathematical model consists of the models of component-risers and connectors which hold risers together. Each riser is modelled as a thin walled, slender, extensible or inextensible tubular beam-column. It is subject to non-linear three-dimensional deformation dependent hydrodynamic loads, torsion and distributed moments, varying axial tension, and internal and external fluid forces. The problem is solved numerically by developing an algorithm which features substructuring, condensation and non-linear incremental finite elements. Substructuring is used to decompose the riser bundle problem into those of individual component-risers and equilibria of connectors. Condensation is used along with the connector equilibrium equations to produce connector forces and moments. Strong non-linearities present in the model are handled by an incremental finite element approach. Accuracy of the computer code is verified by solving simple three-dimensional cases. Two three-dimensional applications are solved for a bundle with seven component-risers and up to a total of 1267 degrees of freedom. Finally, a comparison is made with numerical results of a two-dimensional analysis code. The influence of problem size on total C P U time is discussed.