A Finite Macro-Element for Orthotropic Cylindrical Layer Modeling

The offshore industry is in constant evolution due to the need to reach increasing water depths for new oil fields exploitation. In this scenario, not only are new types of platforms being designed but also new types of risers, including new flexible pipes and umbilical cable configurations. The greatest difficulty to generate a new concept for a riser is to determine if it is viable or not. Flexible pipes and umbilical cables are complicated to model, due to the interactions between their layers and the large number of possible arrangements. To predict the mechanical behavior of flexible pipes and umbilical cables, adequate models are necessary. One can rely on finite element models (FEM), which show a great difficulty in mesh generation and convergence (especially due to the contact pairs). One can also rely on analytical models, which have many limitations due to simplifications (even though they are necessary). Another possible approach is to define macro-elements, which represent a component, instead of classical finite elements (such as tetrahedric ones). Related to that approach, this paper presents a tubular element to model a cylinder with orthotropic material properties. In the model, the displacement and the loads are described by means of Fourier series, making it possible to treat a broad class of loads. The formulation is presented in detail, giving special attention to surface loading modeling. The results obtained in case studies are compared to those of a classical finite element modeling tool with a good agreement.