A Finite Macro-Element for Cylindrical Layer Modeling

The offshore industry is in constant evolution due to the need of reach increasing water depths for new oil fields exploitation. In this scenario, not only new types of platforms are being designed, but also new types of risers, including flexible pipes and new 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 behavior of flexible pipes and umbilical cables, adequate models are necessary. One can rely on finite element models, which show a great difficulty in mesh generation and convergence (specially 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 elements). Related to that approach, this paper presents a tubular element, which describes a cylinder with isotropic properties and can accept various sorts of loads. This element has its displacements and loads described using Fourier series and, for each term of the series, a solution is obtained. The effect is then superposed and the complete solution is obtained. This formulation is implemented and their results compared to those obtained by a classical finite element modeling tool, with good agreement.