A Three-Dimensional Curved Beam Element for Helical Components Modeling

The offshore industry is in constant evolution due to the need of reaching new oil fields in increasingly water depths. In this scenario, not only new types of platforms are being designed, but also new types of 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 their behavior, adequate models are necessary. One can rely on finite element models, 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 necessary ones). Another possible approach is to define macro elements, which represent a component, instead of classical finite elements (such as tetrahedral elements). Related to that approach, a numeric method using macro-elements is proposed. It consists in creating elements which has the desired characteristics of the problem in its formulation, leading to robust custom-made elements and to coarse meshes (since the complexity of the problem is within the element). Some elements are proposed in this model: a concentric one for cylindrical layer modeling; a three-dimensional curved beam for helices; a bridge element for node connection; and a contact element, for gap and friction treatment. The first two of them are already concluded and the later ones are being designed. This paper presents the three-dimensional curved beam element, which takes into account the effects of curvature and tortuosity. This is accomplished by using a strong coupling between displacements and assuming that the twist and shear strains varies linearly within the element. Using such hypothesis, the shear lock phenomenon is also avoided. This formulation is implemented and their results compared to those obtained by a classical finite element modeling tool, with good agreement.