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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.

The layers of unbounded flexible pipes have relative movement, enhancing its capabilities to handle curvatures and moment loads. In a simplified approach, those pipes can be described using bonded elements; but to really capture this behavior, a frictional contact is utterly needed. In general, dealing with contact problems in computational mechanics is complicated, since it involves the constant evaluation of its status and can lead to convergence problems or simulation failure, due to intrinsically problematic and inefficient contact models or due to contact models that are insufficient to capture the desired details. The macroelement formulation, which was created to deal with flexible pipes in a simplified way, needed a frictional contact element to enhance the quality of results and closeness to real behavior. The major drawback for developing such element is the different nature of the nodal displacements descriptions. The first approach possible is the simplest contact model: it involves only the nodes in each contacting elements. The gap information and distances are evaluated using exclusively the nodal information. This kind of model provides good results with minimum computational effort, especially when considering small displacements. This paper proposes such element: a node-to-node contact formulation for macroelements. It considers that the nodal displacements of both nodes are in cylindrical coordinates with one of them using Fourier series to describe the displacements. To show model effectiveness, a case study with a cylinder using Fourier series and multiple helical elements connected with the contact element is done and shows great results.

The modelling of flexible pipe interlocked carcasses is complicated when considering all the geometric complexity of their profile. A possible approach is to model them as cylindrical equivalent layers. To follow this path several alternatives can be considered in changing the geometrical and material properties. However, the thickness and the mean radius of those layers must not be changed to not interfere with the diameter of the other flexible pipe layers. In this paper, a model of an orthotropic cylindrical layer, with the same thickness and mean diameter of the original carcass layer is constructed and its material parameters are adjusted for axial loads using a finite element model of the real carcass profile.

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