Section Translational Movement Imposition for Macroelements

Abstract

Boundary conditions play a very important role in any mathematical model. They heavily influence the response near the region they are, but the farther the interest region is, the less important the boundary condition influence becomes. Also, the response depends of which movements are constrained or imposed and which are not. This influence can be seen in all type of problems, ranging from simple beams to complicated structures. For tubular structures, such as flexible pipes and umbilical cables, the boundary conditions are usually given in terms of imposed movements in sections, which are commonly assumed, by hypothesis, as rigid bodies. To deal with this type of structures, the authors presented in previous works the macroelements. They are finite elements that incorporate geometrical characteristics in the formulation, leading to well behaved contact models with a smaller number of degrees of freedom. One major feature of the model is the orthotropic cylindrical layer that uses Fourier series for the displacements. This led to specific contact models and bring the difficulty in the representation of boundary conditions in terminal sections, since different nature displacements (one the aforementioned Fourier and other one standard description) must be dealt with. This paper address how to impose translational movement for sections using macroelements. All the description of how the coupling is made and the constraint enforcement done by using a penalty-based formulation. This work also highlights the implementation, finalizing with comparison with a conventional finite element program.