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.

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