Director-based IGA beam elements for sliding contact problems

Summary

The geometrically exact beam theory is one of the most prominent non-linear beam models. It can be used to simulate aerial runways or pantograph-catenaries, where a sliding contact condition between two or more beams is used. A smooth discretization of at least C1continuity is needed to not introduce any unphysical kinks. This can be achieved using the isogeometric analysis, which we apply to a director-based formulation of the geometrically exact beam. For a stable time integration scheme we use an energy-momentum conserving scheme. Using the notion of the discrete gradient, an energy-momentum conserving algorithm is constructed, including the case of sliding contact between beams.