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@article{faucris.262677645,
abstract = {In this work, we consider networks of so-called geometrically exact beams, namely, shearable beams that may undergo large motions. The corresponding mathematical model, commonly written in terms of displacements and rotations expressed in a fixed basis (Geometrically Exact Beam model, or GEB), has a quasilinear governing system. However, the model may also be written in terms of intrinsic variables expressed in a moving basis attached to the beam (Intrinsic GEB model, or IGEB) and while the number of equations is then doubled, the latter model has the advantage of being of first-order, hyperbolic and only semilinear. First, for any network, we show the existence and uniqueness of semi-global in time classical solutions to the IGEB model (i.e., for arbitrarily large time intervals, provided that the data are small enough). Then, for a specific network containing a cycle, we address the problem of local exact controllability of nodal profiles for the IGEB model – we steer the solution to satisfy given profiles at one of the multiple nodes by means of controls applied at the simple nodes – by using the constructive method of Zhuang, Leugering and Li (2018) [52]. Afterwards, for any network, we show that the existence of a unique classical solution to the IGEB network implies the same for the corresponding GEB network, by using that these two models are related by a nonlinear transformation. In particular, this allows us to give corresponding existence, uniqueness and controllability results for the GEB network.},
author = {Leugering, Günter and Rodriguez, Charlotte and Wang, Yue},
doi = {10.1016/j.matpur.2021.07.007},
faupublication = {yes},
journal = {Journal De Mathematiques Pures Et Appliquees},
keywords = {Geometrically exact beam; Networks; Nodal profile controllability; Well-posedness},
note = {CRIS-Team Scopus Importer:2021-08-13},
peerreviewed = {Yes},
title = {{Nodal} profile control for networks of geometrically exact beams},
year = {2021}
}