Leugering G, Rodriguez C, Wang Y (2021)
Publication Type: Journal article
Publication year: 2021
DOI: 10.1016/j.matpur.2021.07.007
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.
APA:
Leugering, G., Rodriguez, C., & Wang, Y. (2021). Nodal profile control for networks of geometrically exact beams. Journal De Mathematiques Pures Et Appliquees. https://dx.doi.org/10.1016/j.matpur.2021.07.007
MLA:
Leugering, Günter, Charlotte Rodriguez, and Yue Wang. "Nodal profile control for networks of geometrically exact beams." Journal De Mathematiques Pures Et Appliquees (2021).
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