  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 [Exact boundary controllability of nodal profile for
Saint-Venant system on a network with loops, in J. Math. Pures Appl., 2018].
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.
