  This paper considers the numerical solution of Timoshenko beam network
models, comprised of Timoshenko beam equations on each edge of the network,
which are coupled at the nodes of the network using rigid joint conditions.
Through hybridization, we can equivalently reformulate the problem as a
symmetric positive definite system of linear equations posed on the network
nodes. This is possible since the nodes, where the beam equations are coupled,
are zero-dimensional objects. To discretize the beam network model, we propose
a hybridizable discontinuous Galerkin method that can achieve arbitrary orders
of convergence under mesh refinement without increasing the size of the global
system matrix. As a preconditioner for the typically very poorly conditioned
global system matrix, we employ a two-level overlapping additive Schwarz
method. We prove uniform convergence of the corresponding preconditioned
conjugate gradient method under appropriate connectivity assumptions on the
network. Numerical experiments support the theoretical findings of this work.
