  With this contribution, we give a complete and comprehensive framework for
modeling the dynamics of complex mechanical structures as port-Hamiltonian
systems. This is motivated by research on the potential of lightweight
construction using active load-bearing elements integrated into the structure.
Such adaptive structures are of high complexity and very heterogeneous in
nature. Port-Hamiltonian systems theory provides a promising approach for their
modeling and control. Subsystem dynamics can be formulated in a
domain-independent way and interconnected by means of power flows. The modular
approach is also suitable for robust decentralized control schemes. Starting
from a distributed-parameter port-Hamiltonian formulation of beam dynamics, we
show the application of an existing structure-preserving mixed finite element
method to arrive at finite-dimensional approximations. In contrast to the
modeling of single bodies with a single boundary, we consider complex
structures composed of many simple elements interconnected at the boundary.
This is analogous to the usual way of modeling civil engineering structures
which has not been transferred to port-Hamiltonian systems before. A block
diagram representation of the interconnected systems is used to generate
coupling constraints which leads to differential algebraic equations of index
one. After the elimination of algebraic constraints, systems in
input-state-output(ISO) port-Hamiltonian form are obtained. Port-Hamiltonian
system models for the considered class of systems can also be constructed from
the mass and stiffness matrices obtained via conventional finite element
methods. We show how this relates to the presented approach and discuss the
differences, promoting a better understanding across engineering disciplines.
