A truly hybrid approach to substructuring problems using mixed assembly and implicit solving strategies

In recent years, the structural dynamic community showed a renewed interest in component coupling (i.e. dynamic substructuring) and decoupling techniques for structural dynamic analysis of assembled systems. Especially for hybrid problems, where some component models are obtained from experimental data and others from numerical modeling, these techniques offer interesting possibilities. However, since measured models are generally expressed in terms of flexibility and numerical models in terms of stiffness, model inversions are needed at least at the component interfaces. This leads to increased computational effort and/or amplification of measurement errors. To avoid the inversions of the component models, a truly hybrid approach to coupling and decoupling problems is proposed in this paper. Using a mixed assembly methodology derived from a so-called "three field formulation", stiffness type components can be directly assembled to flexibility based subsystems. Then only the interface problem remains to be solved. In part one of this paper the theoretical derivation of the proposed methodology is addressed. Furthermore, we outline the differences with respect to the existing methods.