A new exact substructure method using mixed modes

In this paper, the use of free- or fixed-interface modes in exact substructure displacement expansions is briefly summarized. Then the substructural displacements are expressed exactly in terms of mixed modes, i.e., the displacements consist of linear combinations of fixed- and free-interface modes. This yields a new exact mixed-mode substructure method. It is demonstrated that the exact substructure methods with fixed or free interfaces are two limiting cases of this new mixed-mode exact method. Thus, the exact substructure method variants with free-interface, fixed-interface or mixed modes form a systematic theory of substructure methods, which is unified by the new mixed-mode variant. This new exact variant not only has this important theoretical significance but also has great practical significance because it can lead to new approximate methods and to a deeper understanding of existing ones, e.g., quasi-comparison function methods, dynamic condensation methods or substructure modal synthesis methods.