Substructuring is to subdivide an overall structure into two or more substructures to reduce the model-order of the huge structural system. The problem to synthesize the substructures is established by a mathematical system consisting of equilibrium equations and prescribed compatibility conditions. Considering that the compatibility conditions are constraints, this study derives the analytical methods for describing the responses of constrained static and dynamic systems and provides a structural synthesis method based on the Guyan condensation method and the derived equations. The analysis process is carried out by partitioning into two regions of interior and boundary regions, and giving the compatibility conditions. And the dynamic analysis reduces model-order based on the constraint conditions between modal coordinates by the first several mode shape matrix. The validity of the proposed method is illustrated through the structural synthesis of stable and unstable substructures, and the structural reanalysis to evaluate the structural response for changes in the design without solving the complete set of modified simultaneous equation
