An Improved Rayleigh–ritz Substructure Synthesis Method Adopting Mixed Coordinates

This paper presents an improvement of the Rayleigh–Ritz substructure synthesis method that retains all the advantages of the more elaborate existing versions. The displacement field in each component is represented by a set of simple non-admissible shape functions (generalized coordinates). These are subject to a transformation to mixed coordinates (physical and internal). The physical coordinates are defined where necessary to impose boundary conditions and geometrical compatibility. The internal coordinates are chosen in order to optimize the condition number of the matrices involved. Such a change of coordinates makes possible the use of the convenient assembling procedure of the Finite Element Method. The procedure, done in a systematic manner, leaves no free choice to the user and leads to an optimal numerical behavior. Several examples of applications are presented.