Evaluation of substructure reduction techniques with fixed and free interfaces

Abstract

Substructure reduction techniques are efficient methods to reduce the size of large models used to analyze the dynamical behavior of complex structures. The most popular approach is a fixed interface method, the Craig-Bampton method (1968), which is based on fixed interface vibration modes and interface constraint modes. In contrast, free interface methods employing free interface vibration modes together with attachment modes are also used, e.g. MacNeal's method (1971) and Rubin's method (1975). The methods mentioned so far assemble the substructures using interface displacements (primal assembly). The dual Craig-Bampton method (2004) uses the same ingredients as the two aforementioned free interface methods, but assembles the substructures using interface forces (dual assembly). This method enforces only weak interface compatibility between the substructures, thereby avoiding interface locking problems as sometimes experienced in the primal assembly approaches using free interface modes. The dual Craig-Bampton method leads to simpler reduced matrices compared to other free interface methods and the reduced matrices are sparse, similar to the classical Craig-Bampton matrices. In this contribution we evaluate the primal (classical) formulation of the Craig-Bampton method, the MacNeal method, the Rubin method and the dual formulation of the Craig-Bampton method. The presented theory and the comparison between the four substructuring methods will be illustrated on the Benfield truss, on a three-dimensional beam frame and on a two-dimensional solid plane stress problem.