Dual Substructuring (numerically, theoretically)

Research Topics

  • Structural Dynamics
  • Dual Methods
  • Linear Model Order Reduction
  • Basis Augmentation
  • Interface Reduction
  • Dual Craig-Bampton Method

Student Projects

Student projects covering the research topics can be found here.


Description

Dynamic substructuring is an efficient way to reduce the size and to analyse the dynamical behaviour of large models.

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. On the other hand, 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 methods of MacNeal and Rubin, 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. Moreover, the dual Craig-Bampton method leads to simpler reduced matrices compared to other free-interface methods and these reduced matrices are similar to the classical Craig-Bampton matrices.

Compared to MacNeal's and Rubin's method, the weak interface compatibility of the dual Craig-Bampton method avoids locking problems occurring during the application of the aforementioned methods. Therefore, the approximation accuracy is improved. But the fact that a weak interface compatibility is allowed in the dual Craig-Bampton method implies that the infinite eigenvalues related to the Lagrange multipliers in the non-reduced problem are now becoming finite and negative. In practice those negative eigensolutions will appear only in the higher eigenvalue spectrum if the reduction space is rich enough. Nevertheless, the reduction basis has to be selected with care avoiding potential non-physical effects of the possibly occurring negative eigenvalues.