Solving the Over-Constrained Hurty/Craig-Bampton Problem

The Hurty/Craig-Bampton (H/CB) model representation involves a mathematical limitation that the normal modes must be computed with all retained physical degrees of freedom (DoFs) constrained. With this limitation, over-constrained normal modes occur when the number of retained physical DoFs exceeds the number of physical DoFs that the reduced-order model couples to the system (tied DoFs). Experience has shown that over-constrained normal modes present several challenges including complicating the definition for modal truncation, damping, and resulting in slow convergence characteristics. In this paper, a mixed-boundary formulation is utilized to mitigate the over-constrained H/CB problem. The residual flexibility mixed-boundary (RFMB) method allows the computation of the normal modes relative to a subset of the retained physical DoFs thereby removing the H/CB limitation on the normal modes’ boundary conditions. With this, a simplified definition of modal truncation and damping naturally occurs. Furthermore, for the limiting cases, RFMB offers the advantage of exactly converging to the time-tested method of H/CB for the all-fixed boundary and Rubin for the all-free boundary case. Given the advantages that the RFMB method offers, it was implemented as “default” in MSC/NASTRAN soon after its development.