Flexibility-based component mode synthesis: or is it possible to break impasse in mode selection and convergence uncertainties ?

Existing component mode synthesis methods, while attractive for their practicality and heuristic soundness, cannot claim convergence as the Rayleigh-Ritz theory can. Recently, new demands for high accuracy much beyond two or three digits in the modeling of emerging vibration problems such as micro-mechanical systems, has motivated us for the development of high-fidelity component mode synthesis procedures. In this lecture, we present several new component mode synthesis techniques based on the flexibility-based partitioned equations of motion for structures. For each approximation, a corresponding substructural mode selection expression is identified, which can be used for a rational mode selection criterion for each substructure. The present methods can be implemented as a hierarchy-free algorithm for reducing the interface degrees of freedom as opposed to a tree-structure architecture required by the Craig-Bampton method for parallel computations. Numerical experiments show that the present flexibility-based component mode synthesis procedure outperforms stiffness-based methods, including the Craig-Bampton method, for simple plates and a ring modeled with 160,000 DOFs.