Numerical instability of classical free-interface component mode synthesis techniques

Two classical free-interface component mode synthesis (CMS) methods are briefly reviewed, and highlighted the sources of numerical instability. In addition, a modest modification to the classical free-interface CMS formulation by Craig and Chang which alleviates the numerical instability suffered by the original method is presented. To support the discussion, the numerical instability is demonstrated with a simple three-dimensional, two-component finite element model.