CURRENT DYNAMIC SUBSTRUCTURING METHODS AS APPROXIMATIONS TO CONDENSATION MODEL-REDUCTION

Condensation Model Reduction (CMR) theory, when viewed as a dynamic su bstructuring method, is shown to encompass much of the existing dynami c substructuring methods as special cases of a single unified approach . Dynamic substructuring refers to the partitioning of a semi-discrete (continuous-in-time) mathematical model with respect to its dependenc e on the discretized independent variables (usually spatial) with the typical intention of eliminating most of the degrees-of-freedom in eac h partition (substructure) of a subset of isolated partitions. As an e xample, a contiguous subset of finite elements could be viewed as a su bstructure (superelement). One important use of dynamic substructuring is, hence, to analyze complex dynamic systems that are too large for current computers by reducing their size. The three currently used met hods of dynamic substructuring are referred to as Guyan, Improved Redu ced System (IRS), and Component Mode Synthesis (CMS) reduction, the la tter having several variants. (The related Modal Reduction method was not considered here since, in that method, the work associated with re ducing a particular substructure is not limited to that substructure.) In contrast to the current methods, the accuracy of CMR can be system atically improved by the inclusion of nonmodal higher order terms (as well as by the inclusion of additional modes). It is shown that the tr ansformation matrices associated with both IRS and the Craig-Bampton ( fixed interface) version of CMS approximate corresponding special case s of CMR. (The reduced-degree-of-freedom mass, damping, and stiffness matrices are different from those of CMR because CMR does not reduce t he matrices via a matrix transformation.) In addition, the appearance of modes in CMR occurs as a natural consequence of the theory and not, as in CMS, as a heuristic inclusion to the transformation matrix. Cla ssic Guyan reduction, in its entirety, is also shown to approximate a special case of CMR.