Dynamic-Condensation-Based Reanalysis by Using the Sherman–Morrison–Woodbury Formula

Abstract

The demand for large-scale design optimization and probability-based analysis is constantly increasing. In design optimization and stochastic analysis, repeated analyses are required, which impede computational efficiency. Several effective reanalysis techniques using the Sherman–Morrison–Woodbury (SMW) formula have been formulated for application to static analysis. However, it is difficult to directly apply the SMW formula for dynamic reanalysis, and, consequently, substructuring techniques are frequently employed for the dynamic reanalysis. The existing dynamic substructuring finite element techniques require recalculations for all the substructures, including changed elements, even when only a single element is changed; thus, the accuracy is reduced owing to the interface assumption. Therefore, to apply the SMW formula to the dynamic reanalysis, an approach is employed in which, using dynamic condensation, the dynamic problem is transformed into a problem where the SMW formula can be employed. Furthermore, to improve the speed of convergence in the condensation method, the proposed method reuses the condensed matrices calculated in the previous analysis. Thus, the proposed method precisely updates and recalculates only the elements of interest, thus increasing the computation efficiency and accuracy. Several numerical examples are presented to verify the efficiency and accuracy of the proposed method.