Reanalysis-based fast solution algorithm for flexible multi-body system dynamic analysis with floating frame of reference formulation

Abstract

In order to improve the computational efficiency of flexible multi-body system dynamic analysis with floating frame of reference formulation (FFRF), a reanalysis-based fast solution algorithm is developed here. The data of FFRF analysis process can be divided into two parts: unchanged mass and stiffness matrices part kept by deformation, and changed mass and stiffness matrices part caused by rigid motion and joint constraints. In the proposed method, the factorization of the unchanged part is reused in the entire solution process via employing the reanalysis concept; and the changed part is treated as structural modification. Meanwhile, the joint constraints are handled with an exact reanalysis method—the Sherman–Morrison–Woodbury (SMW) formula, which is also beneficial for saving the computational cost. Numerical examples demonstrate that the computational efficiency of the proposed method is higher than that of full analysis, especially in large scale problems. Moreover, since the proposed fast FFRF solution algorithm is-based on exact reanalysis methods, there is no theoretical error between the results obtained by the fast solution algorithm and full analysis method.