Fast exact linear and non-linear structural reanalysis and the Sherman-Morrison-Woodbury formulas

Several exact fast static structural reanalysis techniques, introduced by r esearchers mostly for truss structures and some for frames and plate struct ures, are reviewed. Most utilize the property that the solution of a system of linear equations can be updated inexpensively when the matrix is change d by a low-rank increment. This paper shows that these methods are variants of the well-known Sherman-Morrison and Woodbury (SMW) formulas for the upd ate of the inverse of a matrix. In addition, the paper extends the low-cost linear reanalysis in the spirit of the SMW formulas to some non-linear rea nalysis problems. For a linear reanalysis, the extension reduces to the SMW formulas. Copyright (C) 2001 John Wiley & Sons, Ltd.