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Fast exact linear and nonlinear structural reanalysis and the Sherman-Morrison-Woodbury formulas. (English) Zbl 0971.74076
Summary: We review several exact fast static structural reanalysis techniques for truss structures, plate structures, and for frames. Most utilize the property that the solution of a system of linear equations can be updated inexpensively when the matrix is changed 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 update 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 nonlinear reanalysis problems. For a linear reanalysis, the extension reduces to the SMW formulas.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74K99 Thin bodies, structures
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