Journal ArticleDOI
Fast exact linear and non‐linear structural reanalysis and the Sherman–Morrison–Woodbury formulas
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This paper shows that the exact fast static structural reanalysis techniques introduced by researchers mostly for truss structures and some for frames and plate structures are variants of the well-known Sherman–Morrison and Woodbury (SMW) formulas for the update of the inverse of a matrix.Abstract:
Several exact fast static structural reanalysis techniques, introduced by researchers mostly for truss structures and some for frames and plate structures, are reviewed. 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 non-linear reanalysis problems. For a linear reanalysis, the extension reduces to the SMW formulas. Copyright © 2001 John Wiley & Sons, Ltd.read more
Citations
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Multiresolution green's function methods for interactive simulation of large-scale elastostatic objects
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References
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Journal ArticleDOI
Updating the inverse of a matrix
TL;DR: The history of these fomulas is presented and various applications to statistics, networks, structural analysis, asymptotic analysis, optimization, and partial differential equations are discussed.
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Approximation concepts for optimum structural design — a review
TL;DR: It is shown that, although the lack of comparative data established on reference test cases prevents an accurate assessment, there have been significant improvements in approximation concepts since the introduction of approximation concepts in the mid-seventies.
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Static Reanalysis: A Review
TL;DR: In this paper, the methods of static reanalysis of structures are reviewed and an update on the review written by Arora in 1976 is provided. But the review is limited to static re-analysis.
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Divergence-free velocity fields in nonperiodic geometries
TL;DR: The influence matrix method of enforcing incompressibility in pseudospectral simulations of fluid dynamics, as described by Kleiser and Schumann for channel flow, is generalized to other geometries as mentioned in this paper.