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Updating inverses in matrix analysis of structures
Author(s) -
Castillo E.,
Cobo A.,
FernándezCanteli A.,
Jubete F.,
Pruneda E.
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19981230)43:8<1479::aid-nme482>3.0.co;2-d
Subject(s) - matrix (chemical analysis) , mathematics , algebra over a field , computer science , algorithm , pure mathematics , materials science , composite material
We deal with the problem of updating inverses. Several methods which allow calculating the inverse of a matrix when one or several rows (columns) are changed, or one or several rows and the same number of columns are added or removed are given. They are based on a method for calculating inverses given by Jubete and Castillo, which uses the concept of orthogonal sets, and lead to a considerable saving in computational power. The methods are ideal for being used in the design process of structures, where stiffness matrices are sequentially modified by simply changing rows (columns), and adding or removing rows and columns, as the result of modifying the geometric or structural characteristics of its pieces, the structure's degrees of freedom, and/or the boundary conditions. Some examples of simple structures are given to illustrate the methodology. Finally, a discussion about its practical application and some conclusions and recommendations are given. © 1998 John Wiley & Sons, Ltd.