Updating inverses in matrix analysis of structures

✍ Scribed by E. Castillo; A. Cobo; A. Fernández-Canteli; F. Jubete; E. Pruneda

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 588 KB
• Volume: 43
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/(sici)1097-0207(19981230)43:8<1479::aid-nme482>3.0.co;2-d

✦ Synopsis

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 sti ness matrices are sequentially modiÿed 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.