Solving topologically modified structures

Abstract During the design process, the engineer frequently makes modifications to the structure. At times, the modification involves topological changes such as joint addition or joint deletion which result in an increase or a decrease in the size of the stiffness matrix. These modifications may not lead to a completely different configuration. In such cases the results of a previous analysis can be used to decrease the computational effort which is needed for a complete reanalysis of the modified structure. This paper presents two algorithms for obtaining the inverse of the modified stiffness matrix. The algorithms use the results of a previous solution to obtain solutions when joints are added to or deleted from a structure. The algorithm for joint addition uses Householder's identity to obtain the inverse of that portion of the modified stiffness matrix corresponding to the original stiffness matrix. The inverse of the modified stiffness matrix is then obtained by inversion by matrix partitioning. The algorithm for joint deletion uses the extraction of the inverse of a reduced matrix and Householder's identity to obtain the inverse of the modified stiffness matrix. A comparison of operation counts for the proposed algorithms and a complete inversion indicates that by using the proposed methods a 20–80 per cent saving in the computational effort is achieved.