Norm optimization techniques for improved structural reanalysis

An approximate structural reanalysis method that is based on a binomial series expansion and that employs operations of matrix scaling and norm minimization is presented in this paper. It is shown that the scaling operation significantly reduces several unfavourable effects of the magnitude and nature of design changes on the prediction quality of the model. Norm minimization provides a very effective and optimal scaling factor in a simplified manner. The most significant achievement of the work is the development of an effective and efficient reanalysis model that provides near-exact response quantities even when large and strongly dispersed changes are introduced in the design. The potential capacity of the proposed method of improvement is demonstrated using numerical examples. Graphical interpretation of the concept is also provided.