Applications of singular value decomposition in structural optimisation

The usage of the singular value decomposition (SVD) in scope of structural optimisation is motivated. We briefly outline several applications of SVD from different scientific fields to point out their similarities with structural optimisation. Here, our focus is on model reduction, on numerical defects and on their quantitative description using SVD. In this context we address the singular value decomposition of matrices which appear in an optimisation algorithm, i.e. the pseudo load matrix and the sensitivity matrix. In this contribution on the example of topology optimisation we would like to clarify all the properties of SVD. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)