Design sensitivity analysis of structures based upon the singular value decomposition

The singular value decomposition (SVD) is employed for design sensitivity analysis of structures. As the squares of singular values are the bounds of power, energy and power spectral density ratios between the input and output vectors, shaping the singular values of a structure is equivalent to shaping the response of the structure. Comparison is made of the proposed sensitivity analysis based upon the SVD with the conventional techniques. The issues such as structural robustness, worst loading case and multiple load cases are studied. As shown, design sensitivity analysis based upon the SVD can give good insight into static and dynamic response characteristics of structures; it is more informative than eigenvalue design sensitivity analysis and, in particular, computationally advantageous in case of multiple load cases. Numerical examples are presented to illustrate the proposed approach.