Enhanced analysis of design sensitivities in topology optimization

This paper outlines an enhanced analysis of the design sensitivities beyond the standard computation of the gradient values. It is based on the analytical derivation and efficient computation of the Fréchet derivatives of objectives and constraints with respect to the full space of all possible design variables. This overhead of sensitivity information is examined by a singular value decomposition (SVD) in order to detect major and minor influence and response modes of the considered structure. Thus, this methodology leads to valuable qualitative and quantitative insight which is so far unused in standard approaches to structural optimization. This knowledge enables the optimiser to understand and improve the models systematically which are usually set up entirely by engineering experience and intuition. Furthermore, a reduction of the complete design space to the most valuable subspace of design modifications demonstrates the information content of the decomposed sensitivities. The generic concept is applied to topology optimization which is a challenging model problem due to the large number of independent design variables. The details specific to topology optimization are outlined and the pros and cons are discussed. An illustrative example shows that reasonable optimal designs can be obtained with a small percentage of properly defined design variables. Nevertheless, further research is necessary to improve the overall computational efficiency.