Dynamic compliance optimization: Time vs frequency domain strategies

Dynamic compliance (structural and topology) optimization is a topic of active and fertile research carried on by several research groups aiming to extend to the dynamic regime by now well-consolidated approaches for static compliance optimization. Available approaches on this purpose are first divided into time-domain and frequency-domain strategies and then a comparison between the two is performed with respect to actual significance and CPU time of relevant optimal designs. For this paper sake reference is made to the optimal design of viscoelastic thin beams but the approach may be shown to apply with no modifications to other and possibly more complex systems such as 2D and 3D dynamic-compliance topology optimization. By extensive numerical investigations, it is shown that the frequency-domain approach to be preferred over time-domain schemes even though relevant computations happen to be heavier, mainly as far as the computation of the H∞-norm of the system transfer function is concerned.