Static and dynamic topology optimization: an innovative unifying approach

Abstract This paper presents a topology optimization approach that is innovative with respect to two distinct matters. First of all the proposed formulation capable handle static and dynamic virtually no modifications. Secondly, inherently multi-input multi-output one, i.e., multiple objectives can be pursued in presence loads. The input-to-output transfer matrix, say $${{{\varvec{G}}}}$$ G , key ingredient governs algebraic mapping between applied loads structural response. In statics depends on design variables only, whereas it frequency variable as well case. Singular Value Decomposition (SVD) represents then core approach. values are shown gains input/output used compute proper norms $${{\varvec{G}}}$$ represent goal functions minimized. vectors provide at extra cost plant directions, load combination factors stress structure most. Numerical examples discussed much detail open issues object ongoing investigations highlighted. A full Matlab code handling problem provided an online Appendix manuscript. Its extension case may gathered following Sect. 5.