Using multiple singular values in topology optimization of dynamic systems

Using multiple singular values in topology optimization of dynamic systems

Paolo Venini

download PDF

Abstract. Within the general framework of frequency-domain topology optimization of Multi Input-Multi Output (MI-MO) dynamic systems, suitable norms of the input/output transfer matrix are introduced as possible merit functions to be minimized. Among them, the by now classical H_∞-norm (i.e. the supremum of the maximum singular value over the whole frequency range), and the so-called nuclear norm (i.e. the sum of all the positive singular values are considered. Heuristic motivations are given that suggest which norm should one choose according to the practical objective to be pursued alongside a few numerical examples on topology optimization of 2D linear-elastic multiload SI-SO and MI-MO dynamic systems.

Topology Optimization, Dynamic Systems, Matrix Norms, SVD

Published online 3/17/2022, 6 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: Paolo Venini, Using multiple singular values in topology optimization of dynamic systems, Materials Research Proceedings, Vol. 26, pp 405-410, 2023


The article was published as article 66 of the book Theoretical and Applied Mechanics

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

[1] J.S. Jensen, P.B. Nakshatrala, D.A. Tortorelli, On the consistency of adjoint sensitivity analysis for structural optimization of linear dynamic problems, Struct. Multidisc. Optim. 49 (2014) 831-837.
[2] N. Olhoff, J. Du, Generalized incremental frequency method for topological design of continuum structures for minimum dynamic compliance subject to forced vibration at a prescribed low or high value of the excitation frequency, Struct. Multidisc. Optim. 54 (2016) 1113-1141.
[3] P. Venini, Topology optimization of dynamic systems uncer uncertain loads: an H_∞-norm-based approach, J. Comput. Nonlinear Dynam. 14 (2019) 021007.
[4] J. Du, N. Olhoff, Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps, Struct. Multidisc. Optim. 34 (2007) 91-110.
[5] G. Strang, Linear algebra and learning from data, Wellesley – Cambridge Press, Wellesley, 2019.
[6] S.L. Brunton, J.N. Kutz, Data-driven science and engineering – Machine learning, dynamical systems and control, Cambrige University Press, Cambridge, 2019.
[7] P. Venini, P. Ceresa, A rational H_∞-norm-based approach for the optimal design of of sesmically excited reinforced concrete frames, Earthquake Engng Struct. Dyn. 47 (2018) 1522-1543.