Generating minimal Pareto sets in multi-objective topology optimisation: an application to the wing box structural layou
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RESEARCH PAPER
Generating minimal Pareto sets in multi-objective topology optimisation: an application to the wing box structural layout Fabio Crescenti1
· Timoleon Kipouros2 · David J. Munk3 · Mark A. Savill2
Received: 29 February 2020 / Revised: 27 August 2020 / Accepted: 17 September 2020 © The Author(s) 2020
Abstract Multi-objective topology optimisation problems are often tackled by compromising the cost functions according to the designer’s knowledge. Such an approach however has clear limitations and usually requires information which especially at the preliminary design stage could be unavailable. This paper proposes an alternative multi-objective approach for the generation of minimal Pareto sets in combination with density-based topology optimisation. Optimised solutions are generated integrating a recently revised method for a posteriori articulation of preferences with the Method of Moving Asymptotes. The methodology is first tested on an academic two-dimensional structure and eventually employed to optimise a full-scale aerospace structure with the support of the commercial software Altair OptiStruct . For the academic benchmark, the optimised layouts with respect to static and dynamic objectives are visualised on the Pareto frontier and reported with the corresponding density distribution. Results show a progressive and consistent transition between the two extreme single-objective layouts and confirm that the minimum number of evaluations was required to fill the smart Pareto front. The multi-objective strategy is then coupled with Altair OptiStruct and used to optimise a full-scale wing box, with the clear purpose to fill a gap in multi-objective topology optimisation applied to the wing primary structure. The proposed methodology proved that it can generate efficiently non-dominated optimised configurations, at a computational cost that is mainly driven by the model complexity. This strategy is particularly indicated for the preliminary design phase, as it releases the designer from the burden to assign preferences. Furthermore, the ease of integration into a commercial design tool makes it available for industrial applications. Keywords Multi-objective · Topology optimisation · SIMP method · Smart Normal Constraint method · Wing design
1 Introduction Since the conception of the SIMP (Solid Isotropic Material with Penalisation) method (Bendsøe 1989; Zhou and Rozvany 1991; Mlejnek 1992), density-based topology optimisation has been successfully applied to a wide variety
Responsible Editor: Jianbin Du Fabio Crescenti
[email protected] 1
School of Aerospace, Transport and Manufacturing, Cranfield University, Bedford, MK43 0AL, UK
2
Centre for Propulsion Engineering, Cranfield University, Bedford, MK43 0AL, UK
3
Aerospace Division, Defence Science and Technology Group, 506 Lorimer Street, Fishermans Bend, Victoria, 3207, Australia
of problems, including full-scale aerospace structures (Zhu et al. 2016) and multi-physics applications (Deaton and Grandhi 2014), becoming a genera
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