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.
Highlights
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 varietyResponsible Editor: Jianbin DuUnlike the case of single-objective optimisation, in the presence of many, usually conflicting, criteria, it is more appropriate to generate a set of optimal solutions which constitute the so-called Pareto set
Restricting the comparison to the applications of the uSNC, the results obtained in this paper show that some of the optimal points slightly differ in the frequency or compliance value
This work presented a strategy to deal with multiple objectives in SIMP topology optimisation, offering an alternative to the most common compromise programming, which is employed in almost the totality of the reviewed literature
Summary
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. Metaheuristics, which are out of the scope of this work, for multi-objective structural optimisation problems, were reviewed by Zavala et al (2014), while Marler and Arora (2004) presented a survey of continuous non-linear multi-objective methods In the latter, the authors introduced a classification of these methods depending on how the decision maker is required to express the relative importance or weight of each cost function, usually referred to as designer’s preference. It illustrates the implementation of the multi-objective strategy, presented in this paper, with the commercial software Altair OptiStruct.
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