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Structural optimization with several discrete design variables per part by outer approximation

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Abstract

The article proposes an optimal design approach to minimize the mass of load carrying structures with discrete design variables. The design variables are chosen from catalogues, and several variables are assigned to each part of the structure. This allows for more design freedom than only choosing parts from a catalogue. The problems are modelled as mixed 0–1 nonlinear problems with nonconvex continuous relaxations. An algorithm based on outer approximation is proposed to find optimized designs. The capabilities of the approach are demonstrated by optimal design of a space frame (jacket) structure for offshore wind turbines, with requirements on natural frequencies, strength, and fatigue lifetime.

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Notes

  1. This assumption is by no means critical for the optimal design approach in this article. It is commonly encountered for similar modelling situations in structural optimization e.g. for multi-material topology optimization Bendsøe and Sigmund (1999) and discrete material optimization, see e.g. Lund and Stegmann (2005) and Stegmann and Lund (2005).

  2. This term refers to constraints which should be removed from the problem formulation if the corresponding part is not in the structure described by the current design variables.

  3. Solve should, in this context, be interpreted as finding a point numerically satisfying the first-order optimality conditions.

  4. The outer approximation property is generally not maintained for non-convex problems such as (P x ). The algorithm should therefore be considered as a heuristic.

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Acknowledgements

The research presented in this manuscript is part of the strategic research project ABYSS: Advancing BeYond Shallow waterS - Optimal design of offshore wind turbine support structures (www.abyss.dk). The project is funded by the Danish Council for Strategic Research. The funding is gratefully acknowledged. The authors would like to thank the anonymous reviewers for valuable inputs to the final manuscript. In particular, the suggested benchmark with the genetic algorithm provided new insights to the performance of the presented optimization approach.

We would like to thank our colleague Alexander Verbart for his contributions to JADOP.

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Authors and Affiliations

  1. DTU Wind Energy, Technical University of Denmark, Frederiksborgvej 399, 4000, Roskilde, Denmark

    Mathias Stolpe & Kasper Sandal

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  1. Mathias Stolpe
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  2. Kasper Sandal
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Correspondence to Mathias Stolpe.

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Stolpe, M., Sandal, K. Structural optimization with several discrete design variables per part by outer approximation. Struct Multidisc Optim 57, 2061–2073 (2018). https://doi.org/10.1007/s00158-018-1941-3

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  • DOI: https://doi.org/10.1007/s00158-018-1941-3

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