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Combined shape and topology optimization for minimization of maximal von Mises stress

Abstract

This work shows that a combined shape and topology optimization method can produce optimal 2D designs with minimal stress subject to a volume constraint. The method represents the surface explicitly and discretizes the domain into a simplicial complex which adapts both structural shape and topology. By performing repeated topology and shape optimizations and adaptive mesh updates, we can minimize the maximum von Mises stress using the p-norm stress measure with p-values as high as 30, provided that the stress is calculated with sufficient accuracy.

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Notes

  1. 1.

    A preliminary version of this work was presented at the 4th International Conference on Engineering Optimization (EngOpt 2014).

  2. 2.

    Here, and throughout the paper, the use of ”continuous optimization” refers to solving a discretized optimization problem with continuous design variables.

  3. 3.

    An open-source framework is available at www.github.com/asny/2D-DSC.

  4. 4.

    The design with a sharp corner and filtering of other parts in Le et al. (2011) obtained by applying a nonuniform filter.

  5. 5.

    For all studies we use δ ave = 15mm and \(A = 0.5 \sqrt { 3 \delta _{\text {ave}}^{2} /4 }\textit {mm}^{2}\) unless otherwise stated.

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Acknowledgments

The authors appreciate the support of the Villum foundation through the grant “NextTop” as well as the EU-project “LaScISO”. Also, we would like to express our gratitude to Andreas Bærentzen and Morten Nobel-Jørgensen for assistance, support and valuable discussions.

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Correspondence to Niels Aage.

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Lian, H., Christiansen, A.N., Tortorelli, D.A. et al. Combined shape and topology optimization for minimization of maximal von Mises stress. Struct Multidisc Optim 55, 1541–1557 (2017). https://doi.org/10.1007/s00158-017-1656-x

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Keywords

  • Stress minimization
  • Combined shape and topology optimization
  • Explicit surface representation
  • Deformable simplicial complex method