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
A preliminary version of this work was presented at the 4th International Conference on Engineering Optimization (EngOpt 2014).
Here, and throughout the paper, the use of ”continuous optimization” refers to solving a discretized optimization problem with continuous design variables.
An open-source framework is available at www.github.com/asny/2D-DSC.
The design with a sharp corner and filtering of other parts in Le et al. (2011) obtained by applying a nonuniform filter.
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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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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DOI: https://doi.org/10.1007/s00158-017-1656-x