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Solving stress and compliance constrained volume minimization using anisotropic mesh adaptation, the method of moving asymptotes and a global p-norm

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Abstract

The p-norm often used in stress constrained topology optimisation supposedly mimics a delta function and it is thus characterised by a small length scale and ideally one would also prefer to have the solid-void transition occur over a small length scale, since the material in this transition does not have a clear physical interpretation. We propose to resolve these small length scales using anisotropic mesh adaptation. We use the method of moving asymptotes with interpolation of sensitivities, asymptotes and design variables between iterations. We demonstrate this combination for the portal and L-bracket problems with p=10, and we are able to investigate mesh dependence. Finally, we suggest relaxing the L-bracket problem statement by introducing a rounded corner.

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Notes

  1. Preliminary results related to this work was presented at FEniCS 14 in Paris, June 2014, at the International Meshing Roundtable 23 in London, October 2014 and at the eleventh World Congress of Structural and Multidisciplinary Optimisation in Sydney, June 2015.

  2. except for the one case where an optimisation of the rounded L-bracket problem fails to recover from an infeasible design.

  3. Using an Intel(R) Core(TM) i7 870 @ 2.93GHz.

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Acknowledgments

This work is supported by the Villum Foundation.

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Authors and Affiliations

  1. Department of Earth Science and Engineering, Imperial College London, London, SW7 2AZ, UK

    Kristian Ejlebjerg Jensen

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  1. Kristian Ejlebjerg Jensen
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Correspondence to Kristian Ejlebjerg Jensen.

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Jensen, K.E. Solving stress and compliance constrained volume minimization using anisotropic mesh adaptation, the method of moving asymptotes and a global p-norm. Struct Multidisc Optim 54, 831–841 (2016). https://doi.org/10.1007/s00158-016-1439-9

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  • DOI: https://doi.org/10.1007/s00158-016-1439-9

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