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Minimum feature size control in level set topology optimization via density fields

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Abstract

A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the solid-void interface and the density field describes the distribution of a fictitious porous material using the solid isotropic material with penalization. These fields are governed by two sets of independent optimization variables which are initially coupled using a penalty for hole nucleation. The strength of the density field penalization and projection is gradually increased during the optimization process to promote a 0–1 density distribution. In addition, a second penalty regulates the evolution of the density field in the void phase. The treatment of the density field combined with the second penalty mitigate the appearance of small design features. The minimum feature size of optimized designs is controlled by the radius of the linear filter applied to the density optimization variables. The structural response is predicted by the extended finite element method, the sensitivities by the adjoint method, and the optimization variables are updated by a gradient-based optimization algorithm. Numerical examples investigate the robustness of this approach with respect to algorithmic parameters and mesh refinement. The results show the applicability of the combined density level set topology optimization approach for both optimal hole nucleation and for minimum feature size control in 2D and 3D. This comes, however, at the cost of a more complex problem formulation and additional computational cost due to an increased number of optimization variables.

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Replication of results

Upon request, the authors will provide the full set of input parameters for the problems presented. Any optimization framework with an implementation of the approach described here should be able to reproduce our results.

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Acknowledgements

All authors acknowledge the support of the National Science Foundation (CMMI-1463287). The first author acknowledges partial auspice of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (LLNL-JRNL-820531). The third author acknowledges the support of the Defense Advanced Research Projects Agency (DARPA) under the TRADES program (agreement HR0011-17-2-0022). The opinions and conclusions presented in this paper are those of the authors and do not necessarily reflect the views of the sponsoring organizations.

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Authors and Affiliations

  1. Computational Engineering Division, Lawrence Livermore National Laboratory, 7000 East Ave, Livermore, 94550, CA, USA

    Jorge L. Barrera

  2. OHB System AG, Manfred-Fuchs-Strasse 1, 82234, Wessling, Germany

    Markus J. Geiss

  3. Ann and H.J. Smead Department, of Aerospace Engineering Sciences, University of Colorado at Boulder, 3775 Discovery Dr, Boulder, CO, 80303, USA

    Kurt Maute

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  1. Jorge L. Barrera
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Correspondence to Jorge L. Barrera.

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Barrera, J.L., Geiss, M.J. & Maute, K. Minimum feature size control in level set topology optimization via density fields. Struct Multidisc Optim 65, 94 (2022). https://doi.org/10.1007/s00158-021-03096-7

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