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On the usefulness of non-gradient approaches in topology optimization

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Abstract

Topology optimization is a highly developed tool for structural design and is by now being extensively used in mechanical, automotive and aerospace industries throughout the world. Gradient-based topology optimization algorithms may efficiently solve fine-resolution problems with thousands and up to millions of design variables using a few hundred (finite element) function evaluations (and even less than 50 in some commercial codes). Nevertheless, non-gradient topology optimization approaches that require orders of magnitude more function evaluations for extremely low resolution examples keep appearing in the literature. This forum article discusses the practical and scientific relevance of publishing papers that use immense computational resources for solving simple problems for which there already exist efficient solution techniques.

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Fig. 1
Fig. 2

Notes

  1. Despite its name the ESO method may in fact be categorized as a gradient-based method since it uses sensitivity analysis to determine discrete design updates.

  2. Wu and Tseng (2010) report a compliance value of c = 64.44, however, this value was not reproducible by using the FE-solver from the 99-line Matlab code by Sigmund (2001). Exact agreement was however obtained when comparing objective values with the original examples presented in Wang and Tai (2005).

  3. For some reason the number of iterations for the same problem solved using density filtering is an order of magnitude higher (455). The reason for this difference will be investigated in future work.

  4. Claiming that GTO methods yield non-discrete, grey-scale design is not enough since these results can be easily thresholded as demonstrated in Section 2.1.

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Acknowledgements

The author would like to thank Rafael Haftka, George Rozvany, Ming Zhou and members of the TopOpt-group (www.topopt.dtu.dk) for fruitful discussions with regards to the conclusions and recommendations given in this paper.

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  1. Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, Nils Koppels Alle, B. 404, 2800, Lyngby, Denmark

    Ole Sigmund

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Sigmund, O. On the usefulness of non-gradient approaches in topology optimization. Struct Multidisc Optim 43, 589–596 (2011). https://doi.org/10.1007/s00158-011-0638-7

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