Abstract
Multi-scale topology optimization (a.k.a. micro-structural topology optimization, MTO) consists in optimizing macro-scale and micro-scale topology simultaneously. MTO could improve structural performance of products significantly. However, a few issues related to connectivity between micro-structures and high computational cost have to be addressed, without resulting in loss of performance. In this paper, a new efficient multi-scale topology optimization (EMTO) framework has been developed for this purpose. Connectivity is addressed through adaptive transmission zones which limit loss of performance. A pre-computed database of micro-structures is used to speed up the computing. Design variables have also been chosen carefully and include the orientation of the micro-structures to enhance performance. EMTO has been successfully tested on two-dimensional compliance optimization problems. The results show significant improvements compared to mono-scale methods (compliance value lower by up to 20% on a simplistic case or 4% on a more realistic case), and also demonstrate the versatility of EMTO.
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Acknowledgements
The authors would like to thank École polytechnique for funding this research through an AMX PhD fund.
The authors also thank Krister Svanberg for providing the MATLAB MMA code, and Julien Pedron for his help with the computer Pando.
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All the codes and material used to obtain the results presented in this paper can be found at https://github.com/mid2SUPAERO/EMTO. This includes the databases and the code to build them.
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Appendices
Appendix 1: Code for thresholding densities to 0 or 1
Appendix 2: Initial designs used in micro-structure optimization multi-start strategy
The different initial designs in Figs. 21 and 22 were used as part of the micro-structure optimization multi-start strategy. Each of these designs was the best initial design for at least one of the points in the database.
Initial designs for cells with 2 transmission zones per edge
Initial designs for cells with 3 transmission zones per edge
Appendix 3: Input–output examples from the database
Three random sets of input were tested on the database to exemplify how it works. The database of cells with 3 transmission zones per edge is used. The inputs appear on the left in Figs. 23, 24 and 25. The top input is density, the second input is orientation (in radians), and the lowest input is cubicity, as in Fig. 8. The output tensors and micro-structures appear on the right in those figures.
Random database example 1
Random database example 2
Random database example 3
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Duriez, E., Morlier, J., Charlotte, M. et al. A well connected, locally-oriented and efficient multi-scale topology optimization (EMTO) strategy. Struct Multidisc Optim 64, 3705–3728 (2021). https://doi.org/10.1007/s00158-021-03048-1
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DOI: https://doi.org/10.1007/s00158-021-03048-1