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A multi-material topology optimization method based on the material-field series-expansion model

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Abstract

Multi-material topology optimization is an important issue in the structural and multidisciplinary design. Compared with single-material topology optimization, the multi-material design usually involves more design variables and poses higher requirement for the convergence and efficiency of the topology optimization method. This paper proposes a new multi-material topology optimization strategy based on the material-field series-expansion (MFSE) model. For a structure composed of m different phases of solid materials, m individual material fields are introduced to describe the topology distribution in the multi-material representation model. Herein, each material field is expressed as a linear combination of the eigenvectors and corresponding expansion coefficients based on a reduced series expansion. Thus, the number of design variables can be significantly reduced. Moreover, a new type of smooth Heaviside projection on the material-field function is introduced in the MFSE model, which releases the bound constraints of the material field from the optimization formulation. In this way, the efficiency of the MFSE method is further improved when solving multi-material design problems. Several 2D and 3D numerical examples are presented to show the validity and efficiency of the proposed multi-material method.

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Acknowledgements

The support of the National Natural Science Foundation of China (12002076, 11972104), the LiaoNing Revitalization Talents Program (XLYC1807187), and China Postdoctoral Science Foundation (2019TQ0047, 2019M661089) is gratefully acknowledged.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Yaguang Wang & Yangjun Luo

  2. Province Key Laboratory of Advanced Technology for Aerospace Vehicles, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian, 116024, China

    Yangjun Luo & Yi Yan

Authors
  1. Yaguang Wang
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  2. Yangjun Luo
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  3. Yi Yan
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Correspondence to Yangjun Luo.

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The authors declare that they have no conflict of interest.

Replication of results

The MMA algorithm we use here is Version September 2007 (and a small change August 2008) developed by Professor Krister Svanberg (krille@math.kth.se). The remaining parts of the code can be available only for academic use from the corresponding author on request.

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Responsible Editor: Junji Kato

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Wang, Y., Luo, Y. & Yan, Y. A multi-material topology optimization method based on the material-field series-expansion model. Struct Multidisc Optim 65, 17 (2022). https://doi.org/10.1007/s00158-021-03138-0

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  • DOI: https://doi.org/10.1007/s00158-021-03138-0

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