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Topology optimization of thin-walled cross section using moving morphable components approach

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Abstract

Thin-walled beams are extensively applied in the engineering structures, in which the conceptual design of cross-sectional shape and topology is the most important issue. Traditional topology optimization methods cannot easily obtain the thin-walled features. Therefore, a thin-walled cross-sectional design method using the moving morphable components (MMC) approach is proposed in this paper. To acquire a thin-walled structure with a high stiffness-to-mass ratio, the cross-sectional area is defined as the objective function, and the cross-sectional bending and torsional moments of inertia are selected as constraints. The bending and torsional moments of inertia in arbitrary domain are both solved by using the finite element method. In addition, the sensitivities of cross-sectional area, bending moments of inertia, and torsional moment of inertia with respect to geometrical parameters of components are derived in the MMC framework, respectively. To demonstrate the effectiveness and accuracy of this method, numerical examples are given to consider the torsional, the bending, and the combined conditions, respectively. By post-process, the obtained thin-walled features can be further transformed into stamping sheets.

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Funding

This work was supported by the Plan for Scientific and Technological Development of Jilin Province (Grant No. 20200201272JC), the Science and Technology Research Project of Education Department of Jilin Province (Grant No. JJKH20190013KJ and JJKH20190142KJ), and Exploration Foundation of State Key Laboratory of Automotive Simulation and Control.

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Authors and Affiliations

  1. State Key Laboratory of Automotive Simulation and Control, Jilin University, Changchun, 130025, People’s Republic of China

    Guikai Guo, Yanfang Zhao & Wenjie Zuo

  2. School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130025, People’s Republic of China

    Guikai Guo, Yanfang Zhao, Weihe Su & Wenjie Zuo

Authors
  1. Guikai Guo
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  2. Yanfang Zhao
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  3. Weihe Su
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  4. Wenjie Zuo
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Correspondence to Wenjie Zuo.

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Replication of results

The selected MMA parameters in the paper are given as: c_mma = 1000, asyinit = 0.5, asyincr = 1.2, asydecr = 0.7, and albefa = 0.2. Also the other involved parameters of the Heaviside function and TDF are referred to the paper (Zhang et al. 2016c). Readers interested in the Matlab code are encouraged to contact the authors by e-mail.

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Guo, G., Zhao, Y., Su, W. et al. Topology optimization of thin-walled cross section using moving morphable components approach. Struct Multidisc Optim 63, 2159–2176 (2021). https://doi.org/10.1007/s00158-020-02792-0

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  • DOI: https://doi.org/10.1007/s00158-020-02792-0

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