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A B-spline multi-parameterization method for multi-material topology optimization of thermoelastic structures

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Abstract

A B-spline multi-parameterization method (MPM) is presented in this paper for topology optimization of thermoelastic structures. As thermoelastic topology optimization belongs to a kind of design-dependent problems that are complicated to deal with, this method is aimed to solve thermoelastic problems with multiple materials by means of B-spline parameterization that integrates together the recursive multiphase material interpolation (RMMI) and the uniform multiphase material interpolation (UMMI) schemes. The commonly used discrete pseudo-density variables related to the finite element model are thus replaced with continuous pseudo-density fields dominated by control parameters in the B-spline space. In this sense, B-spline multi-parameterization is used for the first time to represent multiple pseudo-density fields and multi-material properties including elasticity matrix and thermal stress coefficient. Compared with traditional pseudo-density method, the current method has the advantage of not only attaining a reduction of design variables in number but also achieving a regularized distribution of pseudo-density fields with a clear material layout over the whole structure domain. Numerical results show that the stable convergences are achieved with the avoidance of gray elements, checkerboards, and multi-material overlapping owing to the high continuity of B-spline preserved for multi-material distributions. Besides, it is found that the RMMI scheme distributes less stiff materials around stiff materials, while the UMMI scheme tends to gather less stiff materials together.

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Funding

This work is supported by the National Key Research and Development Program of China (2017YFB1102800) and the National Natural Science Foundation of China (11620101002, 11722219).

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Authors and Affiliations

  1. State IJR Center of Aerospace Design and Additive Manufacturing, Northwestern Polytechnical University, Xi’an, 710072, Shaanxi, China

    Zhao Xu, Weihong Zhang, Tong Gao & Jihong Zhu

Authors
  1. Zhao Xu
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  2. Weihong Zhang
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  3. Tong Gao
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  4. Jihong Zhu
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Correspondence to Weihong Zhang.

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The authors declare that they have no conflict of interest.

Replication of results

All the results and datasets in this paper are generated using our homemade MATLAB codes. The source codes can be available only for academic use from the corresponding author with reasonable request.

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Responsible Editor: YoonYoung Kim

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Xu, Z., Zhang, W., Gao, T. et al. A B-spline multi-parameterization method for multi-material topology optimization of thermoelastic structures. Struct Multidisc Optim 61, 923–942 (2020). https://doi.org/10.1007/s00158-019-02464-8

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  • DOI: https://doi.org/10.1007/s00158-019-02464-8

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