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<p>Structural topology optimization aims to optimize the material layout in the design domain to achieve the best performance with certain constraints. Multi-material topology optimization leverages the distinct properties of various materials to create high-performance structures. In this paper, a game theory-based multi-material topology optimization method (referred to as GTMTO) is proposed by treating the original multi-material optimization as a complete information dynamic game and the game is decomposed using a non-linear Gauss–Seidel type algorithm into a series of “solid-void” optimizations. These sub-problems are then efficiently solved using non-parametric optimization methods, which not only enhances computational efficiency but also increases the design degree of freedom. The convergence and optimality demonstration of the proposed method are given by optimality theorem of dynamic programming, guaranteeing that GTMTO can achieve at least a local optimum. Two classic multiple-materials topology optimization examples, including compliance minimization and design of compliant mechanism, are adopted to demonstrate the ability of GTMTO. The results indicate that GTMTO gets better results than AAP and costs less computation. In addition, the effect of material optimization order on the final results and convergence of GTMTO are investigated using 3 materials. The results show that the “solid-void” optimization scheme follows the principle from stronger to the weaker material can ensure the optimality of the optimization process of GTMTO. Finally, approximate reanalysis is introduced to save the computational consumption of GTMTO. Numerical validation cases show that approximate reanalysis is convergent, and the difference caused by approximate reanalysis is acceptable for engineering.</p>

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Game theory-based multi-material topology optimization

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • Weixuan Liu,
  • Zhihao Lei,
  • Kaiming Luo,
  • Haiquan Jing

摘要

Structural topology optimization aims to optimize the material layout in the design domain to achieve the best performance with certain constraints. Multi-material topology optimization leverages the distinct properties of various materials to create high-performance structures. In this paper, a game theory-based multi-material topology optimization method (referred to as GTMTO) is proposed by treating the original multi-material optimization as a complete information dynamic game and the game is decomposed using a non-linear Gauss–Seidel type algorithm into a series of “solid-void” optimizations. These sub-problems are then efficiently solved using non-parametric optimization methods, which not only enhances computational efficiency but also increases the design degree of freedom. The convergence and optimality demonstration of the proposed method are given by optimality theorem of dynamic programming, guaranteeing that GTMTO can achieve at least a local optimum. Two classic multiple-materials topology optimization examples, including compliance minimization and design of compliant mechanism, are adopted to demonstrate the ability of GTMTO. The results indicate that GTMTO gets better results than AAP and costs less computation. In addition, the effect of material optimization order on the final results and convergence of GTMTO are investigated using 3 materials. The results show that the “solid-void” optimization scheme follows the principle from stronger to the weaker material can ensure the optimality of the optimization process of GTMTO. Finally, approximate reanalysis is introduced to save the computational consumption of GTMTO. Numerical validation cases show that approximate reanalysis is convergent, and the difference caused by approximate reanalysis is acceptable for engineering.