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Efficient multi-material topology optimization design with minimum compliance based on ResUNet involved generative adversarial network

基于引入ResUNet生成对抗式网络以柔度最小为目标的高效多材料拓扑优化设计

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Abstract

Topology optimization is a common approach for material distribution in continuous structure due to its rigorous mathematical theory. However, with the increase of material types in design domain, the computational efficiency of traditional topology optimization for multiple materials problem is greatly decreased. In this paper, a novel deep learning-based topology optimization method is proposed to achieve multi-material structural design for improving computational efficiency. A large number of multi-material topological configurations are simulated by solid isotropic material with penalization (SIMP), to construct multi-material topology optimization dataset. Subsequently, ResUNet involved generative adversarial network (ResUNet-GAN) is developed for high-dimensional mapping from design parameters to the corresponding multi-material topological configuration. Finally, the ResUNet-GAN, trained by the multi-material dataset, is utilized to design multi-material topological configuration. Numerical simulations verify that the well-trained ResUNet-GAN is successfully applied to three types of cases: the cantilever beam with double materials, the cantilever beam with triple materials, and the half-MBB with triple materials. The deep learning-based topology optimization approach is superior to the conventional methods in terms of higher computational efficiency, performing the potential of such a data-driven method to accelerate the calculation of structural optimization design.

摘要

拓扑优化由于其严格的数学理论, 成为连续结构设计中决定材料分布的重要方法. 然而, 随着材料类型在设计域内的增加, 传统拓扑优化方法的计算效率大大降低. 本文提出了一种基于深度学习的拓扑优化方法, 用于提高多材料结构拓扑优化设计的计算效率. 首先, 利用固体各向同性材料惩罚(SIMP)方法对大量多材料结构进行优化设计, 构建了多材料拓扑优化数据集. 其次, ResUNet被引入生成对抗式网络形成ResUNet-GAN, 构建了设计参数和优化构型之间的高维映射. 最后, 利用预训练的ResUNet-GAN实现多材料拓扑优化设计. 数值模拟验证了ResUNet-GAN成功地应用于双材料的悬臂梁、三材料悬臂梁、三材料简支梁结构的拓扑优化设计. 研究表明, 基于深度学习拓扑优化方法的计算效率优于传统方法, 为高效拓扑优化设计的发展奠定了理论基础.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11872080) and the Natural Science Foundation of Beijing, China (Grant No. 3192005)

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Authors and Affiliations

  1. Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing, 100124, China

    Jicheng Li  (李继承), Hongling Ye  (叶红玲), Nan Wei  (魏南) & Yongjia Dong  (董永佳)

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  1. Jicheng Li  (李继承)
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  2. Hongling Ye  (叶红玲)
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  3. Nan Wei  (魏南)
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  4. Yongjia Dong  (董永佳)
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Contributions

Author contributions Jicheng Li completed the theoretical model and analytical calculations and wrote the draft of the manuscript. Hongling Ye provided a critical review and directed the execution of the entire study. Nan Wei helped with the code implementation. Yongjia Dong helped with the data collection. All authors reviewed and approved the final manuscript.

Corresponding author

Correspondence to Hongling Ye  (叶红玲).

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Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.

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Li, J., Ye, H., Wei, N. et al. Efficient multi-material topology optimization design with minimum compliance based on ResUNet involved generative adversarial network. Acta Mech. Sin. 40, 423185 (2024). https://doi.org/10.1007/s10409-023-23185-x

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