拓扑优化的迭代过程涉及大量有限元分析与灵敏度更新步骤，且随着划分网格数目的增加，其优化过程将耗费大量的计算成本。利用深度学习方法，通过建立低分辨率中间构型与高分辨率拓扑结构之间的映射关系，可实现结构的跨分辨率拓扑优化设计，从而大幅提高其计算效率。本文基于两种不同的生成对抗网络，构建了可实现跨分辨率预测的拓扑优化方法，并将其扩展至三维结构的优化预测。首先,以柔顺度最小化为目标函数，利用SIMP法生成不同载荷条件、初始位移和体积分数下的优化结构数据集；然后，分别利用Pix2pix和Esrgan网络解决其跨分辨率预测问题，其中对于Pix2pix网络，使用了残差模块代替其生成器内部的卷积模块，以增强网络对低层信息的复用；最后，通过二维和三维算例验证了所提方法的有效性，并与现有基于CGAN网络的方法进行了比较研究。结果表明：综合考虑计算精度和计算效率，基于Esrgan网络的方法表现更优，最适合应用于跨分辨率拓扑优化设计。
Abstract
The iterative process of topology optimization involves a large number of finite element analyses and sensitivity update steps. As the number of mesh divisions increases, the optimization process consumes a significant amount of computational cost. By using deep learning methods and establishing a mapping relationship between low-resolution intermediate configurations and high-resolution topological structures, cross-resolution topology optimization design of structures can be achieved, thus greatly improving computational efficiency. This article constructs a topology optimization method capable of cross-resolution prediction based on two different generative adversarial networks, and extends it to the optimization prediction of three-dimensional structures. Firstly, with the minimization of compliance as the objective function, a dataset of optimized structures under different loading conditions, initial displacements, and volume fractions is generated using the Solid Isotropic Material with Penalization method. Then, the Pix2pix and Esrgan networks are used to solve their cross-resolution prediction problems, where for the Pix2pix network, residual modules are used to replace the convolution modules inside the generator to enhance the reuse of low-level information. Finally, the effectiveness of the proposed method is verified through two-dimensional and three-dimensional examples, and comparative studies are conducted with existing methods based on the CGAN network. The results show that considering both calculation accuracy and computational efficiency, the method based on the Esrgan network performs better and is most suitable for cross-resolution topology optimization design.
关键词
拓扑优化 /
柔顺度 /
跨分辨率预测 /
Pix2pix /
Esrgan
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Key words
topology optimization /
compliance /
cross-resolution prediction /
Pix2pix /
Esrgan
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