Cellular structures found in nature exhibit remarkable properties such as high strength, high energy absorption, excellent thermal/acoustic insulation, and fluid transfusion. Many of these structures are Voronoi-like; therefore researchers have proposed Voronoi multi-scale designs for a wide variety of engineering applications. However, designing such structures can be computationally prohibitive due to the multi-scale nature of the underlying analysis and optimization. In this work, we propose the use of a neural network (NN) to carry out efficient topology optimization (TO) of multi-scale Voronoi structures. The NN is first trained using Voronoi parameters (cell site locations, thickness, orientation, and anisotropy) to predict the homogenized constitutive properties. This network is then integrated into a conventional TO framework to minimize structural compliance subject to a volume constraint. Special considerations are given for ensuring positive definiteness of the constitutive matrix and promoting macroscale connectivity. Several numerical examples are provided to showcase the proposed method.

翻译：自然界中的多孔结构展现出高强度、高能量吸收、优异的热/声绝缘性能及流体输运等显著特性。其中许多结构具有Voronoi特征，因此研究者已针对各类工程应用提出Voronoi多尺度设计方案。然而，由于底层分析与优化的多尺度特性，此类结构的设计往往面临计算成本过高的问题。本研究提出利用神经网络（NN）对多尺度Voronoi结构进行高效拓扑优化（TO）：首先通过Voronoi参数（晶胞位置、厚度、取向及各向异性）训练神经网络以预测均质化本构特性；随后将该网络集成至传统拓扑优化框架中，在体积约束条件下实现结构柔度最小化。研究特别关注本构矩阵的正定性保障与宏观尺度连通性增强。最后通过多个数值算例验证所提方法的有效性。