In the era of Industry 4.0, the prominence of 3D printing as a pivotal manufacturing technology has greatly expanded, particularly within the domain of additive manufacturing (AM). Among the thriving research applications tailored for integration with AM, topology optimization (TO) has emerged as a resounding success. Given the prerequisite of TO for high-resolution meshing to ensure visual clarity in result depiction, researchers have been consistently driven to develop advanced techniques to refine optimal designs, thus elevating the challenge and popularity within this research realm. This paper presents a novel approach integrating an adaptive image-based octree mesh scaled boundary finite element (SBFE) framework with an evolutionary methodology that can effectively address the persistent challenges inherent to TO. A novel hierarchical SBFE mesh analysis not only facilitates efficient and precise TO but also substantially reduces computational resource demands. Furthermore, the pre-conditioned conjugated gradient (PCG) method is adopted to process practical-scale problems, minimizing computer memory resources. Additionally, the proposed work incorporates a post-processing technique utilizing the isosurface function based on a marching cube algorithm, thereby smoothing the boundaries of optimal results. Consequently, this research extends the horizons of design possibilities, particularly in the creation of intricate 3D structures, which can be seamlessly realized through additive manufacturing and 3D printing.

中文翻译：

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基于等值面的行进立方体算法，用于自适应八叉树 SBFE 方法中的平滑几何拓扑优化


在工业 4.0 时代，3D 打印作为关键制造技术的重要性已大大扩大，特别是在增材制造 (AM) 领域。在为与增材制造集成而定制的蓬勃发展的研究应用中，拓扑优化 (TO) 取得了巨大的成功。鉴于 TO 进行高分辨率网格划分以确保结果描述的视觉清晰度的先决条件，研究人员一直致力于开发先进技术来完善最佳设计，从而提高了该研究领域的挑战和受欢迎程度。本文提出了一种新颖的方法，将基于图像的自适应八叉树网格尺度边界有限元 (SBFE) 框架与进化方法相结合，可以有效解决 TO 固有的持续挑战。一种新颖的分层 SBFE 网格分析不仅有助于高效、精确的 TO，而且还大大减少了计算资源需求。此外，采用预条件共轭梯度（PCG）方法来处理实际规模的问题，最大限度地减少计算机内存资源。此外，所提出的工作结合了利用基于行进立方体算法的等值面函数的后处理技术，从而平滑了最佳结果的边界。因此，这项研究拓展了设计可能性的视野，特别是在创建复杂的 3D 结构方面，这些结构可以通过增材制造和 3D 打印无缝实现。