Inverse design of high-resolution and fine-detailed 3D lightweight mechanical structures is notoriously expensive due to the need for vast computational resources and the use of very fine-scaled complex meshes. Furthermore, in designing for additive manufacturing, infill is often neglected as a component of the optimized structure. In this paper, both concerns are addressed using a de-homogenization topology optimization procedure on complex engineering structures discretized by 3D unstructured hexahedrals. Using a rectangular-hole microstructure (reminiscent to the stiffness optimal orthogonal rank-3 multi-scale) as a base material for the multi-scale optimization, a coarse-scale optimized geometry can be obtained using homogenization-based topology optimization. Due to the microstructure periodicity, this coarse-scale geometry can be up-sampled to a fine physical geometry with optimized infill, with minor loss in structural performance and at a fraction of the cost of a fine-scale solution. The upsampling on 3D unstructured grids is achieved through stream surface tracing which aligns with the optimized local orientation. The periodicity of the physical geometry can be tuned, such that the material serves as a structural component and also as an efficient infill for additive manufacturing designs. The method is demonstrated through three examples. It achieves comparable structural performance to state-of-the-art methods but stands out for its significant computational time reduction, much faster than the base-line method. By allowing multiple active layers, the mapped solution becomes more mechanically stable, leading to an increased critical buckling load factor without additional computational expense. The proposed approach achieves promising results, benchmarking against large-scale SIMP models demonstrates computational efficiency improvements of up to 250 times.

翻译：高分辨率、细细节三维轻量化机械结构的逆设计因需要庞大的计算资源和极细尺度复杂网格而众所周知地昂贵。此外，在为增材制造设计时，填充体常被忽略为优化结构的组成部分。本文通过采用解均匀化拓扑优化流程，针对以三维非结构化六面体离散的复杂工程结构解决了这两个问题。以矩形孔微结构（类似于刚度最优正交秩-3多尺度）作为多尺度优化的基材，基于均匀化的拓扑优化可获得粗尺度优化几何形状。由于微结构的周期性，该粗尺度几何可上采样为具有优化填充体的精细物理几何，结构性能损失极小，而成本仅为细尺度解的一小部分。三维非结构化网格上的上采样通过流面追踪实现，该追踪与优化的局部方向对齐。物理几何的周期性可调，使得材料既作为结构组件，又作为增材制造设计的有效填充体。该方法通过三个示例进行演示。它实现了与最先进方法相当的结构性能，但以显著的计算时间减少而脱颖而出，比基线方法快得多。通过允许多个活动层，映射解在机械上更稳定，从而在不增加计算开销的情况下提高临界屈曲载荷因子。所提出的方法取得了有前景的结果，与大规模SIMP模型对比表明计算效率提升高达250倍。