基于自适应网格划分的三维薄壁结构拓扑优化
Topology optimization for 3D thin-walled structures with adaptive meshing
摘要：
提出了一种基于密度的自适应网格划分的三维薄壁结构拓扑优化设计方法。均匀的壁厚是通过使用亥姆霍兹偏微分方程（PDE）同时约束的最小和最大特征尺寸。基于偏微分方程的约束不需要关于相邻单元的信息，因此可以很容易地与自适应网格划分方案相结合。通过显著减少优化过程中出现的大空隙区域的计算量，有效地实现了使用台式PC对薄壁结构进行3D拓扑优化。当应用于3D结构时，统一的特征尺寸约束可以产生具有分支和孔的薄壁几何形状，这在以前很难通过拓扑优化获得。所得到的薄壁结构可以为设计由冲压、熔模铸造和复合材料制造制成的薄壁轻质结构提供有价值的见解。
英文摘要：
This paper presents a density-based topology optimization method for designing 3D thin-walled structures with adaptive meshing. Uniform wall thickness is achieved by simultaneously constraining the minimum and maximum feature sizes using Helmholtz partial differential equations (PDE). The PDE-based constraints do not require information about neighbor cells and therefore can readily be integrated with an adaptive meshing scheme. This effectively enables the 3D topology optimization of thin-walled structures with a desktop PC, by significantly reducing computation in large void regions that appear during optimization. The uniform feature size constraint, when applied to 3D structures, can produce thin-walled geometries with branches and holes, which have previously been difficult to obtain via topology optimization. The resulting thin-walled structures can provide valuable insights for designing thin-walled lightweight structures made of stamping, investment casting and composite manufacturing.
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