A Combinatorial Approach for Constructing Lattice Structures
A Combinatorial Approach for Constructing Lattice Structures
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DOI：
10.1115/1.4044521
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发表时间：
2020-04
影响因子：
3.3
通讯作者：
C. Verma;B. Rankouhi;K. Suresh
中科院分区：
文献类型：
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作者：
C. Verma;B. Rankouhi;K. Suresh
晶格结构具有独特的性能，包括大的表面积和高度分布的负载路径，这使得它们在工程应用中非常有效，其中重量减轻，散热和能量吸收是至关重要的。此外，随着增材制造（AM）的出现，晶格结构现在更容易制造。然而，由于固有的表面复杂性，它们的几何构造可能会带来重大挑战。一个经典的策略，用于构建晶格结构利用分析表面的表面相交，但是，这缺乏鲁棒性和可扩展性。另一种策略是基于体素网格的等值面提取。虽然这是鲁棒和可扩展的，但表面质量取决于网格，并且三角剖分将需要大量的后抽取。第三种策略依赖于显式几何拼接，其中通过一系列几何操作将镶嵌的开放圆柱体拼接在一起。这被证明是有效的和可扩展的，不需要后处理。然而，它仅限于具有均匀光束半径的晶格结构。此外，现有的算法依赖于显式凸壳结构，这是已知的数值不稳定。本文提出了一种组合拼接策略，其中任意半径的棋盘形开口圆柱体使用拓扑操作拼接在一起。凸船体的构造通过简单而鲁棒的投影方法来处理，避免了昂贵的精确算术计算，提高了计算效率。这是通过几个涉及数百万个三角形的例子来证明的。在典型的八核桌面上，该算法每秒可以构建大约一百万个柱面。
Lattice structures exhibit unique properties including a large surface area and a highly distributed load-path. This makes them very effective in engineering applications where weight reduction, thermal dissipation, and energy absorption are critical. Furthermore, with the advent of additive manufacturing (AM), lattice structures are now easier to fabricate. However, due to inherent surface complexity, their geometric construction can pose significant challenges. A classic strategy for constructing lattice structures exploits analytic surface–surface intersection; this, however, lacks robustness and scalability. An alternate strategy is voxel mesh-based isosurface extraction. While this is robust and scalable, the surface quality is mesh-dependent, and the triangulation will require significant postdecimation. A third strategy relies on explicit geometric stitching where tessellated open cylinders are stitched together through a series of geometric operations. This was demonstrated to be efficient and scalable, requiring no postprocessing. However, it was limited to lattice structures with uniform beam radii. Furthermore, existing algorithms rely on explicit convex-hull construction which is known to be numerically unstable. In this paper, a combinatorial stitching strategy is proposed where tessellated open cylinders of arbitrary radii are stitched together using topological operations. The convex hull construction is handled through a simple and robust projection method, avoiding expensive exact-arithmetic calculations and improving the computational efficiency. This is demonstrated through several examples involving millions of triangles. On a typical eight-core desktop, the proposed algorithm can construct approximately up to a million cylinders per second.