In the field of topology optimization, the homogenization approach has been revived as an important alternative to the established, density-based methods because it can represent the microstructural design at a much finer length-scale than the computational grid. The optimal microstructure for a single load case is an orthogonal rank-3 laminate. A rank-3 laminate can be described in terms of frame fields, which are also an important tool for mesh generation in both 2D and 3D. We propose a method for generating multi-laminar structures from frame fields. Rather than relying on integrative approaches that find a parametrization based on the frame field, we find stream surfaces, represented as point clouds aligned with frame vectors, and we solve an optimization problem to find well-spaced collections of such stream surfaces. The stream surface tracing is unaffected by the presence of singularities outside the region of interest. Neither stream surface tracing nor selecting well-spaced surface rely on combed frame fields. In addition to stream surface tracing and selection, we provide two methods for generating structures from stream surface collections. One of these methods produces volumetric solids by summing basis functions associated with each point of the stream surface collection. The other method reinterprets point sampled stream surfaces as a spatial twist continuum and produces a hexahedralization by dualizing a graph representing the structure. We demonstrate our methods on several frame fields produced using the homogenization approach for topology optimization, boundary-aligned, algebraic frame fields, and frame fields computed from closed-form expressions.

中文翻译：

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框架场取向多层结构的合成

在拓扑优化领域，均质化方法已被恢复为已建立的基于密度的方法的重要替代方法，因为它可以以比计算网格更精细的长度尺度表示微结构设计。单负载情况下的最佳微观结构是正交3级层压板。可以用框架场来描述3级层压板，框架场也是2D和3D网格生成的重要工具。我们提出了一种从框架场生成多层结构的方法。与其依靠基于帧场找到参数化的集成方法，不如找到流表面（表示为与帧矢量对齐的点云），并解决优化问题以找到间隔良好的此类流表面的集合。在感兴趣区域之外的奇异点的存在不会影响流的表面跟踪。流表面跟踪和选择间隔良好的表面都不依赖于精梳框架场。除了跟踪和选择流表面，我们还提供了两种从流表面集合生成结构的方法。这些方法之一是通过对与流表面集合的每个点关联的基函数求和来生成体积固体。另一种方法将点采样的流表面重新解释为空间扭曲连续体，并通过对表示结构的图进行对偶来产生六面体化。我们使用拓扑优化的均质化方法，边界对齐的，代数框架场，在几个框架场上展示了我们的方法，