框架场取向多层结构的综合
Synthesis of Frame Field-Aligned Multi-Laminar Structures
摘要：
在拓扑优化领域，均匀化方法已恢复作为一个重要的替代建立，密度为基础的方法，因为它可以表示在一个更精细的长度尺度比计算网格的微结构设计。对于单一载荷情况，最佳微观结构是正交秩3层合板。3阶层合板可以用框架场来描述，框架场也是二维和三维网格生成的重要工具。我们提出了一种从帧场生成多层结构的方法。而不是依赖于综合的方法，找到一个参数化的基础上的帧字段，我们发现流表面，表示为点云与帧向量对齐，我们解决了优化问题，找到这样的流表面的间隔良好的集合。流面跟踪不受感兴趣区域外奇点存在的影响。无论是流面追踪还是选择良好间隔的表面都不依赖于梳理框架字段。除了流表面跟踪和选择之外，我们还提供了两种从流表面集合生成结构的方法。其中一种方法通过对与流表面集合的每个点相关联的基函数求和来产生体积固体。另一种方法将点采样流表面重新解释为空间扭曲连续体，并通过对偶表示结构的图来产生六面体化。我们展示了我们的方法在几个框架领域的拓扑优化，边界对齐，代数框架领域，从封闭形式的表达式计算的框架领域使用均匀化方法。
英文摘要：
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.
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