Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is increasingly widely used in many fabrication applications to achieve a target deformation behavior for a variety of objects. The main idea of this approach is to optimize the distribution of material properties in the object partitioned into relatively coarse cells, and then replace each cell with microstructure geometry that mimics these material properties. In this paper, we focus on adapting this approach to complex shapes in situations when preserving the shape's surface is important. Our approach extends any regular (i.e. defined on a regular lattice grid) microstructure family to complex shapes, by enriching it with individually optimized cut-cell tiles adapted to the geometry of the cut-cell. We propose an automated and robust pipeline based on this approach, and we show that the performance of the regular microstructure family is only minimally affected by our extension while allowing its use on 2D and 3D shapes of high complexity.

翻译：双尺度拓扑优化结合具有广泛有效材料参数的微结构族设计，在众多制造应用中日益广泛地用于实现各类物体的目标变形行为。该方法的核心思想是优化被划分为相对粗网格的物体中的材料属性分布，然后以能够模拟这些材料属性的微结构几何替代每个网格单元。本文重点研究在需要保持物体表面形状重要性的复杂形状中适配该方法。我们的方法通过增加针对剪切单元几何定制的独立优化剪切单元瓦片，将任意规则（即在规则晶格网格上定义的）微结构族扩展到复杂形状。我们提出基于该方法的自动化鲁棒管线，并证明我们的扩展对规则微结构族性能的影响极小，同时使其能够应用于高复杂度的二维和三维形状。