Abstract The focus of this research is to create a methodology to systematically generate spatially-varying, periodic, cellular microstructures that are tailored to attain optimized performance of the macrostructure. The unit cell lattice is represented by Fourier series expansions, and the corresponding amplitudes and phase spectrum are obtained. Then, the material distribution (topology) and orientation of each cell (morphology) are optimized for multiple load cases. The phase of the spatial harmonics is updated based on the optimized orientation, and the analog response is thresholded with the optimized material distribution to find the binary lattices. The framework is tested for three types of lattices with various periodicities. The square cell with a rectangular hole shows the exploitation of the cell's orthotropic properties for structures subjected to a single load case; the triangular cell with the triangular lattice depicts the applicability of other types of cells and lattices to transfer shear for the structures subjected to multiple load cases; and the square cell with pentagonal lattices shows the versatility of the framework. An optimized triangular cellular solid is additively manufactured, and it is validated experimentally that 12% higher stiffness and 57% higher strength can be achieved compared to the conventional topology optimization design.

中文翻译：

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可增材制造的空间变化周期细胞固体的拓扑和形态设计

摘要 本研究的重点是创建一种方法来系统地生成空间变化的、周期性的、蜂窝状微结构，这些微结构经过定制，以获得宏观结构的优化性能。晶胞晶格用傅立叶级数展开表示，得到相应的振幅和相位谱。然后，针对多个载荷情况优化每个单元的材料分布（拓扑）和方向（形态）。根据优化的方向更新空间谐波的相位，并使用优化的材料分布对模拟响应进行阈值处理以找到二元晶格。该框架针对具有各种周期性的三种类型的晶格进行了测试。带有矩形孔的方形细胞显示了细胞的利用' s 承受单一载荷工况的结构的正交各向异性特性；带有三角形格子的三角形单元描述了其他类型的单元格和格子对承受多种载荷情况的结构传递剪切力的适用性；带有五边形格子的方形单元显示了框架的多功能性。一个优化的三角形多孔实体是增材制造的，经实验验证，与传统的拓扑优化设计相比，刚度提高了 12%，强度提高了 57%。带有五边形格子的方形单元显示了框架的多功能性。一个优化的三角形多孔实体是增材制造的，经实验验证，与传统的拓扑优化设计相比，刚度提高了 12%，强度提高了 57%。带有五边形格子的方形单元显示了框架的多功能性。一个优化的三角形多孔实体是增材制造的，经实验验证，与传统的拓扑优化设计相比，刚度提高了 12%，强度提高了 57%。