This paper introduces three dimensional (3D) topology optimization specifically tailored for designing spatially-varying primitive-cubic (CP) type lattice structures. The developed design process consists of three steps: pre-processing, main processing, and post-processing. In the pre-processing step, a surrogate model between lattice geometry variables and effective elasticity tensor is constructed using an artificial neural network. This surrogate model is essential because it enables the quick calculation of the effective elasticity tensor of lattice microstructure. In the subsequent main processing step, multiscale topology optimization is performed. During this step, lattice microstructure size and rotation design variables are optimized together with the macrostructure density design variables. Macrostructures are designed using a well-established three-field density scheme with a SIMP formulation. Formulations for spatially-varying 3D lattice microstructure are newly developed based on a unit quaternion rotation representation scheme. In the final post-processing step, a spatially-varying microstructure is restored using a de-homogenization scheme, newly developed particularly for the primitive-cubic (CP) type 3D lattice structures. The effectiveness and robustness of the proposed formulations are validated through three design examples for the compliance minimization problem. Moreover, a designed lattice structure is fabricated using an additive manufacturing machine.

中文翻译：

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空间变化三维晶格结构设计的多尺度拓扑优化


本文介绍了专为设计空间变化的本原立方 (CP) 型晶格结构而定制的三维 (3D) 拓扑优化。开发设计流程包括三个步骤：前处理、主处理和后处理。在预处理步骤中，使用人工神经网络构建晶格几何变量和有效弹性张量之间的代理模型。该替代模型至关重要，因为它可以快速计算晶格微结构的有效弹性张量。在后续的主要处理步骤中，进行多尺度拓扑优化。在此步骤中，晶格微观结构尺寸和旋转设计变量与宏观结构密度设计变量一起优化。宏观结构采用完善的三场密度方案和 SIMP 公式进行设计。基于单位四元数旋转表示方案，新开发了空间变化 3D 晶格微结构的公式。在最后的后处理步骤中，使用专为原始立方 (CP) 型 3D 晶格结构新开发的去均匀化方案恢复空间变化的微观结构。通过顺应性最小化问题的三个设计实例验证了所提出的公式的有效性和鲁棒性。此外，设计的晶格结构是使用增材制造机器制造的。