A numerical method is presented to generate hierarchical infills for additive manufacturing, using homogenization and optimization. Given the shape and the allowed stages of grading, the macroscopic properties of each level of the hierarchical infill are computed through numerical homogenization. Then, a multi-material optimization problem is formulated to find the distribution of the prescribed discrete set of candidates that maximizes the structural stiffness of the object to be printed for a limited volume fraction. The formulation is endowed with an additional overturning constraint to achieve objects that resist gravity in a stable configuration. Numerical simulations, addressing the design of a self-supporting orthotropic rhombic infill and a stiff isotropic triangular one, are shown.

中文翻译：

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通过多尺度方法进行增材制造的分层填充

提出了一种使用均质化和优化为增材制造生成分层填充的数值方法。给定形状和允许的分级阶段，分层填充的每个级别的宏观特性通过数值均匀化计算。然后，制定了一个多材料优化问题，以找到指定的离散候选集的分布，以在有限的体积分数下最大化待打印对象的结构刚度。该公式被赋予了额外的翻转约束，以实现在稳定配置中抵抗重力的物体。数值模拟显示了自支撑正交各向异性菱形填充物和刚性各向同性三角形填充物的设计。