This paper presents a layered construction approach for embedding the overhang limitation and support structure requirement in topology optimization. This approach accounts for layer-by-layer construction stages, by minimizing the compliance due to body forces together with the compliance of the final loading situation. Hence, deformation caused by body forces is minimized by generating self-supporting structures. Three parameterizations are investigated that correspond to the distribution of solid and void; the distribution of a homogenized lattice meta-material that covers the complete density range; and a two-material scheme where two material phases are distributed simultaneously, one is a continuum solid-void and the other is a homogenized lattice that acts as additional support structure. Even with little additional support material, the two-material parameterization demonstrates significant reduction of overhang violation with negligible compromise of the structural performance. By manipulating the parameters of the layered construction, such as the layer-wise resolution and the weighting factors, further improvement is achieved. The procedures are implemented in a parallel computing environment and are fully scalable, hence suitable for modern high-resolution topology optimization.

本文提出了一种分层构建方法，用于在拓扑优化中嵌入悬垂限制和支撑结构要求。这种方法通过最小化由于体力引起的顺应性以及最终装载情况的顺应性来说明逐层施工阶段。因此，通过产生自支撑结构，将由体力引起的变形最小化。研究了三个参数化，它们对应于固体和空隙的分布。覆盖整个密度范围的均质晶格超材料的分布；以及两种材料方案，其中两种材料相同时分布，一种是连续的实心空洞，另一种是用作附加支撑结构的均质晶格。即使只有很少的辅助材料，两种材料的参数化显示出显着减少了悬伸违规，而对结构性能的影响可以忽略不计。通过操纵分层结构的参数，例如分层分辨率和加权因子，可以实现进一步的改进。该过程在并行计算环境中实现，并且完全可扩展，因此适合于现代高分辨率拓扑优化。