[论文解读] Self-supporting Topology Optimization for Additive Manufacturing

Dengyang Zhao, Ming Li+1 more|arXiv (Cornell University)|Aug 24, 2017

Topology Optimization in Engineering参考文献 3被引用 10

一句话总结

本文提出了一种面向增材制造的新型自支撑拓扑优化方法，通过将自支撑约束表述为单元密度的显式二次函数，消除了对支撑结构的需求。该方法实现了高效、可并行的敏感性计算，并在二维和三维基准测试中，使柔顺度值保持在非自支撑参考结构的1%以内，通过离散卷积算子实现支撑检测，展现出高效率与鲁棒性。

ABSTRACT

The paper presents a topology optimization approach that designs an optimal structure, called a self-supporting structure, which is ready to be fabricated via additive manufacturing without the usage of additional support structures. Such supports in general have to be created during the fabricating process so that the primary object can be manufactured layer by layer without collapse, which is very time-consuming and waste of material. The proposed approach resolves this problem by formulating the self-supporting requirements as a novel explicit quadratic continuous constraint in the topology optimization problem, or specifically, requiring the number of unsupported elements (in terms of the sum of squares of their densities) to be zero. Benefiting form such novel formulations, computing sensitivity of the self-supporting constraint with respect to the design density is straightforward, which otherwise would require lots of research efforts in general topology optimization studies. The derived sensitivity for each element is only linearly dependent on its sole density, which, different from previous layer-based sensitivities, consequently allows for a parallel implementation and possible higher convergence rate. In addition, a discrete convolution operator is also designed to detect the unsupported elements as involved in each step of optimization iteration, and improves the detection process 100 times as compared with simply enumerating these elements. The approach works for cases of general overhang angle, or general domain, and produces an optimized structures, and their associated optimal compliance, very close to that of the reference structure obtained without considering the self-supporting constraint, as demonstrated by extensive 2D and 3D benchmark examples.

研究动机与目标

• 消除增材制造构件后处理支撑结构的需求。
• 在逐层制造过程中确保所有单元均自支撑的同时，保持最优的结构性能（柔顺度）。
• 开发一种计算高效且可并行化的自支撑约束敏感性计算方法。
• 在复杂二维和三维几何形状中实现可靠且鲁棒的自支撑结构生成。
• 将适用范围扩展至多孔内部结构和自由形态结构，避免内部支撑去除的挑战。

提出的方法

• 将自支撑约束表述为显式二次函数，要求未支撑单元密度的平方和为零。
• 推导仅依赖于单元自身密度的逐单元敏感性，从而实现并行化实现。
• 引入离散卷积算子以检测未支撑单元，与枚举法相比检测速度提升100倍。
• 在基于密度的（SIMP）拓扑优化框架内应用该方法，采用固定打印方向。
• 采用基于滤波的方法，通过二次公式隐式施加悬垂角度约束。
• 将固定打印方向作为设计输入，以指导自支撑约束的公式化。

实验结果

研究问题

• RQ1 能否开发一种自支撑拓扑优化框架，在无需额外支撑结构的情况下保持接近最优的结构柔顺度？
• RQ2 如何高效计算自支撑约束的敏感性，并实现可并行化？
• RQ3 能否设计一种未支撑单元检测方法，显著优于暴力枚举法的计算速度？
• RQ4 与非自支撑最优设计相比，所提方法在结构性能（柔顺度）方面保持程度如何？
• RQ5 该方法在复杂三维几何形状和不同打印方向下的泛化能力如何？

主要发现

• 所提方法生成的结构完全自支撑，且在几何形态上与未施加自支撑约束的参考结构相似。
• 所有基准示例中，自支撑结构的柔顺度均在非自支撑最优参考结构的1%以内。
• 离散卷积算子使未支撑单元检测速度相比直接枚举提升100倍。
• 由于敏感性仅依赖于单元自身密度，该方法支持并行实现，显著提升了三维问题的收敛速度。
• 包含115.2万个单元的三维办公桌示例在66分钟内求解完成，生成了类似骨骼的多孔腿结构，兼顾了强度与自支撑要求。
• 当使用任意打印方向时，该方法无法收敛，表明选择合适的打印方向作为预处理步骤至关重要。