This paper presents an application framework that provides a complete process to design an optimized self-supporting structure , 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; this process is very time-consuming and waste of material. The main approach resolves this issue by formulating the self-supporting requirements as an explicit quadratic continuous constraint in a topology optimization problem, or specifically, requiring the number of unsupported elements (in terms of the sum of squares of their densities) to be zero. Under the formulation, the required sensitivity of the self-supporting constraint with respect to the design density can be derived straightforward and is only linearly dependent on the density of the element itself. In addition, a novel discrete convolution operator is particularly designed to detect the unsupported elements. The approach works for cases of general overhang angles, and the produced optimized structures have close target compliance to those of the reference structures obtained without considering the self-supporting constraint, as demonstrated by various 2D and 3D benchmark examples.

中文翻译：

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一种新型的自支撑拓扑优化应用框架

本文提出了一个应用框架，它提供了一个完整的过程来设计优化的自支撑结构，准备通过增材制造进行制造，而无需使用额外的支撑结构。这种支撑通常必须在制造过程中创建，以便可以逐层制造主要物体而不会塌陷；这个过程非常耗时且浪费材料。主要方法通过将自支撑要求制定为拓扑优化问题中的显式二次连续约束来解决此问题，或者具体而言，要求无支撑元素的数量（根据其密度的平方和）为零。根据配方，相对于设计密度的自支撑约束所需的灵敏度可以直接导出，并且仅线性地依赖于元件本身的密度。此外，特别设计了一种新颖的离散卷积算子来检测不支持的元素。该方法适用于一般悬垂角度的情况，并且生成的优化结构与在不考虑自支撑约束的情况下获得的参考结构具有接近的目标顺应性，如各种 2D 和 3D 基准示例所示。