The potential of additive manufacturing (AM) in fabricating structurally efficient yet geometrically complicated designs generated from topology optimization is widely recognised. However, various constraints presented in the additive manufacturing process are not directly considered in conventional topology optimization frameworks, potentially impairing the manufacturability of the generated topology. A most noteworthy example is the presence of overhangs, which are downward-facing regions that are not self-supporting. In such areas, traditional AM processes utilise sacrificial supports to act as scaffoldings, which result in additional time, effort and the corresponding cost. Here we present a novel method that can effectively address overhanging features in the bi-directional evolutionary structural optimization framework, creating self-supporting yet structurally efficient designs. By using a simple expression, the overhang problem is formulated as a layer-wise relationship, and elements whose modification does not create overhang are selected as candidates for the element updating scheme. To validate the effectiveness of the algorithm, numerical examples under different design conditions are presented. A comparison of the self-supporting designs against their non-self-supporting counterparts obtained by conventional topology optimization demonstrates their competitiveness in structural performance. Subsequently, physical 3D prints of the examples further prove the effectiveness of the proposed method in creating self-supporting designs.

增材制造（AM）在制造由拓扑优化产生的结构有效但几何复杂的设计中的潜力已得到广泛认可。但是，在常规拓扑优化框架中并未直接考虑增材制造过程中出现的各种限制，这可能会损害所生成拓扑的可制造性。最值得一提的例子是悬垂的存在，这些悬垂是朝下的区域，没有自支撑。在这样的领域中，传统的增材制造工艺利用牺牲性支撑物来充当脚手架，从而导致额外的时间，精力和相应的成本。在这里，我们提出了一种可以有效解决双向进化结构优化框架中突出特征的新颖方法，创建自支撑但结构上高效的设计。通过使用一个简单的表达式，将悬垂问题表述为分层关系，并选择其修改不会产生悬垂的元素作为元素更新方案的候选项。为了验证算法的有效性，给出了不同设计条件下的数值例子。通过常规拓扑优化获得的自支撑设计与非自支撑设计的比较表明，它们在结构性能上具有竞争力。随后，示例的物理3D打印进一步证明了所提出方法在创建自支撑设计中的有效性。悬垂问题被表述为分层关系，并且选择其修改不会产生悬垂的元素作为元素更新方案的候选。为了验证算法的有效性，给出了不同设计条件下的数值例子。通过常规拓扑优化获得的自支撑设计与非自支撑设计的比较表明，它们在结构性能上具有竞争力。随后，示例的物理3D打印进一步证明了所提出方法在创建自支撑设计中的有效性。悬垂问题被表述为分层关系，并且选择其修改不会产生悬垂的元素作为元素更新方案的候选。为了验证算法的有效性，给出了不同设计条件下的数值例子。通过常规拓扑优化获得的自支撑设计与非自支撑设计的比较表明，它们在结构性能上具有竞争力。随后，示例的物理3D打印进一步证明了所提出方法在创建自支撑设计中的有效性。给出了不同设计条件下的数值例子。通过常规拓扑优化获得的自支撑设计与非自支撑设计的比较表明，它们在结构性能上具有竞争力。随后，示例的物理3D打印进一步证明了所提出方法在创建自支撑设计中的有效性。给出了不同设计条件下的数值例子。通过常规拓扑优化获得的自支撑设计与非自支撑设计的比较表明，它们在结构性能上具有竞争力。随后，示例的物理3D打印进一步证明了所提出方法在创建自支撑设计中的有效性。