Topology optimization can devise structures with superior performance, while the results produced by topology optimization are often very complex and difficult to be manufactured directly. The additive manufacturing is a free-form manufacturing technique in which the component is built in a layer-by-layer manner. The integration of topology optimization and additive manufacturing technologies has the potential to bring significant synergy benefits. However, typical topology optimization algorithms have not considered the unique manufacturing limitations of additive manufacturing. This article focuses on the topology optimization for additive manufacturing considering self-supporting constraint based on the Solid Isotropic Material with Penalization (SIMP) framework. An explicit self-supporting constraint model is constructed, and the proposed method realizes self-supported by gradual evolution of supporting structures. The corresponding sensitivity analysis is investigated, which requires less computational cost and can be solved in parallel. Besides, a directional sensitivity filter is specifically proposed to promote the evolution of supporting structures. The performance and functionality of the proposed method is illustrated with three compliance minimization problems. All cases achieve self-supported successfully, and the solutions own good manufacturability.

拓扑优化可以设计出性能卓越的结构，而拓扑优化产生的结果通常非常复杂，难以直接制造。增材制造是一种自由形式的制造技术，其中以分层的方式构建组件。拓扑优化和增材制造技术的集成具有带来巨大协同效益的潜力。但是，典型的拓扑优化算法并未考虑增材制造的独特制造限制。本文重点介绍基于带罚分的固体各向同性材料（SIMP）框架的考虑自支撑约束的增材制造拓扑优化。构造了一个明确的自支撑约束模型，该方法通过支撑结构的逐步演化实现了自支撑。对相应的灵敏度分析进行了研究，这需要较少的计算成本并且可以并行解决。此外，还专门提出了一种定向灵敏度滤波器，以促进支撑结构的演变。通过三个合规性最小化问题说明了所提出方法的性能和功能。所有案例均成功实现了自我支持，解决方案具有良好的可制造性。专门提出了一种定向灵敏度滤波器来促进支撑结构的演变。通过三个合规性最小化问题说明了所提出方法的性能和功能。所有案例均成功实现了自我支持，解决方案具有良好的可制造性。专门提出了一种定向灵敏度滤波器来促进支撑结构的演变。通过三个合规性最小化问题说明了所提出方法的性能和功能。所有案例均成功实现了自我支持，解决方案具有良好的可制造性。