Porous structures are of valuable importance in additive manufacturing. They can also be exploited to improve damage tolerance and fail-safe behavior. This paper presents a projection approach to design optimized porous structures in the framework of density-based topology optimization. In contrast to conventional constraint approach, the maximum local volume limitation is integrated into the material interpolation model through a filtering and projection process. This paper also presents two extensions of the basic approach, including a robust formulation for improving weak structural features and mesh/design refinement for enhancing computational stability and efficiency. The applicability of the proposed methodology is demonstrated by a set of numerical minimum compliance problems. This approach can be used in a wider range of applications concerning porous structures.

多孔结构在增材制造中非常重要。还可以利用它们来提高损坏容限和故障安全行为。本文提出了一种在基于密度的拓扑优化框架内设计优化的多孔结构的投影方法。与常规约束方法相比，最大局部体积限制通过过滤和投影过程集成到材料插值模型中。本文还介绍了基本方法的两个扩展，包括用于改善弱结构特征的健壮公式以及用于增强计算稳定性和效率的网格/设计改进。一组数值最小合规性问题证明了所提出方法的适用性。