The integration of topology optimization and additive manufacturing (AM) is seen as a pivotal approach for creating products with high added value. Nevertheless, the inherent layer-by-layer fabrication process of AM and the widespread manufacturing errors lead to both anisotropy and uncertainty in the printed parts, which poses challenges to constructing material models and optimization strategies. To address these issues, this paper presents a robust topology optimization (RTO) approach coupled with an anisotropic material model and a hybrid interval random model for additively manufactured structures. The method utilizes the bi-directional evolutionary structural optimization (BESO) framework and defines the uncertain material parameters with anisotropic mechanical behavior. An efficient hybrid uncertainty perturbation analysis (HUPA) method is then proposed for estimating the robust objective function, and the sensitivity values of the design variables are further derived. Several 2D and 3D numerical examples are given to verify the effectiveness of the proposed method. The results show that both the material off-angle and the material properties fluctuation exert significant influences on the structural performance, indicating the necessity of considering both anisotropy and uncertainty caused by the AM process in engineering structural optimization.

中文翻译：

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考虑增材制造引起的材料各向异性和不确定性的结构稳健拓扑优化


拓扑优化和增材制造 (AM) 的集成被视为创造高附加值产品的关键方法。然而，增材制造固有的逐层制造过程和广泛的制造误差导致打印零件的各向异性和不确定性，这给构建材料模型和优化策略带来了挑战。为了解决这些问题，本文提出了一种稳健的拓扑优化（RTO）方法，结合各向异性材料模型和增材制造结构的混合区间随机模型。该方法利用双向演化结构优化（BESO）框架，定义具有各向异性力学行为的不确定材料参数。然后提出了一种有效的混合不确定性扰动分析（HUPA）方法来估计鲁棒目标函数，并进一步推导了设计变量的灵敏度值。给出了几个2D和3D数值算例来验证所提方法的有效性。结果表明，材料偏角和材料性能波动均对结构性能产生显着影响，表明在工程结构优化中需要同时考虑增材制造过程引起的各向异性和不确定性。