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Topology optimization of structures considering local material uncertainties in additive manufacturing

机译：考虑增材制造中局部材料不确定性的结构拓扑优化

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Additive manufacturing provides more freedom for the design of structures but also exhibits prominent local uncertainties of material properties, which bring potential challenges. The performance of structures should depend not only on uncertain variations of material properties but also on the spatial occurrence frequency of the extreme material properties. This paper proposes a non-probabilistic reliability-based topology optimization algorithm by considering local material uncertainties in additive manufacturing. The whole design domain is divided into several uncertainty regions (URs), whose size is proportional to the spatial occurrence frequency of extreme material properties. Within each UR, these uncertain-but-bounded variations of materials are correlated by the multi-dimensional ellipsoid model. Then, the multi-ellipsoid model for all URs is established by considering the overall material uncertainties of the structure. Thereafter, a non-probabilistic reliability-based topology optimization (NRBTO) is proposed for minimizing structural volume against displacement constraints by considering material uncertainties during additive manufacturing. Several 2D and 3D examples are presented to illustrate the effectiveness of the proposed method. Compared with solutions resulting from the deterministic topology optimization (DTO), NRBTO provides conservative designs with a larger volume fraction due to material uncertainties. When smaller URs are assigned to indicate the high occurrence frequency of extreme material properties, the NRBTO design becomes even conservative. The extreme case is equivalent to the deterministic topology optimization using the lower bound material. (C) 2019 Elsevier B.V. All rights reserved.
机译：增材制造为结构设计提供了更大的自由度，但同时在材料特性方面也表现出突出的局部不确定性，这带来了潜在的挑战。结构的性能不仅应取决于材料特性的不确定变化，还应取决于极端材料特性的空间出现频率。通过考虑增材制造中局部材料的不确定性，提出了一种基于非概率可靠性的拓扑优化算法。整个设计域分为几个不确定区域（UR），其大小与极端材料属性的空间出现频率成比例。在每个UR中，材料的这些不确定但有界的变化通过多维椭圆模型相互关联。然后，通过考虑结构的整体材料不确定性，建立所有UR的多椭球模型。此后，提出了一种基于非概率可靠性的拓扑优化（NRBTO），通过在增材制造过程中考虑材料的不确定性来最大程度地减小结构体积对位移的限制。提出了几个2D和3D实例来说明所提出方法的有效性。与确定性拓扑优化（DTO）产生的解决方案相比，由于材料的不确定性，NRBTO提供的保守设计的体积分数更大。当分配较小的UR来表示极端材料属性的出现频率很高时，NRBTO设计将变得更加保守。极端情况相当于使用下限材料进行确定性拓扑优化。 （C）2019 Elsevier B.V.保留所有权利。

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