Topology optimization of structures considering local material uncertainties in additive manufacturing

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.