This paper proposes a multiscale topology optimization method using Nitsche-type isogeometric analysis (IGA) for design of structures described by multiple non-uniform rational B-spline (NURBS) patches. In this method, at macroscale, unknown structural responses are calculated by Nitsche-type IGA, which not only ensures the consistency between geometric and analytical models, but also offers an effective way to enforce kinematic compatibility and mechanical equilibrium on interfaces between adjacent NURBS patches. At microscale, mechanical properties of microstructures are predicted by a Kriging metamodel at a low computational cost, which is constructed via some sample lattice unit cells (LUCs). In addition, analytical computation of sensitivities for coupled elements is developed. Finally, the structures are infilled by graded LUCs according to the density distribution within the design space. Some 2D and 3D numerical examples with conforming and non-conforming NURBS patches are presented to test the proposed method. Results indicate that the proposed method is effective for design of structures described by multiple NURBS patches.

本文提出了一种使用 Nitsche 型等几何分析 (IGA) 的多尺度拓扑优化方法，用于设计由多个非均匀有理 B 样条 (NURBS) 面片描述的结构。在此方法中，在宏观尺度上，通过 Nitsche 型 IGA 计算未知结构响应，这不仅确保了几何模型和分析模型之间的一致性，而且还提供了一种有效的方法来加强相邻 NURBS 面片之间界面的运动学兼容性和机械平衡。在微观尺度上，微观结构的力学性能由 Kriging 元模型以低计算成本预测，该模型是通过一些样本晶格单元 (LUC) 构建的。此外，还开发了耦合元件灵敏度的分析计算。最后，根据设计空间内的密度分布，结构由分级 LUC 填充。提出了一些具有符合和不符合 NURBS 补丁的 2D 和 3D 数值示例来测试所提出的方法。结果表明，所提出的方法对于由多个 NURBS 面片描述的结构的设计是有效的。