The present research develops a direct multiscale topology optimization method for additive manufacturing (AM) of coated structures with nonperiodic infill by employing an adaptive mapping technique of adaptive geometric components (AGCs). The AGCs consist of a framework of macro-sandwich bars that represent the macrostructure with the solid coating and a network of micro-solid bars that represent the nonperiodic infill at the microstructural scale. The macrostructure including the coating skin and the internal architecture of the microstructures of cellular structures is simultaneously optimized by straightforwardly searching optimal geometries of the AGCs. Compared with most existing methods, the proposed method does not require material homogenization technique at the microscale; the continuity of microstructures and structural porosities are ensured without additional constraints; Finite element analysis (FEA) and geometric parameter updates are required only once for each optimization iteration. AGCs allow us to model coated structures with porosity infill on a coarse finite element mesh. The adaptive mapping technique may reduce mapping time by up to 50%. Besides, it is easy to control the length scales of the coating and infill as desired to make it possible with AM. This investigation also explores the ability to realize concurrent designs of coated structures with nonperiodic infill patterns using 3D printing techniques.

本研究通过采用自适应几何组件（AGC）的自适应映射技术，开发了一种用于非周期性填充涂层结构的增材制造（AM）的直接多尺度拓扑优化方法。AGC由宏观夹心棒的框架组成，这些夹心棒代表了具有固体涂层的宏观结构，而微实心棒的网络则代表了微观结构范围内的非周期性填充物。通过直接搜索AGC的最佳几何形状，可以同时优化包括涂层皮肤在内的宏观结构和细胞结构微观结构的内部结构。与大多数现有方法相比，该方法不需要微观尺度的材料均质化技术。确保了微观结构和结构孔隙的连续性，而没有其他限制；每次优化迭代只需要一次有限元分析（FEA）和几何参数更新。AGC使我们能够在粗糙的有限元网格上对具有孔隙填充的涂层结构进行建模。自适应映射技术可以将映射时间最多减少50％。此外，很容易根据需要控制涂层和填充物的长度比例，以使AM成为可能。这项研究还探讨了使用3D打印技术实现具有非周期性填充图案的涂层结构同时设计的能力。AGC使我们能够在粗糙的有限元网格上对具有孔隙填充的涂层结构进行建模。自适应映射技术可以将映射时间最多减少50％。此外，很容易根据需要控制涂层和填充物的长度比例，以使AM成为可能。这项研究还探讨了使用3D打印技术实现具有非周期性填充图案的涂层结构同时设计的能力。AGC使我们能够在粗糙的有限元网格上对具有孔隙填充的涂层结构进行建模。自适应映射技术可以将映射时间最多减少50％。此外，很容易根据需要控制涂层和填充物的长度比例，以使AM成为可能。这项研究还探讨了使用3D打印技术实现具有非周期性填充图案的涂层结构同时设计的能力。