Topology optimization of coated structures with layer-wise graded lattice infill for maximizing the fundamental eigenfrequency
Topology optimization of coated structures with layer-wise graded lattice infill for maximizing the fundamental eigenfrequency
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DOI：
10.1016/j.compstruc.2022.106861
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Tiannan Hu;Yaguang Wang;Heng Zhang;Hao Li;Xiaohong Ding;K. Izui;S. Nishiwaki
中科院分区：
文献类型：
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作者：
Tiannan Hu;Yaguang Wang;Heng Zhang;Hao Li;Xiaohong Ding;K. Izui;S. Nishiwaki
网格填充涂层结构结合了网格填充和涂层的优点，在工程中得到了广泛的应用，以实现结构的轻量化或某些功能。本文提出了一种新的并行多尺度拓扑优化（TO）框架，以最大限度地提高结构的基本特征频率与均匀的外涂层和逐层梯度晶格填充微结构。采用基于速度场的水平集方法进行了宏观拓扑优化，该方法继承了传统水平集方法的隐式几何表示和符号距离特性（边界光滑清晰，能够很好地保持涂层厚度的均匀性）。此外，由于采用了一般的数学规划算法，使得基于速度场的水平集方法能够更容易地处理多个约束条件。在微尺度下，基于密度的方法被用来设计逐层梯度晶格结构。微结构的有效材料性能的计算使用渐近均匀化方法，桥梁宏观和微观尺度的设计。研究发现，具有分层梯度晶格填充结构的涂层结构比具有周期性和均匀晶格填充结构的涂层结构具有更高的本征频率，具有更高的设计灵活性。通过数值算例，研究了晶格填充层数和涂层厚度对宏观和微观结构并行优化的影响，验证了所提方法的有效性和优化结果的可制造性。
Combining the advantages of lattice infill and coating, coated structures with lattice infill are widely used in engineering to achieve light-weight structural characteristic or certain functionalities. This paper presents a novel concurrent multiscale topology optimization (TO) framework to maximize the fundamental eigenfrequency of structures with a uniform outer coating and layer-wise graded lattice infill microstructures. The macroscale topology optimization is conducted by using the velocity field-based level set method, which inherits the implicit geometrical representation and signed distance property of the conventional level set method (smooth and clear boundaries and well-maintenance of the uniform thickness of the coating). Besides, the employment of general mathematical programming algorithms enables the velocity field-based level set method to handle multiple constraints in an easier way. At microscale, the popular density-based method is used to design layer-wise graded lattice structures. The effective material properties of microstructures are computed by using the asymptotic homogenization method, which bridges macroscale and microscale designs. With higher design flexibility, it is found that coated structures with layer-wise graded lattice infill have higher eigenfrequencies than those with periodic and uniform lattice infill microstructures. The influence of layers of lattice infill and coating thickness on the concurrent optimization of macrostructures and microstructures are carefully studied by showcasing several numerical examples, and the effectiveness of the proposed method is also confirmed, as well as the manufacturability of optimization results.