TOPOLOGICAL OPTIMIZATION DESIGN METHOD OF LAYER-WISE GRADED LATTICE STRUCTURES WITH HIGH LOAD-BEARING
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摘要:随着增材制造技术的迅速发展, 点阵结构由于其高比强度、高比刚度等优异力学性能受到广泛关注, 但其单胞分布设计大多基于均布式假设, 导致其承载能力相对较差. 基于拓扑优化技术提出了一种梯度分层的点阵结构设计方法. 首先, 基于水平集函数建立点阵单胞几何构型的显式描述模型, 引入形状插值技术实现点阵单胞的梯度构型生成; 其次, 构建基于Kriging的梯度点阵单胞宏观等效力学属性预测模型, 建立宏观有限单元密度与微观点阵单胞等效力学属性的内在联系; 然后, 以点阵结构刚度最大为优化目标, 结构材料用量和力学控制方程为约束条件, 构建点阵结构的梯度分层拓扑优化模型, 并采用OC算法进行数值求解. 算例结果表明, 所提方法可实现点阵结构的最优梯度分层设计, 充分提高了点阵结构的承载性能, 同时可保证不同梯度点阵单胞之间的几何连续性. 最后, 开展梯度分层点阵结构与传统均匀点阵结构和线性梯度点阵结构的准静态压缩仿真分析, 仿真结果表明, 与传统均匀点阵结构和线性梯度点阵结构相比, 梯度分层点阵结构的承载能力明显提高. 研究结果可为高承载点阵结构设计提供理论参考.Abstract:With the rapid development of additive manufacturing technology, lattice structures have attracted extensive attention due to their excellent mechanical properties, such as high specific strength and high specific stiffness. However, the designs of lattice structures are mostly based on the assumption of uniform distribution, resulting in a relatively poor load-bearing capacity. This paper proposes a layer-wise graded lattice structure design method based on a topology optimization technology. Firstly, an explicit description model of lattice geometric configuration is established by using the level set function, and a shape interpolation technology is employed to generate the graded configurations of lattice cells. Secondly, a prediction model of macro effective mechanical property for these graded lattice cells is constructed based on the Kriging metamodel, achieving the essential relationship between the effective density of macro element and the effective mechanical property of micro lattice cell. Then, with the maximum stiffness of lattice structures as the optimization objective, the allowable material usage amount and structural system equilibrium equation as the constraint conditions, a layer-wise graded topology optimization model of lattice structures is established, which is solved numerically by using the OC algorithm. The numerical results indicate that the proposed method can realize the optimal layer-wise graded design of lattice structures, which not only fully improve the load bearing performance of lattice structures, but also ensure the geometric connectivity between different graded lattice cells. Finally, the quasi-static compression simulation analyses of the layer-wise graded lattice structures, the traditional uniform lattice structures and the linear graded lattice structures are carried out and discussed. The simulation results show that, compared with the traditional uniform lattice structures and the linear graded lattice structures, the loading capacity of the layer-wise graded lattice structures is significantly improved. The proposed method provides a theoretical reference for the design of high loading lattice structures.
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图 6梯度点阵结构拓扑优化设计流程图
Figure 6.Flowchart of topology optimization for the design of graded lattice structures
图 8设计域30 cm × 15 cm目标函数及体积分数迭代图
Figure 8.Iterations of objective function and volume fraction for design domain 30 cm × 15 cm
图 10设计域40 cm × 15 cm × 10 cm目标函数及体积分数迭代图
Figure 10.Iterations of objective function and volume fraction for design domain 40 cm × 15 cm × 10 cm
图 11均布斜载荷下的柱状设计域
Figure 11.3D design domain of a culumn under uniformly distributed oblique load
图 1215 cm × 20 cm × 10 cm立体构型及微结构
Figure 12.The structure and microstructure of example 15 cm × 20 cm × 10 cm
图 14750 mm × 750 mm点阵结构应力云图及变形图
Figure 14.Stress and deformation diagrams of lattice structures 750 mm × 750 mm
图 1690 mm × 120 mm × 60 mm点阵结构应力云图及变形图
Figure 16.Stress and deformation diagrams of lattice structures 90 mm × 120 mm × 60 mm
表 1设计域30 cm × 15 cm结构图及柔度
Table 1.The structure and compliance of design domain 30 cm × 15 cm
Uniform Linear graded Topology graded Relative density structure 
compliance 124.24 N·cm 88.84 N·cm 60.55 N·cm 
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表 2设计域15 cm × 15 cm结构图及柔度
Table 2.The structure and compliance of design domain 15 cm × 15 cm
Uniform Linear graded Topology graded Relative density structure 
compliance 293.04 N·cm 229.45 N·cm 172.34 N·cm 下载:
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表 3设计域40 cm × 15 cm × 10 cm结构图及柔度
Table 3.The structure and compliance of design domain 40 cm × 15 cm × 10 cm
Uniform Linear graded Topology graded Relative density structure 
compliance 10171.05 N·cm 13759.11 N·cm 4979.70 N·cm 下载:
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表 4设计域15 cm × 20 cm × 10 cm结构图与柔度
Table 4.The structure and compliance of design domain 15 cm × 20 cm × 10 cm
Uniform Linear graded Topology graded Relative density structures 
compliance 8165.04 N·cm 7708.78 N·cm 6945.11 N·cm 下载:
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