A HYBRID TOPOLOGY OPTIMIZATION METHOD OF SIMP AND MMC CONSIDERING PRECISE CONTROL OF MINIMUM SIZE
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摘要: 拓扑优化作为一种先进设计方法, 已被成功用于多个学科领域优化问题求解, 但从拓扑优化结果到其工程应用之间仍存在诸多阻碍, 如在结构设计中存在难以制造的小孔或边界裂缝和单铰链连接等. 在拓扑优化设计阶段考虑结构最小尺寸控制是解决上述问题的一种有效手段. 在最小尺寸控制的结构拓扑优化方法中, 通用性较强的固体各向同性材料惩罚法SIMP优化结果边界模糊不光滑, 包含精确几何信息的移动变形组件法MMC对初始布局具有较强依赖性. 本文提出一种考虑最小尺寸精确控制的SIMP和MMC混合拓扑优化方法. 所提方法继承了二者优势, 避免了各自缺点. 在该方法中, 首先采用活跃轮廓算法ACWE获取SIMP输出的拓扑结构边界轮廓数据, 提出了SIMP优化结果到MMC组件初始布局的映射方法. 其次, 通过引入组件的3个长度变量, 建立了半圆形末端的多变形组件拓扑描述函数模型. 最后, 以组件厚度变量为约束, 构建了考虑结构最小尺寸控制的拓扑优化模型. 采用最小柔度问题和柔性机构问题验证了所提方法的有效性. 数值结果表明, 所提方法在无需额外约束的条件下, 仅通过组件厚度变量下限设置, 可实现整体结构的最小尺寸精确控制, 并获得了具有全局光滑的拓扑结构边界.
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关键词:
- 固体各向同性材料惩罚法 /
- 移动变形组件法 /
- 混合拓扑优化 /
- 拓扑描述函数 /
- 最小尺寸控制
Abstract: Topology optimization is an advanced design method, which has been successfully used to solve multidisciplinary optimization problems, but there are still many obstacles to the reliable use of topology optimization results in engineering manufacturing, such as tiny holes or boundary cracks and hinges in structural design. An effective means to solve the above problems is to consider the minimum size control of the structure in the topology optimization design stage. In the topology optimization method considering the minimum size control, the boundaries of the widely used solid isotropic material with penalization (SIMP) method optimization result are usually blurred and not smooth, and moving morphable component (MMC), which contains precise geometric information, has a strong dependence on the initial layout of components. This paper proposes a hybrid topology optimization method of the SIMP and MMC considering precise control of minimum size. The proposed method inherits the advantages of both and avoids their respective disadvantages. In this method, a mapping method from the SIMP optimization results to the initial layout of MMC components is firstly proposed, which uses the active contour without edges (ACWE) algorithm to obtain the topological boundary contour data of the SIMP and the geometric parameter matrix of the components. Secondly, the topological description function model of the multi-deformable component with the semicircular end is established by introducing three length variables of the component. Finally, a topology optimization model that considers the minimum size control of the structure is constructed with the component thickness variable as the constraint. The effectiveness of the proposed method is verified by the minimum compliance problem and the compliance mechanism problem. The numerical results show that, the proposed method can achieve precise control of the minimum size of the overall structure and obtain a globally smooth topological structure boundary only by setting the lower limit of the component thickness variable without additional constraints.-
Key words:
- SIMP /
- MMC /
- hybrid topology optimization /
- topology description function /
- minimum size control
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图 2 悬臂梁示意图及SIMP拓扑优化结果
Figure 2. Schematic of the cantilever beam and the topology optimization result of SIMP
图 7 MBB梁混合拓扑优化组件映射过程
Figure 7. Components mapping process of MBB beam with hybrid topology optimization
图 9 组件相交示意图
Figure 9. Schematic of incomplete intersection and overlap between components
图 13 不同变量取值的半圆形末端组件
Figure 13. Components of semicircular ends with different variable values
图 14 基于组件映射结果的悬臂梁优化过程
Figure 14. Optimization process for the cantilever beam based on components mapping results
图 15 悬臂梁MMC拓扑优化过程
Figure 15. Topology optimization process of the cantilever beam using MMC
图 16 悬臂梁不同方法优化过程的收敛历史
Figure 16. The iteration history of the cantilever beam using different methods
图 17 不同最小尺寸约束下的悬臂梁混合拓扑优化结果
Figure 17. Hybrid topology optimization results of the cantilever beam with different minimum length scales
图 18 最小尺寸
$ {d_{\min }}{\text{ = 0}}{\text{.1}} $ 的悬臂梁TsSC拓扑优化结果Figure 18. TsSC topology optimization result of the cantilever beam with minimum length scales
$ {d_{\min }}{\text{ = 0}}{\text{.1}} $ 
图 20 柔性机构混合拓扑优化过程
Figure 20. Hybrid topology optimization process of the compliant mechanism
图 21 柔性机构MMC拓扑优化过程
Figure 21. Topology optimization process of the compliant mechanism using MMC
图 22 增加组件数量后的柔性机构MMC优化结果
Figure 22. Optimization result of the compliant mechanism using MMC after increasing the number of components
图 23 柔性机构不同方法优化过程的收敛历史
Figure 23. The iteration history of the compliant mechanism using different methods
图 24 不同最小尺寸约束下柔性机构混合拓扑优化结果
Figure 24. Hybrid topology optimization results of the compliant mechanism with different minimum length scales
图 25 不同最小尺寸约束下的柔性机构TsSC拓扑优化结果
Figure 25. TsSC topology optimization results of the compliant mechanism with different minimum length scales
图 26 最小尺寸
$ {d_{\min }}{\text{ = 0}}{\text{.02}} $ 的柔性机构ECS拓扑优化结果Figure 26. ECS topology optimization result of the compliant mechanism with minimum length scales
$ {d_{\min }}{\text{ = 0}}{\text{.02}} $ 表 1 不同最小尺寸约束的悬臂梁目标函数
Table 1. Object function of the cantilever beam with different minimum length scales
Method $ {d_{\min }} $ $ \underline {{t_1}} $ $ \underline {{t_2}} $ $ \underline {{t_3}} $ Mean compliance hybrid topology optimization 0.16 0.08 0.08 0.08 39.65 0.20 0.10 0.10 0.10 38.14 0.24 0.12 0.12 0.12 36.26 TsSC 0.10 0.05 0.05 0.05 67.78 
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