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 引用本文: 廉睿超, 敬石开, 李营, 肖登宝, 陈阳. 考虑最小尺寸精确控制的SIMP和MMC混合拓扑优化方法. 力学学报, 2022, 54(12): 3524-3537.
Lian Ruichao, Jing Shikai, Li Ying, Xiao Dengbao, Chen Yang. A hybrid topology optimization method of SIMP and MMC considering precise control of minimum size. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3524-3537.
 Citation: Lian Ruichao, Jing Shikai, Li Ying, Xiao Dengbao, Chen Yang. A hybrid topology optimization method of SIMP and MMC considering precise control of minimum size. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 3524-3537.

## A HYBRID TOPOLOGY OPTIMIZATION METHOD OF SIMP AND MMC CONSIDERING PRECISE CONTROL OF MINIMUM SIZE

• 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.

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.

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