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中文摘要：
采用双向渐进结构优化方法（BESO）研究循环对称结构拓扑优化设计问题。循环对称结构的几何特征无法划分为均匀一致的网格，造成单元灵敏度计算结果与单元体积直接相关，不同网格剖分后的单元体积分布将导致渐进优化过程中不同的单元去除顺序，最终使得优化结果具有单元体积依赖性。针对循环对称结构的特殊性，提出灵敏度密度新概念与消除非等体积单元棋盘格现象的体积加权灵敏度密度过滤新方法，大量算例表明这是一种有效的方法，同时优化结果也充分显示子结构单胞尺寸效应对优化构型的显著影响。
英文摘要：
The topology optimization of cyclic-symmetry structures is studied by means of bi-directional evolutionary structural optimization （BESO） method. Due to the retention of non-uniform finite element discretization relative to one such type of structures, it is found that the sensitivity result depends upon the volume of the concerned finite element. As a result, different finite element discretizations will change the element removal/growth sequence in the BESO procedure. For this reason, a new concept of element sensitivity density is proposed to avoid the element-volume-dependence of the optimal design. Meanwhile, a new volume-weighted filtering technique is developed to control the checkerboard for the corresponding mesh. To verify the proposed method, a variety of numerical tests related to the concentrated load are studied in detail. Discussions show that the size effects of basic cells are important.
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