## 留言板

 引用本文: 铁军, 叶红玲, 彭细荣. 基于磨光反演映射的拓扑优化ICM方法[J]. 应用数学和力学, 2018, 39(4): 424-441.
TIE Jun, YE Hongling, PENG Xirong. An ICM Method for Topology Optimization Based on Polished Inverse Mapping[J]. Applied Mathematics and Mechanics, 2018, 39(4): 424-441. doi: 10.21656/1000-0887.380052
 Citation: TIE Jun, YE Hongling, PENG Xirong. An ICM Method for Topology Optimization Based on Polished Inverse Mapping[J]. Applied Mathematics and Mechanics, 2018, 39(4): 424-441.

• 中图分类号: O39

## An ICM Method for Topology Optimization Based on Polished Inverse Mapping

Funds: The National Natural Science Foundation of China(11672103)
• 摘要: 对结构拓扑优化ICM（independent continuous mapping）方法中的磨光映射和过滤映射加以拓广，利用反演映射极限形式的磨光特性构造其与过滤映射相协调的复合映射.由于该复合映射的叠加离散效应，首先引入幂函数和正弦函数的复合形式过滤函数，用ICM方法建立位移约束下重量最小为目标的连续体结构拓扑优化模型，并采用二次规划精确对偶算法进行求解.再将求得的离散解为主的连续最优解依照动态反演策略，用最佳阈值和理性反演函数求出最严格的01离散解，给出了拓扑优化“离散→连续”和“连续→离散”先后相反的二阶段解法.基于MATLAB软件平台开发了相应的拓扑优化计算程序，给出的数值算例对该文提出的方法进行验证，结果表明：该方法计算效率高，最优解灰度单元少，反演后结构重量更小，并且能够计算出更合理的结构拓扑.
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##### 出版历程
• 收稿日期:  2017-03-08
• 修回日期:  2017-05-31
• 刊出日期:  2018-04-15

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