基于磨光反演映射的拓扑优化ICM方法

铁军; 叶红玲; 彭细荣

doi:10.21656/1000-0887.380052

基于磨光反演映射的拓扑优化ICM方法

doi: 10.21656/1000-0887.380052

¹天津财经大学理工学院, 天津 300222;²北京工业大学机械工程与应用电子技术学院, 北京 100124;³湖南城市学院土木工程学院, 湖南益阳 413000

基金项目: 国家自然科学基金(11672103)

详细信息

作者简介:
铁军(1968—)，男，博士，硕士生导师(E-mail: tielaoshi@sina.com)；叶红玲（1972—），女，副教授，博士(E-mail: yehongl@bjut.edu.cn)；彭细荣（1972—），男，副教授，博士(通讯作者. E-mail: pxr568@163.com).

中图分类号: O39
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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

An ICM Method for Topology Optimization Based on Polished Inverse Mapping

¹School of Polytechnic, Tianjin University of Finance and Economics, Tianjin 300222, P.R.China; ²College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing 100124, P.R.China;³College of Civil Engineering, Hunan City University, Yiyang, Hunan 413000, P.R.China

Funds: The National Natural Science Foundation of China(11672103)

摘要

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.
- 拓扑优化 /
- ICM方法 /
- 磨光反演映射 /
- 叠加离散效应 /
- 复合过滤函数 /
- 位移约束
Abstract: The polish mapping and the filter mapping in the ICM (independent continuous mapping) method for topology optimization were extended, and the composite function was used to coordinate the filter function. Due to the superposed discrete effects of composite functions, the composite function of the power function and the sine function was introduced to identify the presence and absence of the elements. The ICM method was used to establish the topology optimization model for the continuum structure with the minimum weight under the displacement constraints, which was solved with the exact dual algorithm of the quadratic programming. Then based on the dynamic inversion strategy, the rational inversion function was constructed with the optimal threshold to obtain the most strict discrete solution. Moreover, the 2-stage ‘discrete-continuous’ and ‘continuous-discrete’ solution method was established for topology optimization. Moreover, a calculator program was developed and compiled based on the MATLAB according to this new method. The results show that the proposed method has the advantages of higher computational efficiency, less optimal gray values and less structural weight after inversion, and gives a more reasonable structural topology.
- topology optimization /
- ICM method /
- polished inverse mapping /
- superposed discrete effect /
- composite filter function /
- displacement constraint

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