面向连续体结构拓扑优化的分区密度修正敏度过滤方法研究  

Partition Density Modified Sensitivity Filtering Method for Topology Optimization of Continuum Structure

作　　者：张国锋 徐雷[1] 王鑫[1] 李大双 ZHANG Guofeng;XU Lei;WANG Xin;LI Dashuang(School of Mechanical Engineering,Sichuan University,Chengdu 610065,China)

机构地区：[1]四川大学机械工程学院,成都610065

出　　处：《机械科学与技术》2022年第11期1641-1649,共9页Mechanical Science and Technology for Aerospace Engineering

基　　金：四川省智能制造重大专项(2017ZB073)。

摘　　要：变密度法因设计变量少、效率高等优点,已成为解决连续体结构拓扑优化问题的一种有效方法。传统变密度法在优化过程中常出现数值不稳定问题,其优化结果常具有灰度单元,使得优化模型提取较为困难。Sigmund敏度过滤方法虽然能有效减少数值不稳定现象,但该方法容易产生边界扩散的问题,不具备良好的可制造性。为得到边界清晰的拓扑优化结果,提出一种面向连续体结构的分区密度修正敏度过滤方法,该方法将原过滤区域进行划分,采取新的复合卷积因子对不同区域处理,进一步采用一种带有预设密度修正权值的方法,有效弱化边界扩散的问题。通过对多个算例及不同处理方法进行比较分析,验证该方法的可行性及稳定性。The SIMP method has become an efficient method to solve the topology optimization issue of the continuum because of its advantages such as less design constraints and high performance.In the traditional SIMP method,numerical instability often occurs during the optimization process,and the optimization results often have gray units,which make it difficult to extract the optimization model and have not good manufacturability.Although the Sigmund sensitivity filtering method can effectively improve the checkerboard phenomenon,this method is prone to the problem of boundary diffusion.In order to achieve the topological optimization results with clear boundaries,a partition density correction sensitivity filtering method for continuum structure is proposed in this study.This method divides the original filtering area,uses a new mixed convolution index to process different areas,and further adopts a method with preset density correction weights that effectively weakens the problem of boundary diffusion.By combining and analyzing multiple analytical examples and different filtering methods,the feasibility and reliability of the method are verified.

关 键 词：拓扑优化 连续体 变密度法 敏度过滤 灰度抑制 

分 类 号：TH112[机械工程—机械设计及理论]