基于改进双向渐进法的轻量化设计方法  

Lightweight design method based on improved BESO method

作　　者：王颖 张争艳[1] 雷焱阳 唐瑀 孙立新[1] WANG Ying;ZHANG Zhengyan;LEI Yanyang;TANG Yu;SUN Lixin(School of Mechanical Engineering,Hebei University of Technology,Tianjin 300130,China)

机构地区：[1]河北工业大学机械工程学院,天津300130

出　　处：《河北工业大学学报》2022年第2期14-22,39,共10页Journal of Hebei University of Technology

基　　金：国家自然科学基金(61802108);河北省自然科学基金(E2017202296)。

摘　　要：双向渐进法是近年来结构拓扑优化领域的一个热点,针对现有结构拓扑优化方法容易出现的网格依赖性和局部极值等数值不稳定现象,以及计算速率慢的问题,提出一种双重过滤增删的双向渐进法,简称为DBESO方法。该方法通过对典型的Michell结构、短悬臂结构和MBB梁结构进行不同过滤增删次数的计算,得出二次增删过滤为最佳的过滤增删次数,即在执行灵敏度过滤和单元的增删的基础上,将结果存入中间变量再对灵敏度过滤及单元的增删进行计算,并且设定一个判定结构性能的指标进行收敛。在MATLAB编程环境下,通过二维短悬臂结构和三维简支梁结构的拓扑优化算例,证明DBESO方法在保证力学性能不变的情况下,有效地提高结构轻量化的收敛速率,更好地抑制双向渐进方法的网格依赖性和局部极值等数值不稳定现象。The Bi-directional evolutionary structural optimization method is a hot topic in the field of structural topology optimization. To solve the problem of slow iteration rate and numerical instability such as mesh-dependency and local minima in the existing structural topology optimization method, the paper proposes a Bi-directional evolutionary structural optimization method of double sensitivity filter and double addition and deletion( DBESO). In this method, through the different addition and deletion filtering of typical Michell structure, short cantilever structure and MBB beam structure were calculated. It is concluded that the second addition and deletion filtering is the best filtering addition and deletion times. The sensitivity filter and the element addition and deletion are calculated again through an intermediate variable after the implementation of the sensitivity filter and the element addition and deletion. And set an index to determine the performance of the structure of the convergence condition. By the topology optimization example of two-dimensional short cantilever beam and three-dimensional simply supported beam structure in MATLAB programming environment,verify under the condition of ensuring the same mechanical performance, the convergence rate of the lightweight structure is effectively improved and the numerical instability of the Bi-directional evolutionary structural optimization method is preferably eliminated.

关 键 词：双向渐进法 轻量化 中间变量 灵敏度 MATLAB 

分 类 号：TB21[一般工业技术—工程设计测绘]