文献类型：期刊文献

中文题名：基于最低灵敏度区域更新的改进双向渐近结构优化方法

英文题名：Improved BESO method based on updating the region with the lowest sensitivity

作者：刘辉 杨旭东 孙栋

第一作者：刘辉

机构：[1]贵州大学机械工程学院,贵州贵阳550025;[2]贵州理工学院机械工程学院,贵州贵阳550025

第一机构：贵州大学机械工程学院,贵州贵阳550025

年份：2025

卷号：42

期号：9

起止页码：1759-1770

中文期刊名：机电工程

外文期刊名：Journal of Mechanical & Electrical Engineering

收录：;北大核心:【北大核心2023】；

基金：贵州省科技计划项目(黔科合成果〔2023〕一般812);贵州省工业和信息化发展专项(202308)。

语种：中文

中文关键词：机械设计;拓扑优化;双向渐近结构优化方法;灵敏度过滤;收敛准则;非线性;微结构

外文关键词：mechanical design;topology optimization;bi-directional evolutionary structural optimization(BESO)method;sensitivity filtering;convergence criterion;nonlinearity;microstructure

摘要：针对双向渐近结构拓扑优化方法(BESO)中灵敏度过滤引发的原始信息偏差及算法收敛性不足的问题,提出了一种最低灵敏度区域更新法。首先,找出了灵敏度值过滤前的最低一批单元在有限元划分后的网格中的位置信息(简称为最低灵敏度区域),在灵敏度过滤后,仅在最低灵敏度区域中进行了设计变量的更新,即可在不丢失网格无关滤波器的作用下,在一定程度上保障灵敏度过滤方法对灵敏度信息的偏差影响,确保算法仅在真正小的一批单元中更新设计变量,在一定程度上能够确保演化的正确方向;然后,判断了目标函数的稳定性,通过逐步缩小最低灵敏度区域,缩减了设计变量的更新范围,迫使结构的拓扑形状趋于稳定;最后,针对静载荷作用下的线弹性材料刚度最大化设计、几何非线性结构的刚度最大化设计以及微结构的剪切模量最大化设计,分别进行了对比验证。研究结果表明:最低灵敏度区域更新法比原BESO方法的总迭代次数降低了约16%,平均柔度降低了1.6%,平均迭代时长降低了约20%。该结果证明,最低灵敏度区域更新法可获得更优的解,并具有较好的收敛性,且提高了算法的收敛速度。
In the bi-directional evolutionary structural topology optimization(BESO)method,sensitivity filtering creates bias in original sensitivity information.Poor convergence is also observed.A minimum sensitivity region update method was proposed to resolve these issues.First,elements with the lowest pre-filtered sensitivity values were identified in the finite element mesh(termed the minimum sensitivity region).After the sensitivity filtering,the design variables were updated only in the lowest sensitivity region.This could ensure that the role of the mesh-independent filter was not lost,and to a certain extent,it could guarantee the deviation impact of the sensitivity filtering method on the sensitivity information.It ensured that the algorithm update the design variables only in a truly small batch of units,and to a certain extent,it could ensure the correct direction of the evolution.Then,objective function stability was evaluated by progressively shrinking the design variable update range in the minimum sensitivity region.The update range of the design variables was reduced,forcing the topological shape of the structure to tend towards stability.Finally,the comparative verification was conducted on the maximization design of the stiffness of linear elastic materials under static loads,the stiffness of geometrically nonlinear structures,and the shear modulus of microstructures.The research results show that the lowest sensitivity region update method reduces the total number of iterations by about 16%,the average flexibility by 1.6%,and the average iteration time by about 20%compared to the original BESO method.This verifies that the lowest sensitivity region update method obtains better solutions.It has good convergence and improves convergence speed of algorithm.