引入水平集带的参数化水平集结构拓扑优化方法  

Parameterized Level Set Structural Topology Optimization Method by Introducing Level Set Band

作　　者：魏鹏[1,2] 蒋子润 WEI Peng;JIANG Zirun(School of Civil Engineering and Transportation//State Key Laboratory of Subtropical Building Science,South China University of Technology,Guangzhou 510640,Guangdong,China;Guangdong Key Laboratory of Earthquake Engineering and Application Technology,Guangzhou University,Guangzhou 510006,Guangdong,China)

机构地区：[1]华南理工大学土木与交通学院//亚热带建筑科学国家重点实验室,广东广州510640 [2]广州大学广东省地震工程与应用技术重点实验室,广东广州510006

出　　处：《华南理工大学学报（自然科学版）》2021年第10期87-94,122,共9页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家重点研发计划资助项目(2020Yfb1709401);国家自然科学基金资助项目(12072114);广东省地震工程与应用技术重点实验室开放基金项目(2017B030314068)。

摘　　要：传统水平集方法通过在初始设计中布置一定数量的孔洞来克服其不能自动开孔的缺陷,但孔洞布置方式的差异造成了强烈的初始设计依赖性,改进的参数化水平集方法可以自动开孔,但初始设计对优化结果仍存在一定的影响。水平集带方法可以将水平集方法与变密度法相结合,在零水平集附近引入一个水平集带区域,区域内的材料密度通过水平集函数进行插值。在迭代过程中通过减小水平集带宽度可以逐渐去除中间密度材料,使结构最终收敛到0-1解。引入水平集带可以通过结合变密度法思想提高目标函数和约束函数在拓扑变化中的连续性,从而减轻初始设计对优化结果的影响。通过柔顺度最小化问题验证了该方法可以有效减轻优化结果的初始设计依赖性,并且能够得到更优的目标函数值。此外还探究了水平集带带宽减小速度对优化结果的影响,并将该方法拓展到不规则设计域优化问题中,得到了合理的优化结果。The traditional level set method overcomes the defect that it cannot automatically create holes by arranging a certain number of holes in the initial design,but the distribution form of holes causes a strong dependency on the initial design.The improved parameterized level set method could automatically create holes,but the initial design still affected the optimization results.The level set band method can combine the level set method with the va-riable density method and introduce a level set band region near the zero level set,and the material density in this region was interpolated by the level set function.The intermediate density materials were gradually removed through gradually reducing the width of the level set band in the iterative process,so that the structure finally converged to a 0-1 solution.Introducing level set band can improve the continuity of objective function and constraint function in topology change by combining variable density method,so as to reduce the influence of initial design on optimization results.The compliance minimization problem proves that this method can effectively reduce the initial design dependency of the optimization results and get a better objective function value.Furthermore,the influence of the reduction speed of the width of the level set band on the optimization results was studied,and this method was extended to the optimization problem with irregular design domain and reasonable optimization results were obtained.

关 键 词：水平集方法 初始设计 水平集带 不规则设计域 

分 类 号：TB125[理学—工程力学]