基于参数化水平集方法的微结构拓扑优化设计  

Topology optimization for the design of microstructure base on parameterized level set method

作　　者：魏鹏[1,2] 范海坚 李雪平 苏成[1] WEI Peng;FAN Hai-jian;LI Xue-ping;SU Cheng(State Key Laboratory of Subtropical Building Science,School of Civil Engineering and Transportation,South China University of Technology,Guangzhou 510640,China;Guangdong Provincial Key Laboratory of Technique and Equipment for Macromolecular Advanced Manufacturing,South China University of Technology,Guangzhou 510640,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,广州510640 [2]华南理工大学广东省高分子先进制造技术及装备重点实验室,广州510640

出　　处：《计算力学学报》2021年第4期471-478,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(12072114);广东省高分子先进制造技术及装备重点实验室开放课题(2020kfkt03)资助项目.

摘　　要：相比于单一材料,复合材料具有轻质高强等优点,拓扑优化方法是设计复合材料的方法之一。本文采用改进的参数化水平集方法,更新了水平集迭代格式,并应用水平集带方法在优化过程中引入中间密度,使水平集方法与变密度法无缝结合以改善水平集方法的拓扑寻优能力,降低其初始设计依赖性。本文以最大化体积模量、剪切模量和负泊松比作为材料设计目标,结合均匀化方法预测材料的宏观等效性能,研究了不同体积分数、多种初始设计及水平集带方法的引入对优化结果的影响,并得到了多种满足不同目标函数的微结构拓扑形式。数值算例验证了本文方法在复合材料微结构设计问题中的有效性。Compared with solid materials,composite materials have the advantages of lightweight and high strength.Topology optimization is one of the methods to design composite materials.In this study,an improved parameterized level set method is adopted,the level set iterative scheme is updated,and the level set band method is used to introduce intermediate density in the optimization process,so that the level set method and the variable density method are seamlessly combined to improve the capability of topology change of the level set method and alleviate its initial design dependence.In this paper,maximizing bulk modulus,shear modulus,and negative Poisson’s ratio are taken as the material design objectives.The homogenization method is used to predict the macro-equivalent properties of the material.The results with different volume fractions and various initial designs are compared,and the use of the level set band method are studied.A variety of microstructure topological forms for different objective functions have been obtained.Numerical examples verify the effectiveness of this method for material design problems.

关 键 词：拓扑优化 材料设计 水平集方法 均匀化方法 

分 类 号：O343[理学—固体力学]