基于联合仿真的曲面共形多孔结构拓扑优化方法  

Topological optimization method for conformal cellular structures on surfaces based on co-simulation

作　　者：付君健 徐勇 周祥曼 舒正涛 田启华 FU Junjian;XU Yong;ZHOU Xiangman;SHU Zhengtao;TIAN Qihua(Hubei Key Laboratory of Hydroelectric Machinery Design&Maintenance,Yichang 443002,China;College of Mechanical&Power Engineering,China Three Gorges University,Yichang 443002,China;Stale Key Laboratory of Intelligent Manufacturing Equipment and Technology,Wuhan 430074,China)

机构地区：[1]水电机械设备设计与维护湖北省重点实验室,宜昌443002 [2]三峡大学机械与动力学院,宜昌443002 [3]智能制造装备与技术全国重点实验室,武汉430074

出　　处：《北京航空航天大学学报》2024年第9期2781-2790,共10页Journal of Beijing University of Aeronautics and Astronautics

基　　金：国家自然科学基金(51775308);湖北省自然科学基金(2021CFB236);智能制造装备与技术全国重点实验室开放基金(IMETKF2023016)。

摘　　要：针对宏观曲面结构上多孔结构单胞构型与设计域外形不匹配,导致曲面结构优化困难的问题,提出一种基于联合仿真的曲面共形多孔结构拓扑优化方法。基于三周期极小曲面隐式水平集函数,实现多孔结构的参数化建模。采用等参单元法理论,建立自然坐标系到笛卡儿坐标系的映射关系,实现曲面多孔结构的共形建模。构造线性插值函数,保证多孔结构单胞之间的C0连续。引入可变切割水平集函数,建立MATLAB与ANSYS联合仿真的多孔结构拓扑优化框架。数值算例表明:所提方法可有效实现曲面多孔结构的拓扑优化设计,确保多孔结构单胞与设计域外形的匹配,提升多孔结构的力学性能。The optimization design for structures with surface is challenging due to the mismatch between cellular unit cell configuration and the design domain shape.Thus,a topological optimization design method for conformal cellular structures on surfaces based on co-simulation is proposed.The parametric modelling of cellular structures is achieved by utilising the implicit level set functions derived from triply periodic minimal surfaces.By using the isoparametric element method,the mapping relationship between the natural coordinate system and the cartesian coordinate is established to realize the conformal modeling of the cellular structures on surfaces.A linear interpolation function is constructed to ensure the C0 continuity of the cellular unit cell.An optimization framework for cellular structures is built by combining MATLAB and ANSYS with the use of variable cutting level set functions.Numerical examples show that this method can effectively realize the topological optimization design of cellular structures on surfaces.The method also ensures the matching of the cellular structures unit cell with the shape of the design domain,and improves the mechanical properties of the cellular structures.

关 键 词：拓扑优化 多孔结构 共形建模 可变切割水平集函数 联合仿真 

分 类 号：TH112[机械工程—机械设计及理论]