考虑宏观结构性能的多材料微结构拓扑优化设计  

Multi-material microstructure topology optimization design consideringmacroscopic structural performance

作　　者：张磊[1,2] 倪绍豪 蒋国璋 张严 宫逸文[1,2] ZHANG Lei;NI Shaohao;JIANG Guozhang;ZHANG Yan;GONG Yiwen(MOE Key Lab of Metallurgical Equipment and Control,Wuhan University of Science and Technology,Wuhan 430081,China;Hubei Provincial Key Lab of Mechanical Transmission and Manufacturing Engineering,Wuhan University of Science and Technology,Wuhan 430081,China;Precision Manufacturing Research Institute,Wuhan University of Science and Technology,Wuhan 430081,China)

机构地区：[1]武汉科技大学冶金装备及其控制教育部重点实验室,武汉430081 [2]武汉科技大学机械传动与制造工程湖北省重点实验室,武汉430081 [3]武汉科技大学精密制造研究院,武汉430081

出　　处：《振动与冲击》2024年第11期185-193,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金项目(52301381;52205280);湖北省自然科学基金(2022CFC004);湖北省交通运输厅交通运输科技项目(2022-11-1-4);中国博士后科学基金(2021M692486);数字制造装备与技术国家重点实验室开放基金(DMETKF2022017);湖北省博士后创新研究岗位项目;武汉科技大学冶金装备及其控制教育部重点实验室开放基金资助项目。

摘　　要：多孔微结构材料以其质量轻、比刚度/比强度高、抗冲击等优异力学性能,被广泛应用于航空航天等工程领域。相比单一材料设计,多材料设计可获得力学性能更优的微结构拓扑构型。拓扑优化是实现多材料布局设计的有效方法之一。通过构建基于差集的多材料水平集描述模型和交替活动相算法,提出了基于参数化水平集的多材料微结构拓扑优化设计方法。首先,构建了基于差集的多材料水平集描述模型,利用N个水平集函数实现N+1相材料拓扑的精确描述。然后,引入交替活动相算法,将原始N+1相多材料优化问题分解为N(N+1)/2个双相材料优化子问题,以减少设计变量与约束条件,提高计算效率。最后,采用均匀化方法计算多材料微结构的等效弹性张量,以宏观结构柔度最小化为优化目标,各相材料用量为约束条件,构建多材料微结构拓扑优化模型,并利用优化准则法实现上述优化模型的高效求解。数值算例结果表明,所提方法可有效实现多材料微结构的拓扑优化设计,所设计微结构均具有光滑的结构边界和清晰的材料界面。Porous microstructure materials are widely used in engineering fields of aerospace,etc.due to their excellent mechanical properties of light weight,high specific stiffness/strength and impact resistance.Compared to single material design,multi-material design can obtain microstructural topology configurations with better mechanical properties.Topology optimization is one of the effective methods for realizing multi-material layout design.Here,a multi-material microstructure topology optimization design method based on parameterized level set was proposed through constructing difference set-based multi-material level set description model and alternating activity phase algorithm.Firstly,a multi-material level set description model based on difference set was constructed,and N level set functions were used to accurately describe the topology of N+1 phase materials.Then,the alternating active phase algorithm was introduced to decompose the original N+1 phase multi-material optimization problem into N(N+1)/2 biphase material optimization subproblems to reduce design variables and constraints,and improve computational efficiency.Finally,the homogenization method was used to calculate the equivalent elastic tensor of multi-material microstructure.Minimizing compliance of macroscopic structure was taken as the optimization objective,and amounts of various phase materials was taken as constraint conditions to construct a multi-material microstructure topology optimization model.The optimization criterion method was used to efficiently solve the above optimization model.Results of numerical examples showed that the proposed method can effectively realize topology optimization design of multi-material microstructures,and all designed microstructures have smooth structural boundaries and clear material interfaces.

关 键 词：拓扑优化 多材料微结构 水平集方法 均匀化方法 交替活动相算法 

分 类 号：TH122[机械工程—机械设计及理论]