基于变体积约束的阻尼材料微结构拓扑优化研究  

Research on Topology Optimization of Damping Material Microstructures With Varied Volume Constraints

作　　者：张东东[1,2] 栾福强 赵礼辉 郑玲[3] ZHANG Dongdong;LUAN Fuqiang;ZHAO Lihui;ZHENG Ling(School of Mechanical Engineering,University of Shanghai for Science and Technology,Shanghai 200093,P.R.China;Shanghai Technology Service Platform of Reliability Evaluation for New Energy Vehicles,Shanghai 200093,P.R.China;College of Mechanical and Vehicle Engineering,Chongqing University,Chongqing 400044,P.R.China)

机构地区：[1]上海理工大学机械工程学院,上海200093 [2]上海市新能源汽车可靠性评价公共技术平台,上海200093 [3]重庆大学机械与运载工程学院,重庆400044

出　　处：《应用数学和力学》2022年第6期648-659,共12页Applied Mathematics and Mechanics

基　　金：上海市青年科技英才扬帆计划(18YF1418500)。

摘　　要：阻尼复合结构的抑振性能取决于材料布局和阻尼材料特性.该文提出了一种变体积约束的阻尼材料微结构拓扑优化方法,旨在以最小的材料用量获得具有期望性能的阻尼材料微结构.基于均匀化方法,建立阻尼材料三维微结构有限元模型,得到阻尼材料的等效弹性矩阵.逆用Hashin-Shtrikman界限理论,估计对应于期望等效模量的阻尼材料体积分数限,并构建阻尼材料体积约束限的移动准则.将获得阻尼材料微结构期望性能的优化问题转化为体积约束下最大化等效模量的优化问题,建立阻尼材料微结构的拓扑优化模型.利用优化准则法更新设计变量,实现最小材料用量下的阻尼材料微结构最优拓扑设计.通过典型数值算例验证了该方法的可行性和有效性,并讨论了初始微构型、网格依赖性和弹性模量等对阻尼材料微结构的影响.The vibration suppression performance of a damping composite structure depends on the material layout and the damping material properties.A topology optimization method was proposed for damping material microstructures with varied volume constraints,to obtain the damping material microstructure with desired properties under the smallest material consumption.Based on the homogenization method,a 3D finite element model for the damping material was established,and the effective elastic matrix of the damping material was formulated.The Hashin-Shtrikman bounds theory was used inversely to estimate the volume fraction bound of the damping material corresponding to the desired effective modulus,and a movement criterion for volume constraint bounds of damping materials was constructed.Then the optimization problem of achieving the desired properties of damping materials with microstructures was converted to another problem of maximizing the desired modulus under volume constraints,and a topology optimization model for the damping material microstructure was established.The optimality criteria method was employed to update the design variables,and the optimized topology configurations of damping material microstructures were obtained.The feasibility and effectiveness of the proposed method were verified with several numerical examples,and the influences of the initial configurations,the mesh density and Young’s modulus on the microstructure configurations of the damping material were also discussed.

关 键 词：阻尼材料 变体积约束 等效模量 均匀化方法 Hashin-Shtrikman界限理论 

分 类 号：TB53[理学—物理]