双尺度分级结构时域动刚度问题的并行拓扑优化  

Concurrent topology optimization for time-domain dynamic stiffnessproblem of two-scale hierarchical structure

作　　者：江旭东[1] 马佳琪 滕晓燕 JIANG Xudong;MA Jiaqi;TENG Xiaoyan(School of Mechanical and Power Engineering,Harbin University of Science and Technology,Harbin 150080,China;School of Mechanical and Electrical Engineering,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]哈尔滨理工大学机械动力工程学院,哈尔滨150080 [2]哈尔滨工程大学机电工程学院,哈尔滨150001

出　　处：《振动与冲击》2023年第15期31-41,共11页Journal of Vibration and Shock

基　　金：国家自然科学基金(51675144);黑龙江省自然科学基金联合引导项目(LH2020E064)。

摘　　要：提出双尺度分级结构时域动刚度问题的并行拓扑优化方法,实现结构宏观拓扑构型和材料微观分布协同优化。利用三场密度方法实施宏观与微观结构的设计,基于能量的均匀化方法(energy-based homogenization method, EBHM)在微观结构上计算等效的宏观力学特性。针对比例阻尼系统,将HHT-α方法作为时间积分算法,求解多尺度结构的动力学有限元模型。融合先离散-后微分方法与伴随方法,在时间与空间离散的拓扑优化模型上实施敏度分析,避免了将时间作为连续变量而导致的灵敏度计算的一致性误差问题。以多尺度结构的动柔度最小化为目标,宏观与微观结构体积为约束,分别求解了正弦半波和余弦半波冲击载荷作用下多尺度结构的并行拓扑优化问题。最后,通过2种典型算例的数值结果验证了所提算法的有效性。Here,the concurrent topology optimization method for dynamic stiffness in the domain problem of dual-scale hierarchical structure was proposed to realize collaborative optimization of macroscopic topological configuration of structure and microscopic distribution of materials.Three-field density method was used to perform designing macro and micro structures,and energy-based homogenization method(EBHM)was used to calculate equivalent macro mechanical properties for micro structures.Aiming at proportional damping systems,HHT-αmethod was taken as a time integration algorithm to solve dynamic finite element model of multi-scale structure.Fusing the first discrete-then differential method and the adjoint method,sensitivity analysis was performed for the topological optimization model with discrete time and space to avoid the consistency error problem of sensitivity calculation due to taking time as a continuous variable.With the objective to minimize the dynamic flexibility of multi-scale structure and taking volumes of macro and micro structures as constraints,concurrent topology optimization problems of multi-scale structure under sinusoidal and cosine half-wave impact loads were solved,respectively.Finally,the effectiveness of the proposed algorithm was verified with numerical results of 2 typical examples.

关 键 词：双尺度分级结构 并行拓扑优化 时域动刚度 HHT-α方法 基于能量的均匀化方法(EBHM) 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3