基于双向渐进结构优化方法的连续体结构动刚度拓扑优化  

Topological Optimization of Dynamic Stiffness in Continuum Structure Based on Bidirectional Evolutionary Structural Optimization

作　　者：江旭东[1] 刘铮 滕晓艳[2] JIANG Xu-dong;LIU Zheng;TENG Xiao-yan(School of Mechanical and Power Engineering,Harbin University of Science and Technology,Harbin 150080,China;College 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：《哈尔滨理工大学学报》2020年第5期136-142,共7页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(51505096);黑龙江省自然科学基金(E2015026,QC2016056);黑龙江省博士后科研启动金项目(LBH-Q15070)。

摘　　要：以结构动柔顺度最小为目标,融合等效静载荷方法与双向渐进结构优化方法,提出了动载荷作用下连续体结构的动刚度拓扑优化方法。为了有效降低结构动力学拓扑优化问题的求解规模,通过等效静载荷方法将动态拓扑优化问题转变为静态拓扑优化问题,结合双向渐进结构优化方法实现结构的静力学拓扑优化。提出了一种设计域减缩方法降低连续体结构拓扑优化计算规模,构建了一种新颖的体积进化和优化收敛准则,显著提高了连续体结构的动刚度优化效率。数值算例结果表明,结构动柔顺度与约束体积均能渐进收敛于最优值,最优拓扑构形能够有效抑制动载荷作用下的结构振动,其优化算法具有一定的鲁棒性和适应性。提出的连续体结构动刚度拓扑优化方法拓展了基本渐进结构优化方法的应用范围,对于结构动力学优化设计具有重要的理论意义。By minimizing structural dynamic compliance, the programming scheme of optimal stiffness for continuum structure under dynamic load is proposed, by combination of Equivalent Static Loads with Bidirectional Evolutionary Structural Optimization. To effectively decrease calculation scale for dynamic optimization in structural topology, the Equivalent Static Loads Method is applied to transforming dynamic optimization to static one that is solved by Bidirectional Evolutionary Structural Optimization in structural topology. To enhance the optimal efficiency of the original BESO method to optimization of dynamic stiffness in continuum structure, a design domain reduction method is developed to establish a new volume control and a stop criterion in this study. Numerical results show that the dynamic compliance is asymptotically convergent to optimal solution with volume constraint precisely satisfied, and optimal configuration can effectively inhibit the vibration induced by dynamic load. Whereby the presented optimization algorithm is verified to be robust and adapt. Consequently it is provided with theoretical significance to extend the original Evolutionary Structural Optimization Method to dynamic optimization in structural design.

关 键 词：连续体结构 拓扑优化 动刚度 等效静载荷 双向渐进结构优化 

分 类 号：TB535.1[理学—物理]