基于应变能与频率灵敏度的静动力双目标ESO  

Static and dynamic bi-objective Evolutionary Structural Optimization based on sensitivity of both strain energy and frequency

作　　者：张鹄志[1,2] 张棒 周云[2] 谢献忠[1] ZHANG Hu-zhi;ZHANG Bang;ZHOU Yun;XIE Xian-zhong(School of Civil Engineering,Hunan University of Science and Technology,Xiangtan 411201,China;College of Civil Engineering,Hunan University,Changsha 410082,China)

机构地区：[1]湖南科技大学土木工程学院,湘潭411201 [2]湖南大学土木工程学院,长沙410082

出　　处：《计算力学学报》2023年第2期192-197,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(51508182);湖南省自然科学基金(2021JJ30270)资助项目.

摘　　要：当前在运用渐进结构优化(ESO)时,大多仅设定了单一的静力或动力目标,难以满足工程结构设计的需求。为此,将单目标优化常用的应变能灵敏度和频率灵敏度进行无量纲处理,再与多目标优化理论结合,开发出静动力双目标ESO。通过多个不同边界条件的深受弯构件数值算例,证实了新方法的运行稳定性和普遍适用性,同时还得到了静力优化与动力优化间的权重系数比取值建议。有限元对比分析结果表明,该新方法相较于传统的单目标优化,能够兼顾结构的静动力性能,使结构耗材减少但静力刚度基本维持,同时材料利用率和一阶固有频率还能不断提升。At present,when evolutionary structural optimization(ESO)is applied,only a single static or dynamic goal is set,which is difficult to meet engineering needs for stuctural design.In this situation,based on dimensionless processing of the strain energy sensitivity and frequency sensitivity commonly used in single objective optimization,and combined with the multi-objective optimization theory,the static and dynamic bi-objective ESO was developed.Several deep flexural members with different boundary conditions are taken as numerical examples to prove the stability and universal applicability of the new method,and meanwhile obtain the value suggestion of the weight coefficient ratio between the static optimization and the dynamic optimization.The results of finite element comparative analysis show that the new method can take the static and dynamic performance of the structure into account.Compared with the traditional single objective optimization,it can reduce material consumption but basically maintain the static stiffness of the structure,and the material utilization rate and the first-order natural frequency are continuously improved.

关 键 词：渐进结构优化 双目标优化 动力优化 应变能灵敏度 频率灵敏度 拓扑优化 结构优化设计 

分 类 号：O302[理学—力学] O224