动态载荷不确定条件下的周期性结构稳健拓扑优化  

Robust Topology Optimization of Periodic Structures under Uncertain Dynamic Loads

作　　者：蔡金虎 黄静 黄龙 付志方 吴宏宇 尹来容[1] CAI Jinhu;HUANG Jing;HUANG Long;FU Zhifang;WU Hongyu;YIN Lairong(School of Automotive and Mechanical Engineering,Changsha University of Science and Technology,Changsha 410114;Aerospace Shentuo(Beijing)Technology Co.,Ltd,Beijing 100176;School of Mechanical Engineering,University of Science and Technology Beijing,Beijing 100083)

机构地区：[1]长沙理工大学汽车与机械工程学院,长沙410114 [2]航天深拓(北京)科技有限公司,北京100176 [3]北京科技大学机械工程学院,北京100083

出　　处：《机械工程学报》2024年第23期304-319,共16页Journal of Mechanical Engineering

基　　金：国家自然科学基金(52175003);湖南省自然科学基金(2024JJ6045,2021JJ40259);湖湘青年英才基金(2020RC3035)资助项目。

摘　　要：周期性结构由于具有轻质、吸能、减震等性能优势而在航空航天、能源动力等领域的结构设计中受到广泛关注。然而,现有的关于周期性结构拓扑优化的研究大多是在静态载荷条件下进行的。考虑到实际工程中存在动态载荷的作用以及载荷不确定性对设计结果的重要影响,有必要开展动态载荷不确定条件下的周期性结构拓扑优化方法研究。综合考虑动态载荷的大小、方向、作用位置和激励频率存在不确定性,以结构动柔度模的均值和标准差的加权和为目标函数、结构体积分数为约束,建立了动态载荷不确定条件下的周期性结构稳健拓扑优化模型,提出了基于复合变量降维法和高斯积分法的不确定性量化与传播方法,导出了目标函数的计算方法及其对设计变量的灵敏度列式。通过数值算例验证了所提方法的有效性以及动态载荷不确定性对周期性结构拓扑优化设计的影响。The periodic structure attracts widespread attention in the structure design of aerospace,energy power and other fields due to the light weight and energy absorption performance.However,most of the existing works of topology optimization for periodic structures only considers the effects of static loads.Considering the inevitable existing of dynamic loads in practical engineering and the impact of loads uncertainty on the design results,it is necessary to carry out the periodic structure topology optimization method under dynamic loads uncertainty.Comprehensive considering the uncertainty of the dynamic load magnitude,direction,position,and excitation frequency,the weighted summation of mean and standard deviation of the module of dynamic structure compliance is set as the objective function with constraint is imposed to the structure volume fraction.The hybrid dimension reduction method and Gaussian integration method are used to quantify and propagate the loads uncertainty and the sensitivity formulation of objective function with respect to the design variables are derived.Two numerical examples are used to verify the effectiveness of the proposed method and the influence of dynamic loads uncertainty on the topology optimization design of periodic structures.

关 键 词：周期性结构 稳健性 拓扑优化 动态载荷 载荷不确定性 

分 类 号：TH122[机械工程—机械设计及理论] O327[理学—一般力学与力学基础]