广义平均距离公式在结构优化中的应用研究  

Research on the Application of Generalized Average Distance Formula in Structural Optimization

作　　者：崔争争 杨晓翔[1] CUI Zheng-zheng;YANG Xiao-xiang(School of Mechanical Engineering and Automation,Fuzhou University,Fujian Fuzhou 350000,China)

机构地区：[1]福州大学机械工程及自动化学院,福建福州350000

出　　处：《机械设计与制造》2018年第9期90-93,97,共5页Machinery Design & Manufacture

摘　　要：针对静态多工况刚度和动态振动频率为目标的多目标优化问题,对广义平均距离公式做了研究,并且将其理论应用在结构多目标优化问题中。通过对平均距离公式中的变量赋予不同的参数,最终灵活地构建出不同的目标函数数学模型;采用加权平均的方法确定刚度和频率的综合目标函数。通过一个实例对其建立的目标函数进行验证,并将在随机抽出的四种目标函数在结果上做了简单对比。研究结果表明,采用目标函数一和目标函数四使第一阶固有频率增加了11.22%,采用目标函数二和目标函数三分别使第一阶固有频率提高了24.02%和22.98%,同时优化后各工况的最后的柔度数值结果基本相同,从而说明了广义平均距离公式思想在构建多目标结构优化数学模型上的可行性和灵活多变性。Aiming at the multi-objective optimization problem,the generalized average distance formula is studied,and the theory is applied to the multi-objective optimization problem.By giving different parameters to the variables in the average distance formula,the mathematical model of different objective function is finally constructed;weighted average method is used to determine the stiffness and frequency of the comprehensive objective function.An example is used to verify the objective function,and the results are compared with the results of four kinds of objective functions.The results show that the first order natural frequency is increased by 11.22%with the objective function one and the objective function four.The first order natural frequency is increased by 24.02%and 22.98%respectively by using the target function two and the objective function three,and the numerical results after optimization of flexibility in different condition is basically the same,which shows that the generalized mean distance formula is flexible and changeable in the multi-objective structure optimization model.

关 键 词：多目标优化 平均距离公式 模态频率 柔度 

分 类 号：TH16[机械工程—机械制造及自动化] TH12