三维循环对称结构的多目标多约束拓扑优化算法研究  

Exploring Multi-Objective Topological Optimization of 3D Cyclically Symmetric Structure under Multiple Constraints

作　　者：王全国[1] 王三民[1] 袁茹[1] 

机构地区：[1]西北工业大学机电学院,陕西西安710072

出　　处：《西北工业大学学报》2008年第4期425-429,共5页Journal of Northwestern Polytechnical University

基　　金：航空科学基金(2006ZB53016)资助

摘　　要：利用循环对称特性建立三维循环对称结构的多目标多约束拓扑优化算法。基于子结构法原理,将三维循环对称结构转化为一个扇形子块,建立在应力和位移约束下强度、刚度和频率的多目标函数拓扑优化模型,采用罚函数法与遗传算法结合,形成多目标多约束拓扑优化算法。在拓扑优化算法中,采用个体相似控制以使初始种群的个体遍布整个可行解的空间,采用混合选择法以增加种群的多样性并提高运行效率,采用最优保存策略以保证算法的收敛性。同时对适应度函数做可调的非线性变换,以提高遗传算法的收敛速度。另外在遗传算法的进化过程中,引入了多样性策略,去除重复的个体,增加新的个体,扩大解的搜索范围。算例结果表明,文中所建立的算法是合理、有效的,且可用于循环对称结构的初始方案设计。Aim. To our knowledge, there is no paper in the open literature dealing with the optimization problem described in the title; hence, we explore. In the full paper, we present the results ot our exploration in some detail; in this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is. the substructure method for doing static and dynamic finite element analysis of 3D cyclically symmetric structure. The second topic is： the topological optimization method based on genetic algorithm （GA）. In this topic, using jointly the penalty function method and the GA, we establish the mathematical model of multi-objective optimization algorithm with stiffness, strength and frequency under stress and displacement constraints considered. Under the topological optimization algorithm, we use the similar species removal technique to spread the individuals among the initial species to the space of all feasibility solutions. We also use the hybrid selection method to increase the variety of species and use the elitist strategy to enhance the efficiency and convergence of the optimization algorithm. Meanwhile, we do the adjustable nonlinear transformation of the fitness function to accelerate the convergence speed of the GA. Finally, we give a numerical example, whose results show preliminarily that our topological optimization method based on GA is better than past methods in that： （1） the stress distribution is more even and （2） the first order natural frequency is higher.

关 键 词：三维循环对称结构 拓扑优化 遗传算法 子结构法 多样性策略 

分 类 号：TP391.71[自动化与计算机技术—计算机应用技术]