离散变量结构优化设计的最优综合效能法  

OPTIMUM SYNTHETIC EFFECTIVENESS METHOD FOR STRUCTURAL OPTIMIZATION WITH DISCRETE VARIABLES

作　　者：曾国华[1] 董聪[1] 

机构地区：[1]清华大学土木系,北京100084

出　　处：《工程力学》2008年第9期106-110,117,共6页Engineering Mechanics

基　　金：北京市自然科学基金重点项目(8021002);北京市重大科技项目(H030630210021)

摘　　要：针对结构优化问题的位移约束,引入关键约束的界约参数,提出了结构位移统一约束的缩减形式,从而简化了结构优化模型。根据离散变量结构优化问题的特点,提出了效能系数的概念,它衡量设计变量在离散邻域范围内变化对目标函数与约束函数值的影响,并研究了基于效能系数取值分类的四种主要调整方式。根据结构应力和位移约束的影响区域属性,以综合效能最大化为引导,提出了求解离散变量结构优化问题的最优综合效能法。算例结果显示该算法具有良好的优化效率,可求得问题的最优解或获得历史上的最优记录。For the displacement constraints of structural optimization problems, the threshold parameter of key constraints is introduced. A reduced-formula of unified displacement constraint is proposed to simplify the structural optimization model. According to the characteristics of structural optimization with discrete variables, the concept of efficiency coefficient is proposed to measure the effect of design variables＇ variation in discrete neighborhood on cost function and constraints, and four adjusting modes in terms of the efficiency coefficient are analyzed. Based on the influence domain of stress and displacement constraints, an optimum synthetic effectiveness algorithm for structural optimization with discrete variables is proposed under the guidance of maximum synthetic effectiveness. From the analysis of numerical examples, it is indicated that the optimal solutions or best records can be obtained with high optimization efficiency by the presented algorithm.

关 键 词：结构优化 离散变量 位移约束 桁架结构 综合效能 

分 类 号：O221[理学—运筹学与控制论] TU318[理学—数学]