应力和位移约束下的板壳结构截面优化  

SECTIONAL OPTIMIZATION OF PLATE AND SHELL STRUCTURES WITH STRESS AND DISPLACEMENT CONSTRAINTS

作　　者：隋允康[1] 金雪燕[1] 杜家政[1] 龙连春[1] 

机构地区：[1]北京工业大学工程数值模拟中心,北京100022

出　　处：《力学学报》2004年第6期701-708,共8页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10072005);北京市自然科学基金(3042002);北京市教委(KM200410005019)资助项目~~

摘　　要：将准则法和数学规划法相结合,根据满应力准则将应力约束化为动态下限,借助单位虚载荷法将位移约束转化为设计变量的近似显函数,建立了满足应力和位移约束的优化模型.为了解决多变量的大型优化问题,根据对偶理论将上千设计变量的优化模型转化为几个变量的对偶模型,并通过二次规划求解.以MSC/Nastran软件为结构分析的求解器,借助MSC/Patran软件为开发平台,完成了板壳结构截面优化程序.程序完全和Patran及Nastran融为一体,在Patran中建立模型,利用Nastran分析计算,根据优化结果对设计变量调整,再用Nastran进行结构重分析,反复迭代直到结构重量收敛.算例表明程序的合理性和有效性,能够满足工程设计的需要.Combining optimality criteria method and mathematical programming, the optimization model is founded to satisfy the stress and displacement constraints. The stress constraint is transformed into movable sectional lower limits with the full stress criterion and the displacement constraint is transformed into an approximate explicitly function of design variables with the unit virtual load method. To resolve large-scale optimization problem with multiple design variables, the model with thousands of design variables is transformed into dual model with several design variables and solved with quadratic programming. With MSC/Nastran software as structural analysis solver and MSC/Patran software as developing platform, the sectional optimization software of plate and shell structures is accomplished. The program is completely in harmony with Patran and Nastran. The model is established with Patran and analyzed with Nastran, the design variables are modified according to the optimization results and then the model is reanalyze with Nastran. Repeating like this until the structural weight is convergent. The examples show the program is reasonable and effective, can meet requirement of engineering application.

关 键 词：板壳结构 位移约束 收敛 近似 对偶理论 Nastran软件 对偶模型 截面优化 应力约束 设计变量 

分 类 号：O342[理学—固体力学] TU318[理学—力学]