多约束作用下连续体结构的拓扑优化  

Topology optimization of continuum structures under multiple constraints

作　　者：边炳传[1] 隋允康[2] 

机构地区：[1]泰山学院应用科学技术系,泰安271021 [2]北京工业大学机械工程与应用电子技术学院工程数值模拟中心,北京100022

出　　处：《计算力学学报》2010年第5期781-788,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10472003);高校博士点基金(20060005010);泰山学院科研基金(Y07-2-08)资助项目

摘　　要：基于ICM(独立、连续、映射)方法建立了以结构重量最小为目标,以屈曲临界力、位移及应力三种约束同时作用的连续体拓扑优化模型:采用独立的连续拓扑变量,借助泰勒展式、过滤函数将目标函数作二阶近似展开。借助瑞利商、泰勒展式、过滤函数将屈曲约束化为近似显函数,借助于过滤函数,将位移约束用莫尔定理显式化;将应力这种局部性约束采用全局化策略进行处理,即借助第四强度理论、过滤函数将应力局部性约束转化为应变能约束,大大减少了灵敏度分析的计算量;将优化模型转化为对偶规划,减少了设计变量的数目,并利用序列二次规划求解,缩小了模型的求解规模。数值算例表明,ICM方法在解决屈曲、位移及应力三种约束共同作用的连续体拓扑优化问题上有优势。In this paper,according to the ICM（Independent Continuous Mapping）method,the topology optimization model for the continuum structure was constructed.The model had the minimized weight as the objective function subjected to the buckling constraints displacement constraints and stress constraints.The continuous independent topological variables were used in this problem.Based on the Taylor expansion and the filtering function,the objective function was approximately expressed as a second-order expressions.Based on the Rayleigh quotient,the Taylor expansion and the filtering function the buckling constraints were approximately expressed as an explicit function.Based on the filter function,the displacement constraints are expressed approximately by Mohr theorem.Using the globalization method of stress constraints and the von Mises＇yield criterion in mechanics of materials,the local stress constraints were translated into the whole structure strain energy constraint.Thus the analysis quantity of the sensitivity was decreased.The optimization model was translated into a dual programming and solved by the sequence second-order programming.The number of the variable was reduced and the model＇s scale was minified.Numerical examples show that this method can solve the topology optimization problem of continuum structures with the buckling and displacement constraints efficiently and give more reasonable structural topologies.

关 键 词：屈曲约束 位移约束 应力约束 ICM方法 拓扑优化 

分 类 号：O346.1[理学—固体力学]