位移约束下预应力钢结构拓扑优化设计  

Topology Optimization Design of Prestressed Steel Structures with Displacement Constrainsts

作　　者：杨海军[1,2] 张爱林[2] 姚力[1] 

机构地区：[1]河北建筑工程学院数理系,河北张家口075024 [2]北京工业大学建筑工程学院,北京100022

出　　处：《应用基础与工程科学学报》2010年第4期599-608,共10页Journal of Basic Science and Engineering

基　　金：国家自然科学基金(50678012);北京市科委科技奥运专项基金(Z0005191040111);河北省科技厅项目(072156184)

摘　　要：为预应力钢结构体系创新进行拓扑优化设计研究.建立了以索力值和结构拓扑为设计变量,以位移为约束条件,以结构重量最小为目标函数的数学优化模型.在求解方法上,采用两阶段设计方法.首先以结构储存应变能最小(刚度最大)确定施加在索上的预拉力,然后通过灵敏度分析,采用渐进结构优化法(ESO方法)删除低位移灵敏度单元实现结构的拓扑优化以减轻结构重量,反复迭代,直至最优.算例结果与相应体系受力性能相吻合,表明本文所提出的优化设计方法可行,为预应力钢结构选型提供了理论依据.A topology optimization design method for prestressed steel structures system innovation was proposed.The optimization mathematical model was established in such form that cables＇ pretension force and structural topology were design variables,the structural displacement was constrain condition,and the minimum structural weight was objective function.In order to solve the problem,two-stage design method was adopted.The cables＇ pretension force could be determined by minimizing structural strain energy（maximizing structural stiffness）.After that, the method of evolutionary structure optimization（ESO） was applied to achieve structural topology optimization by deleting elements with low displacement sensitivity,and the structural weight was also reduced.Two-stage iterated alternately until structural topology achieved optimum.The example results coincided with the corresponding structural performance,which indicated the proposed optimization design method was practicable and could provide theoretical method for prestressed steel structures type selection.

关 键 词：预应力钢结构 两阶段设计 拓扑优化 索力值优化 渐进结构优化法 

分 类 号：TU394[建筑科学—结构工程]