预应力索-桁架结构拓扑优化设计  

Topology Optimization Design of Prestressed Cable-truss Structures

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,北京100124

出　　处：《北京工业大学学报》2011年第9期1360-1366,共7页Journal of Beijing University of Technology

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

摘　　要：对包括索力值、构件截面尺寸和结构拓扑的预应力索-桁架结构优化设计进行研究.以应力为约束条件,建立以结构质量为目标函数的数学模型.在求解方法上,首先建立求解索力值和构件截面尺寸的线性规划模型;证明了在每个迭代步中,该模型的最优解至少使得1个构件截面尺寸为零,并通过删除零力杆实现结构的拓扑优化设计.算例结果与相应体系理论相吻合,表明本文所提出的方法有效,可为预应力索-桁架结构提供合理的布局.It is discussed the optimization design of prestressed cable-truss structures with itsdesign variables including cables＇ pretension force, cross section size of member and structural topology. A relevant mathematics model is founded with its objective function to minimize the structural weight with stress constrain considered. In the order to solve the problem, a liner programming model is established by fully stress method to calculate cables＇ pretension force and cross section size of member. Then a conclusion is proved that the optimal solution of the liner programming model makes at least one member cross-section size zero in each iteration, and topology optimization is completed by deleting the member. The result of the examples in this paper coincides with corresponding structural performance, which indicates the method in this paper is effective and efficient, and can provide reasonable layout for prestressed cable-truss structures.

关 键 词：预应力索-桁架结构 拓扑优化 索力值优化 尺寸优化 

分 类 号：TU394[建筑科学—结构工程]