基于Von Mises应力的预应力钢结构拓扑优化设计  

Topology Optimization Design of Prestressed Steel Structures Based on Von Mises Stress

作　　者：杨海军[1,2] 张爱林[1] 

机构地区：[1]北京工业大学建筑工程学院,北京100124 [2]河北建筑工程学院数理系,河北张家口075024

出　　处：《北京工业大学学报》2010年第4期475-481,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项目资助(Z0005191040111);河北省科技厅项目资助(072156184)

摘　　要：为预应力钢结构设计获得最优拓扑构型和索力值,以结构拓扑和索力值为设计变量,以Von Mises应力为约束条件,建立了以结构质量最小为目标函数的数学优化模型.在求解方法上,首先以结构储存应变能最小(刚度最大)确定施加在结构上的索力值,然后采用渐进结构优化法删除低Von Mises应力单元实现结构的拓扑优化以减轻结构质量.算例结果与相应体系受力性能相吻合.To obtain optimal topology shape and cables＇ pretension force for prestressed steel structure,a mathematical optimization model is established in such a form that the cables＇ pretension force and the structural topology are referred as the design variables,the Von Mises stress as constrain condition,and the minimum of structural weight as the objective function.In order to establish the model, the method of minimizing structural strain energy（maximizing structural stiffness） is applied to calculate the cables＇ pretension force,and then the method of evolutionary structure optimization is provided to minimize the structural weight through deleting elements with minimum Von Mises stress.The result of the examples coincides with corresponding structural performance,and this indicates the method in this paper is effective and efficient.

关 键 词：预应力钢结构 拓扑优化 索力值优化 VonMises应力 渐进结构优化法 

分 类 号：TU394[建筑科学—结构工程]