预应力索-桁架结构拓扑优化设计

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.

Topology Optimization Design of Prestressed Cable-truss Structures

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.