多工况下具有体系可靠性约束的桁架结构拓扑优化设计

TOPOLOGY OPTIMIZATION OF TRUSS STRUCTURES WITH SYSTEMATIC RELIABILITY CONSTRAINTS UNDER MULTIPLE LOAD CASES

建立了多工况下具有位移和体系可靠性约束的桁架结构拓扑优化设计数学模型 .针对结构体系可靠性约束处理的困难 ,提出了一种通过可靠性分配和再分配的方法 ,将体系给定失效概率依据敏度信息分解为各杆件失效概率之和 ,并利用可靠性安全系数和结构力学的基本关系 ,将诸位移和应力概率约束等价显示化为设计变量的显示线性常规约束形式 .对于多约束则采用了紧约束处理 ,并用修正的单纯形法进行优化设计 .

The topology optimal model of truss structures with the constraints of displacement and systematic reliability under multiple load cases is constructed. In order to avoid the difficulty of computing the structure systematic reliability, a solving approach is presented in which the systematic failure probability is divided into the sum of all bars failure probability by means of reliability distribution. In addition, by drawing into the reliability safety factor and the fundamental relationship in structural mechanics, all the probability constraints of displacement and stress are equivalently displayed as conventional form and linear function of the design variables. The optimization problem with multiple constraints is treated by the compact constraint tactics and is solved by the improved simplex method. The examples show that the approach proposed in this paper is feasible and efficient.