用Lagrange乘子法求解结构可靠指标

COMPUTING RELIABILITY INDEX OF STRUCTURE BY USE OF LAGRANGE MULTIPLIER METHOD

摘要: 本文用Lagrange乘子法把求解结构可靠指标的条件极值问题转化为无条件极值问题,对目前已被应用的迭代公式给出了理论证明;同时指出,对于随机变量为一般分布情况下的结构可靠指标的计算,把原来非正态分布随机变量用当量正态分布随机变量代替时,为了保证收敛,迭代过程中当量正态分布随机变量的均值和标准差必须有足够的精度。文中的几个算例表明,采用的计算方案具有较快的收敛速度和计算精度。
- Lagrange乘子法 /
- 极限状态方程 /
- 结构可靠度 /
- 可靠指标 /
- 失效概率
Abstract: In this paper, the problem of conditional extreme-value of solving structural reliability index is transformed into the problem of non-conditional extreme-value by use of Lagrange Multiplier Method. It is pointed out that mean values and standard deviations of the effective normal distribution random variables which replace non-normal distribution random variables must have enough accuracy. The results of the examples in this paper show that the speed of convergence and computing accuracy for the method are satisfied.
- lagrange multiplier method /
- limit state equation /
- structural reliability /
- reliability index /
- failure probability