联合分布函数蒙特卡罗模拟及结构可靠度分析

针对复杂极限状态方程可靠度计算问题,提出了基于理论联合分布函数以及2 种近似联合分布函数的结构失效概率蒙特卡罗模拟方法,并给出了计算流程图.采用2 个算例证明了所提方法的有效性.结果表明:所提的失效概率模拟方法的计算精度很高,尤其适用于复杂极限状态方程的可靠度计算问题.2 种联合分布函数近似构造方法得到的失效概率精度相当,近似方法与精确方法结果的差异随失效概率的减小而增大,而且随着变量间相关性的增加而增加.当失效概率小于10-3时,近似方法的失效概率误差较大.

MONTE CARLO SIMULATION OF MULTIVARIATE DISTRIBUTION AND ITS APPLICATION TO STRUCTURAL RELIABILITY ANALYSIS

The reliability analysis of complex limit state functions involving random variables represented by joint probability distributions cannot be evaluated by direct integration. This paper aims to propose a Monte Carlo simulation based on the method for simulating the joint probability functions and estimating the probability of failure of complex limit state functions. A flow chart of probability of failure based on Monte Carlo simulation is presented. Two examples are presented to demonstrate the validity and capability of the proposed methods. The results indicate that the proposed Monte Carlo simulation can produce sufficiently accurate results, especially it is suitable for the reliability problems with complex limit state functions. Both the approximate method P and the approximate method S can lead to the results with a sufficient accuracy. The difference in probabilities of failure between the two approximate methods and the exact method increases with decreasing probability of failure. It increases as the correlation between variables becomes stronger. Significant errors associated with the two approximate methods could be observed when the probability of failure is below 10-3.