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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。
In order to solve the problem of the reliability of complex limit state equations, a Monte Carlo simulation method of structural failure probability based on the theory of joint distribution function and two kinds of approximate joint distribution function is proposed and the calculation flow chart is given. Two examples are given to demonstrate the effectiveness of the proposed method. The results show that the proposed method of failure probability simulation has high computational accuracy and is especially suitable for the reliability calculation of complex limit state equations. The accuracy of the failure probability obtained by the two approximate methods of joint distribution function is comparable, and the difference between the approximate method and the accurate method increases with the decrease of failure probability, and increases with the increase of the correlation between the variables. When the failure probability is less than 10 3, the approximation method has larger failure probability error.