| Monte Carlo simulation (MCS) is usually used as a benchmark to verify the accuracy of other stochastic methods in structural analysis. It shows that the displacement response resulted from the MCS often fluctuates when coefficient of variation of the normally distributed elastic modulus is large. It is of great engineering and mathematical significance on structure stochastic analysis to study the cause of MCS response results fluctuation and eliminate this phenomenon, expand the application scope of MCS. This paper study on the condition and cause of MCS results fluctuation of stochastic structural response systematicly, meanwhile, a identified criterion of MCS singular sample is proposed. Further more, a standard normal truncated distribution based on singular sample interval is proposed and efficient and accurate formulas of response statistical moment and reliability are developed. The research work are as follows:(1) The cause of MCS results fluctuation are researched, proved that neighbor zero sample rather than negative range of the normal distribution random variables on denominator caused MCS results occur fluctuations, directly or indirectly removed negative range of normal distribution random variables can not eliminate the fluctuations.(2) Through quantitative and qualitative analysis, proposed a identified criterion of MCS singular sample, the interval that caused MCS results fluctuation are found, truncated singular sample in this interval can eliminate the fluctuations.(3) Define the standard normal truncated distribution based on singular sample interval, derived the distribution function and probability density function of response, the statistical moment formula of response and reliability formula in case that single normally truncated distributed random variable and double normally truncated distributed random variable is given, it has higher accuracy and great significance to stochastic analysis of practical engineering. |
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