Abstract
An improved simulation method is proposed for the assessment of structural failure probabilities. Basic random variables are assumed to be stochastically independent normal variates. The sampling region expressed in polar coordinates is divided into sampling segments by several concentric spheres with the center at the origin. The probability element at a certain radial distance from the origin is the product of the probability density, a volume element of the corresponding sampling segment and an indicator factor. A "hit and miss" Monte Carlo simulation is applied to estimate the indicator factor, which is the proportion of samples falling in the failure region for each sampling segment. The structural failure probability is estimated as the summation of a probability element of each sampling segment. The proposed method gives good estimates of the structural failure probability with small sample size. Numerical examples are provided to show the validity of the method.
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