Structural REliability Analysis Based on Fast Monte Carlo Simulation

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Monte Carlo Simulation is a versatile method in structual reliability analysis. In this study, a probability space probing method is presented for the effeicient estimate of failure probability in ealsto-plastic structural problem, where failure functions can not given explicitly. In order to prove the location and the shape of failure functions by a limited number of simulations, the probability space consisting of m-random variables is roughly divided into m-dimensional hypercubes. The structural analyzes are carried out using the values at the corners of each hypercube. If the structure fail or not fail at all the corners of a hypercube, then the subregion is regarded as belonging to the failure or safety domain, respectively. Else if the structure fail at some corners and not fail at the other corners of a hypercube, then the subregion is regarded as lying across the failure function. For the hypercubes lying across the failure function, the subregions are divided into half size in each axis, and the structural analyzes are carried out again using the values at the corners of the half size hypercubes. Then the subregions are classified into the above three groups. Repeating this subdivision process for several times, the failure function comes up clearly in the probability space. The failure probability of the structure can be obtained by the numerical integration of theprobability density in the failure domain. The proposed method is applied to the mathematical problems and the structural problems. Through the numerical simulation it is made clear that the proposed method is more efficient tan the importance sampling method when the number of random variables is less than four. Further it is found that the efficiency of the proposed method is not influenced by the level of failure probability.