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For the probabilistic finite element analysis of structures and materials considering uncertainty parameters, the Monte Carlo (MC) simulation is often used. However, the accuracy to predict the tail distribution of the quantity of interest (QoI) is not always good enough. Therefore, this paper proposes a multi-step MC method focusing on the tail distribution. The first step aims at predicting the expected value of QoI accurately with least number of sampling points. By analyzing the results of sampling points in the first step, a region in the parameter space is determined whose sampling points may result in extreme value in the tail distribution of QoI. The next step employs the sampling points in the above limited region to obtain accurately the tail distribution. The main contribution of this paper is to present the newly developed automated algorithm to determine the above region in parameter space. Its usefulness has been shown in the simulation of tensile test of perforated thin plate considering the scattering of geometrical size of holes due to laser processing. Predicted scattered initial fracture load was compared with experimental results.

mechanical engineering letters

Numerical prediction of scattered initial fracture load of perforated thin plate under tension by Monte Carlo FEM simulation with stepwise limited sampling