1 Separable Sampling of the Limit State for Accurate Monte

Reliability-based design simulations often use the Monte Carlo method as a sampling procedure for predicting failure. The combination of designing for very small failure probabilities (~10-8 – 10-6) and using computationally expensive finite element models, makes Monte Carlo simulations very costly. This paper uses an improved sampling procedure for calculating the probability of failure, called separable Monte Carlo. Separable Monte Carlo takes advantage of statistical independence of limit state random variables of the response and capacity for improved accuracy in reliability calculations. The separation of response and capacity sampling enables flexible sample sizes, permitting low samples of the more expensive component (usually the response). In turn, this motivates the beneficial reallocation of uncertainty by reformulating the limit state. Previous research has shown significant improvements for simple limit state problems, however in this work we extend the separable Monte Carlo to a non-separable limit state. The example considered in this study is for predicting failure in a composite laminate with the Tsai-Wu failure criterion. It was found that grouping sets of random variables that involve inexpensive calculations and sampling them separately in the limit state improved the accuracy in the probability of failure estimate. Nomenclature ija = coefficients of effective laminate stiffness matrix C = random variable for capacity of a system CV = coefficient of variatio