Separable Monte Carlo Simulation Applied to Laminated Composite Plates Reliability

An efficient simulation-based method for estimating the probability of failure, called separable Monte Carlo, is analyzed for various applications to composite laminates.  Separable Monte Carlo (SMC) is a technique that takes advantage of statistical independence of random variables that affect structural response and capacity for reliability calculations. The separation allows improvement to the accuracy of probability calculation with a given number of expensive response samples compared with traditional Monte Carlo. Two procedures for implementing SMC are discussed, along with variance estimators. The first type of SMC is performed when the random response is sampled while the distribution of the capacity is given analytically. In this case the approach reduces to the well known conditional Monte Carlo approach. The other type of SMC is for when the CDF of the capacity must be approximated from random samples as an empirical CDF. It is shown that the variance predictors for SMC can be estimated from the samples used to calculate the reliability. Separable Monte Carlo is applied to three example problems, including flexural response a laminated plate, and maximum strain failure from thermal loading. In the flexural response problem, the versatility of separable Monte Carlo is used to improve the accuracy of the failure probability estimate by reformulating the limit state. Finally, the experimental and predicted variances of the probability of failure for separable and crude Monte Carlo are compared for each of the example engineering applications.