Non-probabilistic credible reliability analysis of the composite laminate

Abstract

For the reliability analysis of composite laminate structures, there is a problem of difficult data acquisition. Traditional reliability analysis methods require a large amount of data to maintain calculation accuracy. Therefore, the traditional reliability analysis method is not applicable to composite laminates. For the above-mentioned problems, this paper presents a method to calculate the credible reliability of composite laminate structures using the Bayesian theorem. The method is distinguished from the traditional uncertainty analysis methods. The likelihood function and the newly introduced samples are first used to correct the prior distribution of the uncertain parameters. Furthermore, the posterior distribution, containing information from both the sample and prior distributions, can be obtained. Ultimately, based on the acquired posterior distribution, the probability density function can be updated with newly introduced samples. Using the Hashin failure criterion, the failure probabilities of the fibers and matrix of the composite laminate structure are quantified, respectively. Then, the credible reliability of the composite laminate is obtained. Numerical example results show the proposed method can maintain high accuracy with fewer samples and demonstrate the validity of the model. For the numerical calculations, the deterministic parameters of the distribution function and the functional distribution parameters were verified, composite laminates and aircraft wing structures were analyzed. The experimental results show that the error between the probability density function of the parameters and the probability density function predicted by the sample is less than 0.045. Compared with the traditional reliability analysis methods for composite structures, this method can effectively measure the credible reliability of composite laminate structures with fewer samples and similar accuracy. The method enables real-time updating of the parameter probability density function by newly introduced samples and improves the confidence level.