A data driven polynomial chaos based approach for stochastic analysis of CFRP laminated composite plates

Abstract

A polynomial chaos (PC) based stochastic finite element methodology is developed for uncertainty quantification and failure probability estimation in CFRP laminated composite plates. The methodology is based on modelling the spatial inhomogeneities in the material properties as 2D non-Gaussian random fields and representing them as PC expansions. Constructing the PC representation requires knowledge of the marginal probability density function (mpdf) and the autocorrelation function. In reality, only measurements at discrete points are available from experiments. Treating this data as a finite dimensional approximation of the random fields, corresponding PC representations are developed using a sequence of Rosenblatt’s transformations that lead to matching target mpdfs and target correlation defined through the Spearman’s rank correlation coefficient, both of which are estimated from the observed measurements. Subsequently, a stochastic finite element framework is developed that enable quantification of the uncertainty propagation in the developed local stresses. The proposed methodology enables representing the structure matrices as functions of vector random variables which can be easily simulated using Monte Carlo simulations. Estimates of the failure probability are obtained from a relative frequency definition applied to the Tsai–Hill criterion. Discussions on the salient features of the proposed methodology are highlighted using numerical examples.