Probabilistic failure analysis of quasi-isotropic CFRP structures utilizing the stochastic finite element and the Karhunen–Loève expansion methods

Abstract

The accuracy of structural analysis in composite structures depends on the proper estimation of the uncertainties mainly related to the mechanical properties of the constituent materials. On this basis, a sophisticated numerical tool is proposed, able to perform stochastic finite element analysis on composite structures with material uncertainties by distributing stochastic mechanical properties along the domain of a composite structure. The output of the analysis is a probability density function for the deformation, strain, stress and failure fields. The proposed tool exploits the Karhunen–Loève expansion and the Latin Hypercube Sampling methods for the stochastic distribution of the mechanical properties, the well-established First-Order Shear Deformation theory in conjunction with a random variable approach for the calculation of stochastic stiffness matrices, and the Puck’s failure criterion for the conduction of probabilistic analysis of different failure modes in composite structures. A quasi-static tensile testing campaign was conducted with quasi-isotropic coupons in order to assess the fidelity of the method and the efficiency of the stochastic distribution algorithm is compared with the full field data acquired by the digital image correlation approach. The current paper provides a thorough presentation of the development of the proposed stochastic finite element method and validation results which ensure the efficiency of the proposed stochastic numerical tool. • The Karhunen–Loève expansion is utilized for efficient random distribution of mechanical properties. • The Latin Hypercube Sampling is utilized for randomness generation and it outperforms the Monte Carlo Simulation. • Stochastic finite elements are developed for probabilistic failure analysis using Puck’s failure criterion. • Digital image correlation data are obtained from tensile experiments to assess the inherent randomness of composites.