Analytical probabilistic modeling of initial failure and reliability of laminated composite structures

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An analytical approach based on the theory of stochastic processes is developed for the stochastic initial failure analysis and reliability predictions of thin-walled laminated composite structures. The probability of initial failure is calculated using theory of rare passages of the random strain vector field out of the prescribed region of allowable states. The region is limited by the ultimate strain surfaces adopted for each individual layer in the laminate. The surfaces, in their turn, are defined in terms of the scatters in the ultimate strains for the composite layer. Reliability function of a composite layer having random elastic characteristics and loaded with random in-plane tractions is determined through the probability of its initial failure. The reliability function of the laminated composite structure is then calculated through the failure probabilities of individual layers, using the weakest link model. The proposed approach allows one to solve diverse stochastic problems and requires substantially less computational expenses than Monte Carlo simulation technique. The approach may be invaluable for a quick evaluation of various competitive design projects when considering laminated composite structures under the reliability constraint. Applications of the developed approach are illustrated on the examples of reliability predictions of laminated composite cylindrical shells under the effect of random internal pressure and laminated composite plates under random biaxial loading. Numerical results reveal specific probabilistic phenomena related to the effects of ply lay-up, scatters in mechanical and strength characteristics and random loading histories. Results obtained from the developed analytical approach are compared to those calculated with Monte Carlo simulation technique.