Keywords: composite structures, uncertainty propagation, global sensitivity, local importance measure, variance based methods.

The problem of uncertainty propagation in reliability-based design optimization (RBDO) of composite laminate structures is studied. First, an approach based on the optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. This corresponds to an inverse reliability problem performed for the mean values of the mechanical properties of composite laminates. Then, using the uniform design method (UDM), a set of design points is generated over a domain centred at mean values of random variables, aimed at studying the space variability. The Tsai number associated with the most probable failure point (MPP), the structural reliability index and the sensitivities indices associated with response functions are obtained for each UDM design point, using the previously calculated maximum load as a reference. Second, using the generated UDM design points as input/output patterns, an artificial neural network (ANN) is developed based on supervised evolutionary learning. Third, using the ANN developed and a Monte Carlo procedure, the uncertainty propagation in structural reliability index is evaluated as a function of ply angle. The objective of the proposed approach is to evaluate the variance of the structural response based on sensitivity indices, identifying the most important sources of uncertainty and to reduce the large number of input parameters involved in uncertainty analysis of laminated composite structures. In particular normalized indices can be established using the conditional expectation as named Sobol first-order sensitivity indices.

A study of the anisotropy influence on uncertainties propagation of composites is carried out based on the proposed methodologies. The study proves that the variability of the structural response as a function of uncertainty of the mean values can be very high. This high variability is also corroborated by the evaluated relative sensitivity measures. These aspects must be considered for robust design since the high structural response variability may induce a drastic reduction in the quality of the optimal design solutions for composite structures. Furthermore, other aspects related to the standard deviation and density probability distribution of the mechanical properties should also be considered in the analysis. Based on the numerical results, the importance of measuring input parameters on structural response are established and discussed as a function of the anisotropy of composite materials. The uncertainty analysis propagation is very useful in designing laminated composite structures minimizing the unavoidable effects of input parameter uncertainties on structural reliability.

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