Modeling and analysis of composite laminates in the presence of uncertainties

The basic or primitive parameters of composite laminates, such as the constituent materials properties, the thickness of each ply, the ply orientations and the applied loads, exhibit variabilities, hence, the response of the laminated composites also exhibits some degree of variability. Thus, the accuracy and reliability of the laminates cannot be assured if the variabilities present in the basic parameters are ignored. In the past decades, the probabilistic approach has been used widely to simulate the uncertainties in the macromechanics of composite laminates. However, the exact probability distributions of the primitive parameters are not known in most of the applications. This work, for the first time, models the uncertainties in the macromechanics of composite laminates using the interval analysis and the universal grey system theory by representing the primitive parameters as intervals. Also, for comparison, a probabilistic approach is presented with plus/minus three standard deviations about the mean of the response. Due to the so-called dependency problem, the interval analysis predicts wider and inaccurate ranges. Thus, a truncation-based interval analysis procedure with a suitable truncation parameter is used to overcome the limitation associated with the original interval analysis. Specifically, in this work, the uncertainties in the in-plane and flexural engineering constants and laminae stresses are studied. The environmental effects on the laminae stresses are also investigated. Numerical examples are presented to demonstrate the application of the three interval-based uncertainty methods for the behavior of composite laminates by considering different stacking sequences of graphite/epoxy and glass/epoxy laminates.