Uncertainty quantification of natural frequencies of flax/epoxy composite laminates based on a polynomial chaos expansion method

Non-homogeneous mixture and unintentional flaws during the production stage have always given rise to uncertainties in the structural response of composite materials. This is intensified in the composites reinforced with natural fibers due to the natural origin of the fibers. In this study, an uncertainty analysis of the frequency response of a unidirectional flax/epoxy composite, as one of the common natural fiber composites, were carried out. The variability of the fiber elastic properties, fiber density, fiber volume fraction, and the misalignment of ply orientations were considered as the uncertainty sources. The uncertain input variables were divided into normal and uniform variables through the Anderson-Darling test, based on the various experimental data acquired from the literature. Due to the high number of uncertain input variables, a computationally efficient response surface approach based on the polynomial chaos expansion was adopted and modified accordingly to take the multi-type stochasticity of the input parameters into account. Moreover, the uncertainty analysis results obtained from the response surface method were validated by the direct Monte Carlo simulation, and the accuracy and efficiency of the surrogate model were demonstrated.