Analysis of Parametric and Non-Parametric Uncertainties in the Dynamics of Composite thin Walled Curved Beams

Abstract

This article is devoted to the dynamic analysis of slender initially curved structures constructed with fiber reinforced composite materials. There are many ways to manufacture a composite material for uses in structural constructions, for example filament winding and resin transfer molding, among others. Depending on the manufacturing process composite materials may have deviations with respect to the calculated response (or deterministic response). These manufacturing aspects lead to uncertainty in the structural response associated with constituent proportions or geometric parameters among others. Another focus of uncertainty can be the mathematical model that represents the mechanics of the slender structure. In many structural models, the type of hypotheses invoked reflect the most relevant aspects of the physics of a structure, however in some circumstances these hypotheses are not enough, and cannot represent properly the mechanics of the structure. Uncertainties should be considered in a structural system in order to improve the predictability of a given modeling scheme. There are two strategies to face the uncertainties in the dynamics of structures: The parametric probabilistic approach and the non-parametric probabilistic approach. The first is related to quantify the uncertainty of given parameters such as variation of the angles of fiber reinforcement, material constituents, etc. The second is related to the uncertainty of the model which implies to consider uncertain the matrices of the whole system. In this study a shear deformable model of composite curved thin walled beams is employed as the mean model. The probabilistic model is constructed by adopting random variables for the uncertain entities (parameters or matrices) of the model. The probability density functions of the random variables are derived appealing to the Maximum Entropy Principle under given constraints. Once the probabilistic model is discretized in the context of the finite element method, the Monte Carlo method is employed to perform the simulations. Then the statistics of the simulations is evaluated and the parametric and nonparametric approaches are compared. Finally recommendations are outlined in the conclusion section.