Structural Uncertainty Effect on Classical Wing Flutter Characteristics

Flutter-critical velocity is usually estimated from deterministic analyses by assuming that physical and geometrical parameters are perfectly known. However, aleatory and epistemic uncertainties, especially those associated with the definition of material properties, are intrinsically present partly because of the random nature of every physical system and partly because those properties are evaluated from a finite number of observations. The paper focuses on the combination of structural reliability analysis with aeroelastic simulation to give a correct flutter speed evaluation for design purposes. Two typical aeronautical test cases have been considered: (1) an isotropic material structure and (2) a composite material structure. Different computational methodologies (classical and developed by authors) have been coupled with a simple two-dimensional aeroelastic model to study the qualitative consequences of uncertainty in determination of critical flutter speed and to provide a comparison between different reliability methods such as Monte Carlo (MC) simulation, first-order reliability method (FORM), second-order reliability method (SORM), and response surface by fixed or adaptive order regressor coupled with FORM and MC. For the isotropic case best prediction of MC results is always obtained with high-order response surface (HORS) (coupled with both MC and FORM) above all for low levels of coefficient of variation (C.V.) (10% or under) for which results are basically equivalent. FORM and SORM give acceptable results only above cumulative distribution function values of 35-40%. Only response surface with a fixed polynomial order always gives totally misrepresentative results even for very low variability of basic physical quantities. For the composite case, no generic conclusion can be made about the influence of physical quantities on uncertainty propagation because it strongly depends on layup configuration. From a design point of view, variability in composite materials is even more important because, in a general sense, more variables are involved. The flutter speed reductions reveal greater slope of the linear regressors with respect to the isotropic counterpart, with stronger differences when the uncertainty afflicting the basic random variables is higher.