Limit analysis of the statistics of quasi-steady non-linear aerodynamic forces for small turbulence intensities

This paper focuses on the estimation of statistical characteristics of a specific quasi-steady wind loading used in buffeting analyses. In this loading, the intrinsic non-linearity of aerodynamic coefficients is considered and approached by a polynomial expression of any a priori chosen degree. As rigorous developments of the statistical moments would result in impractical formulations, we suggest to consider the smallness of the turbulence intensities to construct, by means of a limit analysis, approximate expressions of the raw moments of aerodynamic forces. From these expressions, approximate cumulants and associated dimensionless characteristics, such as skewness and excess coefficients, are derived. The accuracy of the proposed analytical relations is assessed by comparison with Monte Carlo simulations, and the relevance of the sophisticated non-linear loading under consideration is compared to more traditional models.