Probabilistic and Fuzzy Nonlinear Discontinuous Aeroelastic Analysis of In-plane FG Panels in Supersonic Flow with Mechanical and Thermal In-plane Loadings

Abstract

This paper is concerned with the uncertain discontinuous nonlinear aeroelastic behavior of in-plane bi-directional functionally graded (FG) metal nanocomposite panels. The panels are subjected to supersonic flow and in-plane mechanical and thermal loadings. This type of FG structures is manufactured using additive manufacturing technologies which might lead to uncertain properties of the manufactured parts due to manufacturing uncertainties, modeling uncertainties in the mathematical and physical formulations used to predict their properties, or uncertainties in the constituent materials properties themselves. These sources of uncertainties might be known with defined probability density functions or defined with uncertain intervals only (fuzzy). Therefore, the mechanical and thermal properties of the nanocomposite material are modeled as uncertain random variables or random fields with known probability distribution function (pdf) or uncertain fuzzy variables or fields with given intervals. The random fields are modeled using the Karhunen–Loève expansion (KLE), and the uncertain output variables are modeled using the Hermite polynomial chaos expansion method (HPCE). The effects of the material properties uncertainties type (fuzzy vs. probabilistic), the cross-correlation between the thermal and mechanical properties, the random fields properties (correlation length, stationary vs. non-stationary, etc.) on the dynamic stability thresholds and the nonlinear limit cycle oscillation are studied.