Deterministic and peridynamic operator-based uncertain nonlinear aeroelastic analyses of in-plane functionally graded panels with elastic boundary supports and yawed supersonic flow

The work in this paper aims to study the off-design performance of in-plane functionally graded (FG) nanocomposite panels subjected to supersonic flow and thermal in-plane loading. The off-design conditions are represented by elastic edge supports (each elastic edge is supported by sets of out-of-plane and in-plane springs) and yawed supersonic flow. The study presents a novel parametric analysis to analyze the effects of the elastic edges’ flexibility levels and their direction relative to the flow angle on the instability thresholds with the existence of thermal loading. It also presents a new study on the effects of different elastic boundary conditions on the nonlinear limit cycle oscillation amplitude which have not been addressed before. It also proposes a novel uncertainty analysis scheme using the peridynamic operator as a metamodel for highly nonlinear discontinuous functions to study the effects of the uncertain elastic edge supports on the uncertainty of the limit cycle oscillation amplitude. The Kirchhoff–Love plate theory with the nonlinear von Kármán strains is used for the structural modeling, and the first-order piston theory is used for the aerodynamic modeling. The finite element method is used for numerical analysis. Comparisons between the performance of the homogenous panels and the performance of the in-plane functionally graded panels due to these off-design conditions are also presented to assess the effects of the in-plane material inhomogeneity. The results show slight variations in the behavior of the FG panels and the homogenous panels. The flow yaw angle can have a significant effect on the flutter speed and the LCO amplitude depending on the panel’s aspect ratio and the degree of the edge’s flexibility. The trailing elastic edges have the dominant effect on the aeroelastic behavior compared to the leading edges. The in-plane edges flexibility has less effect on the nature of the post-flutter response compared to the out-of-plane edges flexibility. The proposed peridynamic operator scheme seems to be an efficient tool for the uncertainty analysis of nonlinear discontinuous aeroelastic systems.