Three-Dimensional Deformation Calculation of Wind Tunnel Flexible Wall Using Orthogonal Beam Function

Transonic/supersonic wind tunnels are indispensable equipment for advanced aircraft to operate across subsonic, transonic, and supersonic regimes. The deformation of the flexible nozzle is the key to accurately controlling the Mach number of transonic wind tunnels. However, solving the deformation of flexible wall plates remains challenging due to the highly nonlinear relationship between wall loading and deformation, as well as the lack of simple yet effective mathematical models under complex boundary conditions. To accurately describe the deformation of flexible wall plates and improve computational efficiency, this study systematically investigates the deformation characteristics of flexible walls in two orthogonal directions and proposes an orthogonal beam function (OBF) model for characterizing small-deflection deformations. For large-deflection deformations in a flexible wall, an elliptic integral (EI) solution is introduced, and the OBF model is correspondingly modified. Experimental validation confirms that the OBF model effectively describes large-deflection deformations in a flexible wall. This research contributes to solving large-deflection deformation in flexible wall plates, enhancing both computational efficiency and accuracy.