Large-Deflection Mechanical Modeling and Surrogate Model Optimization Method for Deformation Control of Flexible Pneumatic Structures

Advances in material science and intelligent systems have led to an increasing use of large-deflection flexible structures in the aerospace industry, including flexible-wall wind tunnel nozzles, deformable wings, and variable nozzles for aircraft engines. These structures have attracted significant research interest due to their variable aerodynamic performance, functional diversity, and dynamic response characteristics that distinguish them from rigid structures. Large-deflection flexible aerodynamic structures typically consist of flexible structural surfaces and actuators. Precise deformation control and optimized structural design are crucial for achieving their full performance potential. However, few existing technological tools can effectively guide the implementation of such deformation control and optimized design. In this paper, we first established a mechanical model of a multi-pivot flexible nozzle based on a typical wind tunnel flexible nozzle. We then derived a theoretical model of beam deformation with multi-point dynamic constraints using the principle of variability. Next, we created a deformation solution method based on radial basis point interpolation to evaluate nozzle profile accuracy. Finally, we established a complete surrogate-based optimization process for a large-deflection flexible nozzle and experimentally verified it using a wind tunnel nozzle prototype equipped with laser tracking and flexible sensors. The results show that the nozzle’s profile accuracy remains within ±0.2 mm under specified operational conditions.