The importance of flexibility has been widely noticed and concerned in the design and application of space solar arrays. Inspired by origami structures, we introduce an approach to realizing stretchable and bendable solar arrays via horseshoe-shaped substrate design. The structure has the ability to combine rigid solar cells and soft substrates skillfully, which can prevent damage during deformations. The finite deformation theory is adapted to find the analytic model of the horseshoe-shaped structure via simplified beam theory. In order to solve the mechanical model, the shooting method, a numerical method to solve ordinary differential equation (ODE) is employed. Finite element analyses (FEA) are also performed to verify the developed theoretical model. The influences of the geometric parameters on deformations and forces are analyzed to achieve the optimal design of the structures. The stretching tests of horseshoe-shaped samples manufactured by three-dimensional (3D) printing are implemented, whose results shows a good agreement with those from theoretical predictions. The developed models can serve as the guidelines for the design of flexible solar arrays in spacecraft.

Smart deformable structures that integrate designing, sensing, and controlling technology have been widely applied in the fields of aerospace, robotics, and biomedical engineering due to their multi-functional requirements. The deformation reconstruction method essential for security monitoring and shape controlling, especially for the large deflection deformation, remains a challenge on accuracy and efficiency. This paper takes a wind tunnel’s fixed-flexible nozzle (FFN) plate as the research object to develop a highly accurate deformation reconstruction method based on sensing information from flexible strain sensors. The mechanical behaviors of the FFN plate with large deflection deformation, which is modeled as a cantilever beam, are studied to analyze the relationship of the strain and moment. Furthermore, the large deflection factor and shell bending theory are creatively utilized to derive and modify the strain–moment based reconstruction method (SMRM), where the contour of the FFN plate is solved by particular elliptic integrals. As a result, structural simulation based on ABAQUS further demonstrates that the reconstruction error of SMRM is 21.13% less than that of the classic Ko-based reconstruction method (KORM). An FFN prototype accompanied by customized flexible sensors is developed to evaluate the accuracy and efficiency of the SMRM, resulting in a maximum relative error of 3.97% that is acceptable for practical applications in smart deformable structures, not limited to the FFN plate.

This paper examines sensing mechanisms and stability issues of flexible sensors used in morphing wing applications. A key challenge is the lack of theoretical frameworks that accurately predict sensor behavior during complex deformation. Current models struggle to fully capture the relationships between mechanical strain, electrical response, and material properties. We first analyze the microscopic mechanisms and macroscopic sensing characteristics of 2D material-based sensitive films, developing strain-sensitive models based on crack effects and pressure-sensitive models based on slip effects. Through power spectrum analysis, we establish a quantitative model linking microscopic cracks to macroscopic electrical properties. Using this model, we study the factors affecting flexible sensing stability and propose a quantitative description model using dual-layer multi-channel flexible sensors. After simulation validation, our model successfully guides the structural design of flexible sensing films, offering a clear approach to improve flexible sensor stability.

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.

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.

Nozzle facilities, which can generate high Mach number flows, are the core portions of the supersonic wind tunnel. Different from traditional fixed nozzles, a flexible nozzle can deform to designed contours and supply steady core flows in several Mach numbers. Due to the high-quality demands from the thermo-aerodynamic testing, the deformation of the flexible nozzle plate should be carefully designed. This problem is usually converted into the large deformation problem of a cantilever with movable hinge boundary conditions. In this paper, a generalized variational method is established to analyze the deformation behavior of the flexible nozzle. By introducing axial deformation constraint and Lagrange multiplier, an analytical model is derived to predict the deformed morphology of the flexible plate. Finite element analyses (FEA) of a single-jack flexible nozzle model is performed to examine the predicted deformations and reaction forces. Furthermore, the large deformation experiments of an elastic cantilever with a movable hinge connection are carried out to simulate the scenarios in supersonic flexible nozzle facility. Both the FEA and experimental results show high accuracy of current theoretical model in deformation predictions. This method can also serve as a general approach in the design of flexible mechanisms with movable boundaries.