## 1 Introduction  
In recent times, the tape spring has garnered increasing attention due to its advantageous engineering characteristics. Notably, structures constructed from tape springs possess a multitude of beneficial features, including a low mass, uncomplicated mechanics, high efficiency of enfoldment, and an absence of mechanical joints. Moreover, they are capable of spontaneous deployment without requiring external driving forces [1,2]. While conventional tape springs made from metallic materials such as beryllium-copper or high-strength steel have been utilized in space deployable structures for several decades, the demand for cheaper, simpler, and more reliable deployable structures has brought carbon fiber reinforced plastic (CFRP) tape springs to the fore. Such springs are increasingly gaining prominence owing to their tailorable performance, low mass, and low coefficient of thermal expansion [3]. Short leaf springs are used for automatic locking in the deployed state, as shown in Figure 1, such as the locking mechanism of solar sails. Long tape springs are used to deploy space antennas, as shown in Figure 2. The tape spring driving mode belongs to a passive driving mode. The tape spring components are arranged according to the design requirements at the mechanism members' or rods' nodes or midpoints. When folded, the spring stores elastic potential energy due to pre-stress. After the mechanism is unlocked, the spring releases the energy, and the mechanism is deployed. Tape spring structures include single tape springs, two tape springs, and more tape springs [4]. [PERSON] [7; 8; 9] studied the folding and unfolding performance of single-tape springs and double-tape springs, analyzed their unfolding behavior, and derived the relationship between the curvature radius and the driving moment during the bending process. [PERSON] [10] provided a photography method to study the post-buckling curvature at the folding position, including two-dimensional (2D) and three-dimensional (3D) analyses. The results revealed the strain distribution at the folding position of the tape hinge, which generates an opening moment related to the curvature, making the modeling of unfolding using these hinges more accurate. [PERSON] [11] studied the influence of different geometric parameters on the mechanical properties of tape springs, especially on their driving and anti-interference capabilities during the bending process. This provides reference values to improve the kinematic accuracy and reliability of deployable structures. [PERSON] et al. [12] studied the shape memory polymer composites (SMPC) reinforced by carbon fiber fabric and thermosetting styrene-based matrix. They demonstrated the feasibility of using SMPC hinges as deployable structures. The main advantage of shape memory polymers (SMP) is their high recovery rate, low density, and low cost. [PERSON] et al. [13] verified experimentally the response of a thin-wall flexible structure represented by tape spring under static and vibrational loads and compared the material parameters of single-curved and double-curved surface designs. [PERSON] [14] studied the folding and unfolding behavior of single-layer and double-layer tape spring hinges by analyzing numerical and experimental methods. They also explored the establishment of a surrogate model for a multi-layer tape spring (MLTS) hinge using response surface methodology (RSM) and the solution of multi-objective optimization design problems using a modified non-dominated sorting genetic algorithm (NSGA-II). [PERSON] et al. [15] embedded strain gauged in the bistable composite tape springs and obtained the change of strain during the bending and folding process of the bistable composite tape springs. [PERSON] [16] investigated the energy storage performance of bistable composite tape  
Figure 1: Applications of tape spring structures [5]. Figure 2: Applications of composite tape spring structures [6].