## 2 Theoretical Analysis
\begin{array} []{l}2\alpha\ c_{1}\ \cos\left(\frac{\alpha s}{2}\right)\ \sinh\left(\frac{\alpha s}{2}\right)-2\alpha\ c_{1}\ \cosh\left(\frac{\alpha s}{2}\right)\ \sin\left(\frac{\alpha s}{2}\right)+\\ 2\alpha\ c_{2}\ \cos\left(\frac{\alpha s}{2}\right)\ \sinh\left(\frac{\alpha s}{2}\right)+2\alpha\ c_{2}\ \cosh\left(\frac{\alpha s}{2}\right)\ \sin\left(\frac{\alpha s}{2}\right)\end{array} \right] \tag{24}\]  
Establishing the calculation example, taking L = 350 mm, R = 35 mm, and a composite material spring model with [\(-\)45 45]s layup, assuming a single layer thickness of 0.1 mm, the geometric dimensions of the composite material spring are shown in Table 1, and the material parameters are shown in Table 2. Since plain weave and triaxial fabrics are used, all laminates have equal tensile stiffness [21]. Substituting the parameters into Equation (20) yields the curve of the curvature radius-moment variation of the reverse bending process of the spring structure shown in the figure. From Figure 6, it can be seen that as the curvature radius increases, the required bending moment sharply increases to 2249 Nmm, which is called the critical bending moment, reflecting the anti-interference ability of the spring. Then, it sharply decreases and tends to a constant value of 625 Nmm, which is called the steady-state bending moment. By changing the thickness from 0.08 mm to 0.12 mm, as shown in Figure 7, the relationship between the curvature radius and the bending moment of the composite material spring during the bending process can be obtained. The performance of the composite material spring is significantly improved with an increase in thickness. By changing the central angle of the section from 60\({}^{\circ}\) to 90\({}^{\circ}\), as shown in Figure 8, the relationship between the curvature radius and the bending moment of the composite material spring during the bending process with different central angles of the section can be obtained. It can be seen that the performance of the composite material spring linearly improves with an increase in the central angle of the section. Specific values are shown in Tables 3 and 4. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Length L/mm & 350 \\ Radius R/mm & 35 \\ Central angle \(\theta\)/(\({}^{\circ}\)) & 90 \\ \hline \end{tabular}
\end{table} 
Table 1: Geometry parameters of tape spring. Figure 6: Relationship between curvature radius and bending moment during the bending process of composite tape spring. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Elastic modulus E1 & 50 GPa \\ Elastic modulus E2 & 7 GPa \\ Shear modulus G12 & 6.2 GPa \\ Poisson’s ratio u & 0.3 \\ \hline \end{tabular}
\end{table} 
Table 2: Composite spring material parameters (M40 JB). Figure 7: Relationship between curvature radius and bending moment during the bending process of composite springs with different thicknesses. Combining with previous work [20,22], we compared three types of materials and structures of the spring, as shown in Figure 9. It can be seen that compared with the negative Poisson ratio honeycomb structure spring, the composite material spring has a lower critical bending moment and a higher steady-state bending moment. The unit mass mechanical properties of the three types of materials and structures of the spring are shown in Table 5. It can be seen that in the indicator of critical bending moment, the unit mass critical bending moment performance of the composite material spring is close to that of the ordinary spring, far lower than that of the negative Poisson ratio structure spring. In terms of steady-state bending moment indicators, the composite material spring is better than the ordinary spring and the negative Poisson ratio honeycomb structure spring. Specifically, in terms of critical bending moment, the performance of composite tape spring structures, in terms of unit mass, is improved by 0.2% compared to traditional