# Design and Shear Analysis of an Angled Morphing Wing Skin Module
## 4 Results  
### Comparison of Standard and Angled Skin Modules  
To understand the deformation mechanism in more detail, numerical models were established, as outlined in this section. The effectiveness of the initial angle is presented here by comparing the standard model \(\theta_{0}\) = 90\({}^{\circ}\) as proposed in reference [31] and the angled one \(\theta_{0}\) = 50\({}^{\circ}\). The numerical deformation processes of the two models are shown in Figure 8a. Moreover, the maximal and minimal principal stresses, \(\sigma_{1}\) and \(\sigma_{2}\), at the intersection point are extracted from the numerical and theoretical models and drawn against the morphing angled \(\theta\) in Figures 8b and 8c, respectively. The deformation of model \(\theta_{0}\) = 90\({}^{\circ}\) is first analyzed to explore the deformation mechanism. Since the deformation below 90\({}^{\circ}\) is the mirror image of that above 90\({}^{\circ}\), only the branch above 90\({}^{\circ}\) is considered. As the morphing angle \(\theta\) increases, the compressive stress appears immediately in the skin but no wrinkle shows. This can be attributed to the existence of CFRP rods and KFRP fibers that increase the bending stiffness of the skin and therefore improve stability [31]. When \(\theta\) reaches 120.8\({}^{\circ}\), wrinkles begin to appear, and the magnitude further increases at \(\theta\) = 122\({}^{\circ}\), consistent with the experimental observation that the model showed no wrinkle at 120\({}^{\circ}\) but wrinkled at 122\({}^{\circ}\), as shown in Figure 4a. Moreover, when wrinkles occur at 122\({}^{\circ}\), it is calculated from the  
Figure 7: Deformation mode of the skin. total strain energy of the CFRP rods is 36.14 mJ, whereas that of the KFRP fibers is 6.83 mJ, implying that CFRP rods play a more important role in delaying wrinkles. Comparing the numerical and theoretical values of \(\sigma_{1}\) and \(\sigma_{2}\) in Figure 8b,c, it can be found that when the skin has a smooth surface, the numerical and theoretical principal stresses match very well. When wrinkles occur, however, the numerical stresses deviate from the theoretical ones. This is because the theoretical values are calculated on the condition that the skin does not buckle, and becomes invalid when it wrinkles. Subsequently, model \(\theta_{0}=50^{\circ}\) is studied as a comparison. First, consider the branch of increasing \(\theta\) from \(50^{\circ}\). The deformation process can be divided into three ranges. First, in the range of \(50^{\circ}\leq\theta\leq 92^{\circ}\), both \(\sigma_{1}\) and \(\sigma_{2}\) are positive, which indicates that wrinkles will not occur regardless of the presence of reinforcement. This is a significant difference from model \(\theta_{0}=90^{\circ}\), in which compressive stress exists from the beginning of deformation. Second,  
Figure 8: (a) Deformation process; (b) maximal principal stress versus morphing angle curves; (c) minimal principal stress versus morphing angle curves. when \(\theta\) is between 92\({}^{\circ}\) and 133.4\({}^{\circ}\), \(\sigma_{2}\) becomes negative and the magnitude gradually increases, but the skin remains smooth, consistent with the experiment result in which specimen M50 was smooth at 130\({}^{\circ}\) but wrinkled at 132\({}^{\circ}\), as shown in Figure 4b. At this range, it is mainly the CFRP rods and KFRP fibers that limit the occurrence of wrinkling, and the deformation mechanism is the same as that in model \(\theta_{0}\) = 90\({}^{\circ}\). In addition, model \(\theta_{0}\) = 50\({}^{\circ}\) exhibits a smaller magnitude of compressive stress \(\sigma_{2}\) and a larger magnitude of tensile stress \(\sigma_{1}\) than those of model \(\theta_{0}\) = 90\({}^{\circ}\) throughout this range due to the different initial angle. Previous studies [35] have found that for a plate loaded with a compressive load in one direction, applying a tensile load in the orthogonal direction will increase the critical buckling load and improve the stability of the plate.