## 2 Design of Experiment (DOE)
### Implementation of Flexible Skin  
The SMTE flap is composed of two main components: (1) the middle flap section, which undergoes downward bending deformations; and (2) the transition sections on the right and left sides, which adapt to the deformation of the middle flap. The transition sections experience twist deformation due to their attachment to both rigid wing structure and the SMTE flap. Consequently, these sections require enhanced flexibility of the skin material. To accommodate complex deformation patterns, a flexible skin material with suitable mechanical properties was selected to allow elasticity for tension in the upper skin and compression in the lower skin. In previous work [37], two materials were tested for the skin: (1) Thermoplastic Polyurethane (TPU), an elastic polymer widely used in 3D printing; and (2) silicone rubber. A preliminary skin analysis was conducted in ANSYS 2021 R2 software to evaluate the suitability of these materials (see [37] for more details). The TPU exhibited yielding under tension in long runs, likely due to stress relaxation. This behavior was attributed to the release of residual stresses induced during manufacturing when subjected to a constant constraint over time, even within the elastic limit. In contrast, in terms of stretchability and elongation, silicone rubber was an extremely soft and flexible material. Its extended fatigue resistance made it a very good option for morphing wings, as repeated deformations during flight require a material with a very strong fatigue resistance. As a result, it retained its flexibility through repeated morphing without a noticeable material deterioration. Therefore, it demonstrated an excellent performance in supporting the morphing capabilities of the transition sections. Based on these findings, the TPU was replaced with silicone rubber for the skin material. Table 4 summarizes the material properties of silicone rubber. Figure 11: Cross-section view of the control system in the wing box with GT2 pulley. Figure 10: The correlation between the pulse width and the position of the servo motor. However, even with silicone rubber, the buckling contraction on the wing lower surface remained unchanged, and the creation of waves on the lower skin was observed. This buckling of the skin was due to its low stiffness and high slenderness ratio. In the structural analysis, for a longitudinal compression of a column, slenderness is defined as the ratio between the section and the length of the column. The higher this ratio is, the more the structure tends to buckle. The slender ratio is given by the following:  
\[\lambda=\frac{l}{\sqrt{I/A}} \tag{1}\]  
where \(l\) is the effective length, \(l\) denotes the second moment of inertia and \(A\) is the section of the column. To address the buckling issue on the wing lower surface, a solution was obtained without altering the skin material. Since buckling occurs only under compression, the solution was to maintain tension within the working range of the skin. To ensure uniform tension across the entire skin and to maintain consistent tension across all skin panels, a screw-driven pre-tensioning device was designed and 3D printed. This device securely grasps both sides of the skin panel and, by turning two long screws, the distance between the jaws increases, thereby applying uniform tension along the panel. The applied tension can then be accurately measured using a caliper. Figure 12 illustrates the pre-tensioning device. As shown in Figure 12, the skin was first laid down using the pre-tensioning device. It was clamped between the two jaws and then tensioned by tightening the long screws. An elongation of 40% was applied, which corresponded to 32 mm for a 75 mm skin panel at rest. After applying the intended tension to the skin, it was secured in its designated position using cyanoacrylate glue, which was precisely applied with surgical syringes equipped with non-sharp needles. Figure 13 shows the procedure for attaching the SMTE skin to the flap.