# A Morphing Deployable Mechanism for Re-Entry Capsule Aeroshell
## 5 Morphing Tab Concept
### Parametrization and Results  
On the basis of the model illustrated above, a parametric study was organized. The target was to maximize the deflection of the tip of the tab, meeting the requirements in terms of structural safety discussed in the previous section. In Table 4, the parameters are considered, and their variation range are reported. The width of the plate was kept constant at 40 mm, while a maximum temperature of 500 \({}^{\circ}\)C was considered to guarantee full activation, even crossing the effective limit of complete conversion of the martensite. Despite the generally critical role played by the weight for aerospace applications, this parameter was not considered at this stage of the work. From one side, 16 SMA rods (each with a length of about 90 mm and a diameter no greater than 4 mm) scarcely contributed to the over-all weight (0.11 over 24 kg), and, from the other side, this additional parameter could have led astray the parameterization process with losses in terms of actuation performance. The morphing tab system was conceived to withstand the operational loads without the contribution of the SMA rods. In this sense, attention was paid to the action during the parameterization process due to the pre-stretching of the SMAs on the tab's main structures to prevent from any instability, even in fully deflected conditions. Some considerations drove the selection of the mentioned parameters:  
* The thickness of the plate increases the robustness of the structure but, at the same time, reduces the actuation performance. * The SMA diameter increases its authority and reduces the stress level; however, large diameters may cause the collapse of the structure. * Finally, the shorter the SMA the higher the stretching needed for the connection to the structure, with a, consequently, higher amount of martensite production and, thus, strain recoverability; however, large stretching causes higher stress levels within the SMA and greater transmitted forces, potentially causing the collapse of the flat plate. A total of 125 configurations were simulated by considering 5 different values for each parameter. Only nine configurations met the safety requirements. They are compared in Figure 13 in terms of tip displacement, normalized with respect to the maximum one and its safety margins that are referred to the beam and the SMA material. The case/configuration 18 (red thick line), clearly enveloping all the others, was selected for this preliminary design. Its main features and performance are summarized in Tables 5 and 6, respectively. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Range** \\ \hline Flat plate thickness & 1.8–2.2 mm \\ SMA rod diameter & 1.35–1.65 mm \\ SMA initial length & 81–99 mm \\ \hline \end{tabular}
\end{table} 
Table 4: Parameters and ranges. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Flat plate thickness & 1.8 mm \\ SMA rod diameter & 1.58 mm \\ SMA initial length & 90 mm \\ \hline \end{tabular}
\end{table} 
Table 5: Optimal cases. Then, the evolution of the displacement of the tip and the stress produced in the beam and in the SMA rods were computed and plotted in Figure 14 against the iteration step. The different phases were highlighted using different colors. The simulation started with the stretching of the SMA rods (yellow region); the beam was not affected by this operation, and thus both tip displacement and beam stress were zero. Then, the edges of the SMA rods were linked to the tip and released to enable elastic recovery (green region); no displacement of the tip occurs, owing to the symmetry of the loading, but the stress level rises in the beam and slightly decreases within the SMA rods. At the end of this phase, the upper SMA is heated (red region on the left); after having achieved the activation temperature threshold, the transformation starts, and the tip moves upwards until all the martensite is transformed into austenite (225 \({}^{\circ}\)C).