# On the Design of Bionic Hierarchical H-Type Whip Restraints for Nuclear Power Plants
## 4 Parametric Analysis
### Effect of Bionic Hierarchical Cross-Section Characteristics  
In Section 2.1, the cross-section characteristics of different NBHMCs were delineated. For NBISHMC, its cross-section characteristics are divided into two aspects: the number of inner tube triangles **m** and the spiral tube triangle height **TH**. Based on the three spirals bionic structure (**S** = 3), nine cross-sectional configurations are obtained by adjusting the count of inner tube triangles and the spiral tube triangle height, as shown in Figure 22.  
The force-displacement curve and energy absorption of NBISHMCs with different cross-section characteristics are shown in Figures 23 and 24. The plots show that as the \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Structure** & **t (mm)** & **m (kg)** & **EA (kJ)** & **IFF (kN)** & **SEA (kJ/kg)** & **MCF (kN)** & **CFE (\%)** \\ \hline \multirow{4}{*}{2 spirals} & 0.5 & 5.8 & 71.447 & 301.920 & 12.318 & 158.780 & 52.590 \\  & 1 & 11.6 & 197.527 & 607.717 & 17.028 & 438.950 & 72.241 \\  & 1.5 & 17.4 & 368.876 & 922.221 & 21.200 & 819.770 & 88.891 \\  & 2 & 23.2 & 602.028 & 1343.330 & 25.950 & 1337.844 & 99.592 \\ \hline \multirow{4}{*}{3 spirals} & 0.5 & 7.25 & 94.9 & 378.006 & 13.09 & 210.847 & 55.779 \\  & 1 & 14.5 & 264.6 & 761.48 & 18.248 & 587.972 & 77.216 \\  & 1.5 & 21.8 & 490.33 & 1230.28 & 22.492 & 1089.774 & 88.579 \\  & 2 & 29 & 797.626 & 1801.18 & 27.504 & 1772.55 & 98.411 \\ \hline \multirow{4}{*}{4 spirals} & 0.5 & 8.7 & 118.652 & 452.825 & 13.622 & 263.664 & 58.226 \\  & 1 & 17.4 & 326.364 & 910.792 & 18.757 & 725.248 & 79.633 \\  & 1.5 & 26.1 & 598.321 & 1498.25 & 22.924 & 1329.588 & 88.743 \\  & 2 & 34.8 & 978.366 & 2200.59 & 28.114 & 2174.162 & 98.799 \\ \hline \multirow{4}{*}{5 spirals} & 0.5 & 10.1 & 140.37 & 518.512 & 13.898 & 311.899 & 60.153 \\  & 1 & 20.2 & 389.242 & 1060.26 & 19.269 & 865.076 & 81.834 \\  & 1.5 & 30.3 & 709.627 & 1774.77 & 23.42 & 1578.144 & 88.921 \\  & 2 & 40.5 & 1200.732 & 2606.7 & 29.648 & 2594.02 & 99.514 \\ \hline \end{tabular}
\end{table} 
Table 4: Crashworthiness characteristics for each hierarchical level of different wall thickness. Figure 22: Basic cross-section configurations of NBISHMC: The cross-section characteristics are divided into the number of inner tube triangles **m** and the spiral tube triangle height **TH**. height of the spiral tube triangle increases, the plateau force increases significantly, leading to an enhanced energy absorption capacity. Maintaining a constant value for m, the energy absorption capacity of the structure decreases as the spiral tube triangle height increases. This phenomenon arises from the increase in **m** and the decrease in **TH**, which lead to the generation of more deformation folds, thereby enhancing the energy absorption capacity. Figure 23: Force–displacement curves of NBISHMCs with different cross-section characteristics: (a) m = 8, (b) m = 16, (c) m = 24. Figure 24: EA–displacement curves of NBISHMCs with different cross-section characteristics: (a) m = 8, (b) m = 16, (c) m = 24. The detailed crashworthiness parameters of NBISHMC are summarized in Figure 25 and Table 5. From Figure 25, when the **TH** remains constant, a large **m** can cause an increase in the crashworthiness parameters, such as SEA and IPF. Conversely, with **m** held constant, an increase in **TH** results in a reduction in the crashworthiness parameters. However, it is noteworthy that when the **m** value attains a value of 24, the rise in **TH** significantly alters IPF, causing a subsequent increase in CFE. Therefore, considering the need to enhance energy absorption and decrease the initial peak crushing force, it is advisable to select a moderate value for **m** and **TH** to achieve a balance. crashworthiness of the bionic thin-walled tubes under axial impact and oblique impact. The conclusions are as follows:  
* Compared with hollow tubes and NBDHMCs, several NBDHMCs have shorter wavelengths and more folds under pressure, and exhibit better energy absorption capacity.