## 4 Results and Discussion
### Parametric Study of Various End Plates  
As depicted in Table 3, NB0000 with the ring-type groove at the bottom of the end plate exhibits small deformation; it also exhibits small stress because of the removal of the concentrated stress region (i.e., the groove). For NN0510, the total deformation was increased by 23.5%, and the weight was decreased by 5.6%, which is a relatively greater weight reduction with a smaller total deformation. For CN0000, the total deformation increased by 14.7%, and the weight decreased by 17.4%, compared with the conventional circular end plate. The total deformation increased as the weight decreased;  
Figure 5: Code names of the parametric designs for the (**a**) circular and (**b**) square end plates.  
plates is much larger than that of the circular end plates by one order of the magnitude. The fillet of the end plates (NF00) does not affect the weight reduction significantly.  
In contrast, NF10, NF20, NN10, and NN20 contribute to weight reduction from the center cut of the upper side of the end plates. For NN10, the total deformation decreased by 4.4%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 39.4%, and the weight decreased by 17.5% compared with the conventional square end plate. The total deformation increased as the weight decreased; CN10 modeling was derived by adding CN00, which had the largest weight reduction among square end plate parameters. The results imply a light square end plate after confirming an increase of 38.5% and a decrease of 23.3% in weight, similar to the results in CN10.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Geometry** & **Equivalent Stress** & **Total Deformation** \\ \hline NF00 & & \\ NF20 & & \\ NN10 & & \\ NN20 & & \\ CN00 & & \\ CN10 & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Equivalent stress distribution and total deformation simulation results of the various geometrical type of square end plates.  
For the circular end plate--as depicted in Figure 6a--when the weight of the circular end plate is reduced, the tendency of the removal portion can be confirmed. The effect of removing the outer edge of the end plate is the largest, and the effect of removing the bottom of the end plate is the smallest. Consequently, when the weight of the circular end plate is reduced, it becomes possible to derive a light end plate design with less deformation by removing it in the order of bottom, round, thickness, and outer edges. The weight reduction and strain data set have a linear relationship because the circular end plate, which is a symmetric rotating body, distributes the stress uniformly to the plate.  
In contrast to the circular end plate, in Figure 6b, the relationship between the strain and the weight reduction of the square end plates illustrates nonlinearity, which indicates the optimized combination of the weight reduction and the shape should be calculated on a case-by-case basis. The effect of removing the outer edge of the square end plate is the largest, and the effect of the removal parameter only applied to the end plate filled is the smallest, as depicted in Figure 6b. Consequently, when the square end plate's weight is reduced, if the fillet, thickness, and outer edge are removed in order, the light end plate design can be derived with less deformation.  
Furthermore, upon comparing the circular and square end plates as presented in Tables 3 and 4, the square end plates had greater stress concentration and deformation than the circular end plates. Moreover, as depicted in Figure 6b, the square end plates can deteriorate cells.  
Figure 6: Weight and strain relationship of various end plate types for (**a**) circular and (**b**) square end plates.