## 4 Results and Discussion  
### Topology Optimization and Design Parameters  
Figure 3 illustrates the results of the conventional end plate stress and deformation analysis. As depicted in Figure 3a,b, the maximum stress of the circular end plate was 62.248 MPa, the total deformation was 0.015193 mm, and the weight was 50.766 kg (end plate + current collector + bolt head). The maximum deformation occurred at the outer edge of the end plate due to the stress concentration in \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multicolumn{2}{c}{**Conventional**} & \multirow{2}{*}{**Current Collector**} & \multirow{2}{*}{**Dummy Cell**} \\  & \multicolumn{2}{c}{**End Plate**} & & & \\ \cline{2-2} \cline{5-6}  & **Circular** & **Square** & **Circular** & **Square** & **Circular** & **Square** \\ \hline Diameter (circular) or & & & & & & \\ side length (square) (cm) & 44.28 & 37.84 & 30.28 & 26.84 & 30.28 & 26.84 \\ Area (cm\({}^{2}\)) & 1539.9 & 1431.9 & 720.1 & 720.4 & 720.1 & 720.4 \\ Thickness (mm) & 40 & 40 & 3 & 3 & 5 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dimensions of the simplified PEMWE components. Figure 2: Clamping pressure boundary conditions on (**a**) the circular stack and (**b**) the square stack. the bolt. As depicted in Figure 3c,d, the maximum stress of the square end plate was 239.08 MPa, the total deformation was 0.029516 mm, and the weight was 47.308 kg (end plate + current collector + bolt heads). The maximum deformation occurred at each vertex of the end plate due to the stress concentration in the bolt. From the topology optimization conducted using the Ansys 18.1 bundle, cut regions were suggested in each end plate: the side region between bolt locations (Figure 4a top), the groove of the bottom side (Figure 4a bottom), and the top center region (Figure 4c). For the topology region, whereas Figure 4a,c illustrates which exclusion region was applied only to bolts that were similar to the boundary condition, Figure 4b illustrates which exclusion region was applied to upper and lower sides of the end plate. Both sides remained after the topology optimization; therefore, the side-cut shape differs from that in Figure 4a. Based on the topology optimization depicted in Figure 4, the four parameters were derived as follows: (1) volume removal between the bolts, (2) volume removal at the bottom, (3) round of sector form at the top, and (4) top center cut depth. Figure 4: Topology optimization results of conventional end plate of (**a,b**) circular end plate and (**c**) square end plate. Figure 3: (**a**) Equivalent stress (MPa) and (**b**) total deformation (mm) of the conventional circular end plate; (**c**) equivalent stress (MPa) and (**d**) total deformation (mm) of the conventional square end plate. The designation of the end plates consists of six letters. The order of the removed parameters is as follows: the first letter from the left is the bolt, the second letter is the bottom side, the third and fourth digits are the round radius, and the fifth and sixth digits are the thickness. The first letter is the symbol \"C\" in Figure 4a with a red circle when completely removed, the symbol \"I\" with a red square at the bottom in Figure 4b when partially removed, and the symbol \"N\" when nothing has been removed. The second letter is the symbol \"B\" with a red square at the bottom left of Figure 4a, and the symbol \"N\" is the portion where nothing has been removed. Furthermore, the part where nothing has been removed for the third and fourth digits is indicated by the symbol \"00\", the part where a round R5 has been applied is indicated by the symbol \"05\", and the part where a round R15 has been applied is indicated by the symbol \"15\". The part where nothing has been removed for the fifth and sixth digits was designated \"00\", the portion to be removed to a depth of 10 mm was designated \"10\", and the portion to be removed to a depth of 20 mm was designated \"20\".