Comparative Analysis of Circular and Square End Plates for a Highly Pressurized Proton Exchange Membrane Water Electrolysis Stack

End plates are located at both ends of a proton exchange membrane water electrolysis (PEMWE) stack. If the end plates are thin, clamping pressure is not uniform and the performance of PEMWE can deteriorate from leakage and high electrical contact resistance caused by the deformation of the thin end plates. In this study, end plates were designed to reduce the weight while clamping the stack uniformly by finite element analysis (FEA). The weights of the circular and square end plates were reduced compared to conventional end plates by 22.9% and 23.3%, respectively. The stress and strain distribution of square and circular end plates are analyzed using topology optimization. This analysis can improve the performance of the PEMWE by using new end plate designs verified by dummy cell stack simulation to maintain uniform pressure.


Introduction
Air pollution, carbon dioxide emissions, and fine dust problems have attracted attention due to the use of fossil fuels. Proton exchange membrane water electrolysis (PEMWE) can produce hydrogen without emitting pollutants such as carbon dioxide, in contrast to fossil fuels [1]. If electricity is produced by renewable energy technology, hydrogen from water electrolysis can be stored in an environmentally friendly manner [2]. PEMWE consists of an end plate, current collector, bipolar plate (BP), porous transport layer (PTL), and membrane electrode assembly (MEA) [3]. The end plates-ones of the components of the PEMWE-are located at both ends of the stack to maintain a constant pressure for lower electrical resistance and tight gas sealing [4]. Thick end plates are produced to withstand the high pressure, resulting in heavy weight and unnecessary material consumption. In contrast, using thin plates can produce non-uniform clamping pressure, thus deteriorating the performance of PEMWE due to leakage and large electrical contact resistance [5].
Chang et al. [6] examined the effect of clamping pressure on the performance of a proton exchange membrane fuel cell (PEMFC). Clamping pressure can reduce the interfacial resistance between the BP and the gas diffusion layer (GDL). This study focuses on fuel cell performance based on the diffusion path for mass transfer in the GDL, not in the end plates. Furthermore, Wen et al. [7] conducted an experimental study of the clamping effects on the performance of a single PEMFC, and a 10-cell stack was studied with a pressure-sensitive film. The linear relationship of combinations of bolts and clamping torque was investigated experimentally. The pressure distribution in a 10-cell stack was not simulated in detail. A force of 720,000 N, which is equivalent to the pressure of 10 MPa on the current collector area, was loaded on 14 bolts in the circular and square end plate simulations, respectively. A fixed support was applied to the base side of the current collector under the end plate to restrict the degrees of freedom of points, edges, and faces and for the transition. Table 1 lists the properties of the clamping equipment components. In topology optimization, the region to be optimized is controlled by defining the design and exclusion regions. The design region can be optimized, whereas the exclusion region is fixed to avoid deformation by the solver. Therefore, the exclusion region was applied to the bolt and current collector, while the design region was applied to the end plate-which was similar to the boundary condition [19]. Of the topology optimization options, the maximum number of iterations was set up to the default value of 500, which is repeated by as many times as the convergence or setting value. The minimum normalized density was set to the default value of 0.001, and the percent retained at the response constraints was set to 50% or less to set the weight. Furthermore, the convergence accuracy was set to 0.1%, which is the default value.

Pressure Distribution Analysis
The simplified PEMWE stack consists of bolts, nuts, end plates, current collectors, and 21 dummy cells [20], which are simplified by using plain paper gasket plates as dummy cells without any patterns. The dimensions of main stack components are listed in Table 2. Dummy cell simulation is appropriate for depicting strain distribution. A force of 720,000 N, which is equivalent to the pressure of 10 MPa on the current collector area, was loaded on 14 bolts in the circular and square end plate simulations, respectively. A fixed support was applied to the base side of the current collector under the end plate to restrict the degrees of freedom of points, edges, and faces and for the transition. Table 1 lists the properties of the clamping equipment components. In topology optimization, the region to be optimized is controlled by defining the design and exclusion regions. The design region can be optimized, whereas the exclusion region is fixed to avoid deformation by the solver. Therefore, the exclusion region was applied to the bolt and current collector, while the design region was applied to the end plate-which was similar to the boundary condition [19]. Of the topology optimization options, the maximum number of iterations was set up to the default value of 500, which is repeated by as many times as the convergence or setting value. The minimum normalized density was set to the default value of 0.001, and the percent retained at the response constraints was set to 50% or less to set the weight. Furthermore, the convergence accuracy was set to 0.1%, which is the default value.

Pressure Distribution Analysis
The simplified PEMWE stack consists of bolts, nuts, end plates, current collectors, and 21 dummy cells [20], which are simplified by using plain paper gasket plates as dummy cells without any patterns. The dimensions of main stack components are listed in Table 2. Dummy cell simulation is appropriate for depicting strain distribution. The total number of mesh elements in the stack was established at a similar level of approximately 50,000. The force was calculated (to represent the stack boundary condition similar to the actual phenomenon) by applying a value of 51,429 N for the circular end plate and the square end plate to each bolt, respectively, identical to the boundary conditions at topology optimization, which loads 10 MPa on to the BP area uniformly, as depicted in Figure 2.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 14 The total number of mesh elements in the stack was established at a similar level of approximately 50,000. The force was calculated (to represent the stack boundary condition similar to the actual phenomenon) by applying a value of 51,429 N for the circular end plate and the square end plate to each bolt, respectively, identical to the boundary conditions at topology optimization, which loads 10 MPa on to the BP area uniformly, as depicted in Figure 2.

Experimental Methods
Experiments were conducted at 1/4-length scale with conventional and newly designed end plates with paper gasket dummy cells to confirm the tendency of the dummy cell simulation. The geometry and materials of end plates are identical to the modeling parameters.
Torque is calculated by the equation from Al Shakshir et al. [14].
, (1) where Pc is the clamping pressure on the dummy cell area Ac. C is the friction coefficient (0.2 for steel bolts). D and N are the nominal bolt diameter (inch) and the number of bolts, respectively. τ is the applied torque (inch-pounds). The calculated torque from Equation (1) was 34 lb•in for 14 bolts, respectively. The 21-cell stack was used for validation with the pressure sensing film (Fujifilm Prescale LW, Tokyo, Japan) at the end and the middle of the cells. The color scale of LW film ranged from 2.5 (white) to 10 MPa (red) according to the pressure. 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 the bolt. As depicted in Figure 3c,d, the maximum stress of the square end plate was 302.74 MPa, the total deformation was 0.03727 mm, and the weight was 47.308 kg (end plate + current

Experimental Methods
Experiments were conducted at 1/4-length scale with conventional and newly designed end plates with paper gasket dummy cells to confirm the tendency of the dummy cell simulation. The geometry and materials of end plates are identical to the modeling parameters.
Torque is calculated by the equation from Al Shakshir et al. [14].
where P c is the clamping pressure on the dummy cell area A c . C is the friction coefficient (0.2 for steel bolts). D and N are the nominal bolt diameter (inch) and the number of bolts, respectively. τ is the applied torque (inch-pounds). The calculated torque from Equation (1) was 34 lb·in for 14 bolts, respectively. The 21-cell stack was used for validation with the pressure sensing film (Fujifilm Prescale LW, Tokyo, Japan) at the end and the middle of the cells. The color scale of LW film ranged from 2.5 (white) to 10 MPa (red) according to the pressure. 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 Appl. Sci. 2020, 10, 6315 5 of 14 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.

Topology Optimization and Design Parameters
Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 14 collector + bolt heads). The maximum deformation occurred at each vertex of the end plate due to the stress concentration in the bolt.  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.
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  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.   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.
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 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. 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".
Based on the topology optimization of the square end plate depicted in Figure 4c, three parameters were derived: (1) volume removal between the bolts, (2) fillet formation, and (3) thickness reduction of the top region. Before proceeding with the parametric stress and strain analysis derived from the topology optimization of the square end plate, seven types were designed like the circular end plate, as illustrated in Figure 5b. The designed square end plate consists of four letters in total, in the order of removed parameters: the first letter from the left is the bolt, the second letter is the fillet, and the third and fourth digits are the thickness. The first letter is depicted in Figure 4c as a red circle, where the symbol "C" was completely removed, and the part where nothing was removed is indicated by the symbol "N". The second digit is indicated by the symbol "F" in the part where the symbol fillet is formed and the symbol "N" in the part where nothing is removed. Finally, the third and fourth digits are marked with the symbol "00" where nothing was removed, "10" where the part to be removed is 10 mm deep, and "20" where the part to be removed is 20 mm deep.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 14 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." Based on the topology optimization of the square end plate depicted in Figure 4b, three parameters were derived: (1) volume removal between the bolts, (2) fillet formation, and (3) thickness reduction of the top region. Before proceeding with the parametric stress and strain analysis derived from the topology optimization of the square end plate, seven types were designed like the circular end plate, as illustrated in Figure 5b. The designed square end plate consists of four letters in total, in the order of removed parameters: the first letter from the left is the bolt, the second letter is the fillet, and the third and fourth digits are the thickness. The first letter is depicted in Figure 4b as a red circle, where the symbol "C" was completely removed, and the part where nothing was removed is indicated by the symbol "N". The second digit is indicated by the symbol "F" in the part where the symbol fillet is formed and the symbol "N" in the part where nothing is removed. Finally, the third and fourth digits are marked with the symbol "00" where nothing was removed, "10" where the part to be removed is 10 mm deep, and "20" where the part to be removed is 20 mm deep.

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; CN0510 modeling was derived by adding CN0000, which had the lowest total deformation of the circular end plate parameters. For CN0510, the results imply a light circular end plate after confirming a 40.5% increase in total deformation and a 22.9% decrease in weight compared with the conventional circular end plate.

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; CN0510 modeling was derived by adding CN0000, which had the lowest total deformation of the circular end plate parameters. For CN0510, the results imply a light circular end plate after confirming a 40.5% increase in total deformation and a 22.9% decrease in weight compared with the conventional circular end plate.                         Table 3. Equivalent stress distribution and total deformation simulation results based on circular end plate geometry.

CN0510
As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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. As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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. Table 4. Equivalent stress distribution and total deformation simulation results of the various geometrical type of square end plates.

Geometry
Equivalent Stress Total Deformation 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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. Table 4. Equivalent stress distribution and total deformation simulation results of the various geometrical type of square end plates.

Geometry
Equivalent Stress Total Deformation 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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. Table 4. Equivalent stress distribution and total deformation simulation results of the various geometrical type of square end plates.

Geometry
Equivalent Stress Total Deformation 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 NF20 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 NN20 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 As depicted in Table 4, the stress and strain behaviors were confirmed by modeling the square end plate. The maximum deformation was observed at the outer edge of the end plate due to the stress concentration in the bolt, similar to the conventional square end plate. The stress of the square end 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 1.3%, and the weight decreased by 5.8%. For CN00, the total deformation increased by 24.3%, and the weight decreased by 14.3% 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 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.
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.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 14 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. 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 fillet 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. 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 fillet 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. Table 5 illustrates the strains of the end and middle cells of the 21-cell stacks to which the conventional circular end plate and CN0510 end plate, which was optimized by the parametric study, were applied. The strain ranges are similar at the end and the middle cells of the stacks, respectively, between the conventional and CN0510 end plates. The wavy shape inside on the end cell occurred because the upper cut of the sector formed, which disappeared on the middle cell with CN0510 end plates. The outside of the cell was bent and appeared severely deformed with more than 0.001 of strain. Experimental results of pressure sensing films for circular end plate dummy cells have similar distribution of pressure. Both end plates pressed inside (pink) of the dummy cells lighter than outside (strong red). Table 5. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the circular end plates of the dummy-cell stack.

Equivalent Strain from Simulations Measured Pressure Distribution
End cell (Conv.) 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. Table 5 illustrates the strains of the end and middle cells of the 21-cell stacks to which the conventional circular end plate and CN0510 end plate, which was optimized by the parametric study, were applied. The strain ranges are similar at the end and the middle cells of the stacks, respectively, between the conventional and CN0510 end plates. The wavy shape inside on the end cell occurred because the upper cut of the sector formed, which disappeared on the middle cell with CN0510 end plates. The outside of the cell was bent and appeared severely deformed with more than 0.001 of strain. Experimental results of pressure sensing films for circular end plate dummy cells have similar distribution of pressure. Both end plates pressed inside (pink) of the dummy cells lighter than outside (strong red). Table 5. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the circular end plates of the dummy-cell stack.

Equivalent strain from simulations
Measured pressure distribution Furthermore, after comparing the cells located in the middle of the stacks to which the conventional circular end plate had been applied and those to which the CN0510 end plate had been applied, the strain was smaller, and the color was more uniform than for the end cells. The clamping pressure was uniformly applied to the end plates; thus, the CN0510 end plate and uniform clamping pressure were equivalent to that of a conventional circular end plate.
The strain of the end and the middle cells of the stacks in which the conventional square end plate and those in which the CN10 end plate, which was selected from the parametric study, were 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. Table 5 illustrates the strains of the end and middle cells of the 21-cell stacks to which the conventional circular end plate and CN0510 end plate, which was optimized by the parametric study, were applied. The strain ranges are similar at the end and the middle cells of the stacks, respectively, between the conventional and CN0510 end plates. The wavy shape inside on the end cell occurred because the upper cut of the sector formed, which disappeared on the middle cell with CN0510 end plates. The outside of the cell was bent and appeared severely deformed with more than 0.001 of strain. Experimental results of pressure sensing films for circular end plate dummy cells have similar distribution of pressure. Both end plates pressed inside (pink) of the dummy cells lighter than outside (strong red). Table 5. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the circular end plates of the dummy-cell stack.

Equivalent strain from simulations
Measured pressure distribution Furthermore, after comparing the cells located in the middle of the stacks to which the conventional circular end plate had been applied and those to which the CN0510 end plate had been applied, the strain was smaller, and the color was more uniform than for the end cells. The clamping pressure was uniformly applied to the end plates; thus, the CN0510 end plate and uniform clamping pressure were equivalent to that of a conventional circular end plate.
The strain of the end and the middle cells of the stacks in which the conventional square end plate and those in which the CN10 end plate, which was selected from the parametric study, were 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. Table 5 illustrates the strains of the end and middle cells of the 21-cell stacks to which the conventional circular end plate and CN0510 end plate, which was optimized by the parametric study, were applied. The strain ranges are similar at the end and the middle cells of the stacks, respectively, between the conventional and CN0510 end plates. The wavy shape inside on the end cell occurred because the upper cut of the sector formed, which disappeared on the middle cell with CN0510 end plates. The outside of the cell was bent and appeared severely deformed with more than 0.001 of strain. Experimental results of pressure sensing films for circular end plate dummy cells have similar distribution of pressure. Both end plates pressed inside (pink) of the dummy cells lighter than outside (strong red). Table 5. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the circular end plates of the dummy-cell stack.

Equivalent strain from simulations
Measured pressure distribution Furthermore, after comparing the cells located in the middle of the stacks to which the conventional circular end plate had been applied and those to which the CN0510 end plate had been applied, the strain was smaller, and the color was more uniform than for the end cells. The clamping pressure was uniformly applied to the end plates; thus, the CN0510 end plate and uniform clamping pressure were equivalent to that of a conventional circular end plate.
The strain of the end and the middle cells of the stacks in which the conventional square end plate and those in which the CN10 end plate, which was selected from the parametric study, were Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 14 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. Table 5 illustrates the strains of the end and middle cells of the 21-cell stacks to which the conventional circular end plate and CN0510 end plate, which was optimized by the parametric study, were applied. The strain ranges are similar at the end and the middle cells of the stacks, respectively, between the conventional and CN0510 end plates. The wavy shape inside on the end cell occurred because the upper cut of the sector formed, which disappeared on the middle cell with CN0510 end plates. The outside of the cell was bent and appeared severely deformed with more than 0.001 of strain. Experimental results of pressure sensing films for circular end plate dummy cells have similar distribution of pressure. Both end plates pressed inside (pink) of the dummy cells lighter than outside (strong red). Table 5. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the circular end plates of the dummy-cell stack.

Equivalent strain from simulations
Measured pressure distribution Furthermore, after comparing the cells located in the middle of the stacks to which the conventional circular end plate had been applied and those to which the CN0510 end plate had been applied, the strain was smaller, and the color was more uniform than for the end cells. The clamping pressure was uniformly applied to the end plates; thus, the CN0510 end plate and uniform clamping pressure were equivalent to that of a conventional circular end plate.
The strain of the end and the middle cells of the stacks in which the conventional square end plate and those in which the CN10 end plate, which was selected from the parametric study, were 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. Table 5 illustrates the strains of the end and middle cells of the 21-cell stacks to which the conventional circular end plate and CN0510 end plate, which was optimized by the parametric study, were applied. The strain ranges are similar at the end and the middle cells of the stacks, respectively, between the conventional and CN0510 end plates. The wavy shape inside on the end cell occurred because the upper cut of the sector formed, which disappeared on the middle cell with CN0510 end plates. The outside of the cell was bent and appeared severely deformed with more than 0.001 of strain. Experimental results of pressure sensing films for circular end plate dummy cells have similar distribution of pressure. Both end plates pressed inside (pink) of the dummy cells lighter than outside (strong red). Table 5. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the circular end plates of the dummy-cell stack.

Equivalent strain from simulations
Measured pressure distribution Furthermore, after comparing the cells located in the middle of the stacks to which the conventional circular end plate had been applied and those to which the CN0510 end plate had been applied, the strain was smaller, and the color was more uniform than for the end cells. The clamping pressure was uniformly applied to the end plates; thus, the CN0510 end plate and uniform clamping pressure were equivalent to that of a conventional circular end plate.
The strain of the end and the middle cells of the stacks in which the conventional square end plate and those in which the CN10 end plate, which was selected from the parametric study, were Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 14 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. Table 5 illustrates the strains of the end and middle cells of the 21-cell stacks to which the conventional circular end plate and CN0510 end plate, which was optimized by the parametric study, were applied. The strain ranges are similar at the end and the middle cells of the stacks, respectively, between the conventional and CN0510 end plates. The wavy shape inside on the end cell occurred because the upper cut of the sector formed, which disappeared on the middle cell with CN0510 end plates. The outside of the cell was bent and appeared severely deformed with more than 0.001 of strain. Experimental results of pressure sensing films for circular end plate dummy cells have similar distribution of pressure. Both end plates pressed inside (pink) of the dummy cells lighter than outside (strong red). Table 5. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the circular end plates of the dummy-cell stack.

Equivalent strain from simulations
Measured pressure distribution Furthermore, after comparing the cells located in the middle of the stacks to which the conventional circular end plate had been applied and those to which the CN0510 end plate had been applied, the strain was smaller, and the color was more uniform than for the end cells. The clamping pressure was uniformly applied to the end plates; thus, the CN0510 end plate and uniform clamping pressure were equivalent to that of a conventional circular end plate.
The strain of the end and the middle cells of the stacks in which the conventional square end plate and those in which the CN10 end plate, which was selected from the parametric study, were 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. Table 5 illustrates the strains of the end and middle cells of the 21-cell stacks to which the conventional circular end plate and CN0510 end plate, which was optimized by the parametric study, were applied. The strain ranges are similar at the end and the middle cells of the stacks, respectively, between the conventional and CN0510 end plates. The wavy shape inside on the end cell occurred because the upper cut of the sector formed, which disappeared on the middle cell with CN0510 end plates. The outside of the cell was bent and appeared severely deformed with more than 0.001 of strain. Experimental results of pressure sensing films for circular end plate dummy cells have similar distribution of pressure. Both end plates pressed inside (pink) of the dummy cells lighter than outside (strong red). Table 5. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the circular end plates of the dummy-cell stack.

Equivalent strain from simulations
Measured pressure distribution Furthermore, after comparing the cells located in the middle of the stacks to which the conventional circular end plate had been applied and those to which the CN0510 end plate had been applied, the strain was smaller, and the color was more uniform than for the end cells. The clamping pressure was uniformly applied to the end plates; thus, the CN0510 end plate and uniform clamping pressure were equivalent to that of a conventional circular end plate.
The strain of the end and the middle cells of the stacks in which the conventional square end plate and those in which the CN10 end plate, which was selected from the parametric study, were Appl. Sci. 2020, 10, x FOR PEER REVIEW 10 of 14 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. Table 5 illustrates the strains of the end and middle cells of the 21-cell stacks to which the conventional circular end plate and CN0510 end plate, which was optimized by the parametric study, were applied. The strain ranges are similar at the end and the middle cells of the stacks, respectively, between the conventional and CN0510 end plates. The wavy shape inside on the end cell occurred because the upper cut of the sector formed, which disappeared on the middle cell with CN0510 end plates. The outside of the cell was bent and appeared severely deformed with more than 0.001 of strain. Experimental results of pressure sensing films for circular end plate dummy cells have similar distribution of pressure. Both end plates pressed inside (pink) of the dummy cells lighter than outside (strong red). Table 5. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the circular end plates of the dummy-cell stack.

Equivalent strain from simulations
Measured pressure distribution Furthermore, after comparing the cells located in the middle of the stacks to which the conventional circular end plate had been applied and those to which the CN0510 end plate had been applied, the strain was smaller, and the color was more uniform than for the end cells. The clamping pressure was uniformly applied to the end plates; thus, the CN0510 end plate and uniform clamping pressure were equivalent to that of a conventional circular end plate.
The strain of the end and the middle cells of the stacks in which the conventional square end plate and those in which the CN10 end plate, which was selected from the parametric study, were 2.5 MPa (White)-10 MPa (Red) Furthermore, after comparing the cells located in the middle of the stacks to which the conventional circular end plate had been applied and those to which the CN0510 end plate had been applied, the strain was smaller, and the color was more uniform than for the end cells. The clamping pressure was uniformly applied to the end plates; thus, the CN0510 end plate and uniform clamping pressure were equivalent to that of a conventional circular end plate.
The strain of the end and the middle cells of the stacks in which the conventional square end plate and those in which the CN10 end plate, which was selected from the parametric study, were applied, can be confirmed from Table 6. The strain of the end and the middle cells of the stacks with the conventional square end plates and those with the CN10 end plate are at the same level, while the strains of the square end plates are 10 times larger than those of the circular end plates. The outside of the cell was bent and appeared severely deformed similar to the circular end plates. Table 6. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the square end plates of the dummy-cell stack.

Equivalent Strain from Simulations Measured Pressure Distribution
End cell (Conv.) Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 14 applied, can be confirmed from Table 6. The strain of the end and the middle cells of the stacks with the conventional square end plates and those with the CN10 end plate are at the same level, while the strains of the square end plates are 10 times larger than those of the circular end plates. The outside of the cell was bent and appeared severely deformed similar to the circular end plates. Table 6. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the square end plates of the dummy-cell stack.

Equivalent strain from simulations Measured pressure distribution
End cell Furthermore, for cells located in the middle of the stacks with the conventional square end plate and those with the CN10 end plate, after comparing the end cells with rectangle contour inside, the strain was smaller, and the contour was circular. Evidently, the clamping pressure was applied uniformly, and so the square end plate with less weight and uniform clamping pressure was equivalent to that of the conventional square end plate. The contour distribution and color uniformity were confirmed by the experimental results with pressure sensing films. Figure 7 is a graph comparing each of the four types of stacks in which conventional circular, CN0510, conventional square, and CN10 end plates had been applied. For the middle cell, the deviation of the strain is much smaller than at the end cells. The minimum strains of the middle cells are nearly zero, which can result in high ohmic resistance.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 14 applied, can be confirmed from Table 6. The strain of the end and the middle cells of the stacks with the conventional square end plates and those with the CN10 end plate are at the same level, while the strains of the square end plates are 10 times larger than those of the circular end plates. The outside of the cell was bent and appeared severely deformed similar to the circular end plates. Table 6. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the square end plates of the dummy-cell stack.

Equivalent strain from simulations Measured pressure distribution
End cell Furthermore, for cells located in the middle of the stacks with the conventional square end plate and those with the CN10 end plate, after comparing the end cells with rectangle contour inside, the strain was smaller, and the contour was circular. Evidently, the clamping pressure was applied uniformly, and so the square end plate with less weight and uniform clamping pressure was equivalent to that of the conventional square end plate. The contour distribution and color uniformity were confirmed by the experimental results with pressure sensing films. Figure 7 is a graph comparing each of the four types of stacks in which conventional circular, CN0510, conventional square, and CN10 end plates had been applied. For the middle cell, the deviation of the strain is much smaller than at the end cells. The minimum strains of the middle cells are nearly zero, which can result in high ohmic resistance. applied, can be confirmed from Table 6. The strain of the end and the middle cells of the stacks with the conventional square end plates and those with the CN10 end plate are at the same level, while the strains of the square end plates are 10 times larger than those of the circular end plates. The outside of the cell was bent and appeared severely deformed similar to the circular end plates. Furthermore, for cells located in the middle of the stacks with the conventional square end plate and those with the CN10 end plate, after comparing the end cells with rectangle contour inside, the strain was smaller, and the contour was circular. Evidently, the clamping pressure was applied uniformly, and so the square end plate with less weight and uniform clamping pressure was equivalent to that of the conventional square end plate. The contour distribution and color uniformity were confirmed by the experimental results with pressure sensing films. Figure 7 is a graph comparing each of the four types of stacks in which conventional circular, CN0510, conventional square, and CN10 end plates had been applied. For the middle cell, the deviation of the strain is much smaller than at the end cells. The minimum strains of the middle cells are nearly zero, which can result in high ohmic resistance. applied, can be confirmed from Table 6. The strain of the end and the middle cells of the stacks with the conventional square end plates and those with the CN10 end plate are at the same level, while the strains of the square end plates are 10 times larger than those of the circular end plates. The outside of the cell was bent and appeared severely deformed similar to the circular end plates. Furthermore, for cells located in the middle of the stacks with the conventional square end plate and those with the CN10 end plate, after comparing the end cells with rectangle contour inside, the strain was smaller, and the contour was circular. Evidently, the clamping pressure was applied uniformly, and so the square end plate with less weight and uniform clamping pressure was equivalent to that of the conventional square end plate. The contour distribution and color uniformity were confirmed by the experimental results with pressure sensing films. Figure 7 is a graph comparing each of the four types of stacks in which conventional circular, CN0510, conventional square, and CN10 end plates had been applied. For the middle cell, the deviation of the strain is much smaller than at the end cells. The minimum strains of the middle cells are nearly zero, which can result in high ohmic resistance. applied, can be confirmed from Table 6. The strain of the end and the middle cells of the stacks with the conventional square end plates and those with the CN10 end plate are at the same level, while the strains of the square end plates are 10 times larger than those of the circular end plates. The outside of the cell was bent and appeared severely deformed similar to the circular end plates. Furthermore, for cells located in the middle of the stacks with the conventional square end plate and those with the CN10 end plate, after comparing the end cells with rectangle contour inside, the strain was smaller, and the contour was circular. Evidently, the clamping pressure was applied uniformly, and so the square end plate with less weight and uniform clamping pressure was equivalent to that of the conventional square end plate. The contour distribution and color uniformity were confirmed by the experimental results with pressure sensing films. Figure 7 is a graph comparing each of the four types of stacks in which conventional circular, CN0510, conventional square, and CN10 end plates had been applied. For the middle cell, the deviation of the strain is much smaller than at the end cells. The minimum strains of the middle cells are nearly zero, which can result in high ohmic resistance. applied, can be confirmed from Table 6. The strain of the end and the middle cells of the stacks with the conventional square end plates and those with the CN10 end plate are at the same level, while the strains of the square end plates are 10 times larger than those of the circular end plates. The outside of the cell was bent and appeared severely deformed similar to the circular end plates. Furthermore, for cells located in the middle of the stacks with the conventional square end plate and those with the CN10 end plate, after comparing the end cells with rectangle contour inside, the strain was smaller, and the contour was circular. Evidently, the clamping pressure was applied uniformly, and so the square end plate with less weight and uniform clamping pressure was equivalent to that of the conventional square end plate. The contour distribution and color uniformity were confirmed by the experimental results with pressure sensing films. Figure 7 is a graph comparing each of the four types of stacks in which conventional circular, CN0510, conventional square, and CN10 end plates had been applied. For the middle cell, the deviation of the strain is much smaller than at the end cells. The minimum strains of the middle cells are nearly zero, which can result in high ohmic resistance. applied, can be confirmed from Table 6. The strain of the end and the middle cells of the stacks with the conventional square end plates and those with the CN10 end plate are at the same level, while the strains of the square end plates are 10 times larger than those of the circular end plates. The outside of the cell was bent and appeared severely deformed similar to the circular end plates. Furthermore, for cells located in the middle of the stacks with the conventional square end plate and those with the CN10 end plate, after comparing the end cells with rectangle contour inside, the strain was smaller, and the contour was circular. Evidently, the clamping pressure was applied uniformly, and so the square end plate with less weight and uniform clamping pressure was equivalent to that of the conventional square end plate. The contour distribution and color uniformity were confirmed by the experimental results with pressure sensing films. Figure 7 is a graph comparing each of the four types of stacks in which conventional circular, CN0510, conventional square, and CN10 end plates had been applied. For the middle cell, the deviation of the strain is much smaller than at the end cells. The minimum strains of the middle cells are nearly zero, which can result in high ohmic resistance.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 11 of 14 applied, can be confirmed from Table 6. The strain of the end and the middle cells of the stacks with the conventional square end plates and those with the CN10 end plate are at the same level, while the strains of the square end plates are 10 times larger than those of the circular end plates. The outside of the cell was bent and appeared severely deformed similar to the circular end plates. Table 6. Comparison of the simulated equivalent-strain distribution with the experimental pressure distribution, using the square end plates of the dummy-cell stack.

Equivalent strain from simulations Measured pressure distribution
End cell Furthermore, for cells located in the middle of the stacks with the conventional square end plate and those with the CN10 end plate, after comparing the end cells with rectangle contour inside, the strain was smaller, and the contour was circular. Evidently, the clamping pressure was applied uniformly, and so the square end plate with less weight and uniform clamping pressure was equivalent to that of the conventional square end plate. The contour distribution and color uniformity were confirmed by the experimental results with pressure sensing films. Figure 7 is a graph comparing each of the four types of stacks in which conventional circular, CN0510, conventional square, and CN10 end plates had been applied. For the middle cell, the deviation of the strain is much smaller than at the end cells. The minimum strains of the middle cells are nearly zero, which can result in high ohmic resistance. Furthermore, for cells located in the middle of the stacks with the conventional square end plate and those with the CN10 end plate, after comparing the end cells with rectangle contour inside, the strain was smaller, and the contour was circular. Evidently, the clamping pressure was applied uniformly, and so the square end plate with less weight and uniform clamping pressure was equivalent to that of the conventional square end plate. The contour distribution and color uniformity were confirmed by the experimental results with pressure sensing films. Figure 7 is a graph comparing each of the four types of stacks in which conventional circular, CN0510, conventional square, and CN10 end plates had been applied. For the middle cell, the deviation of the strain is much smaller than at the end cells. The minimum strains of the middle cells are nearly zero, which can result in high ohmic resistance.  Figure 8 confirms the strain tendencies for each cell. In Figure 8, the stack applied with the conventional circular and CN0510 end plates had less strain at both ends of the cell compared with the stack with the conventional and CN10 end plates. The strains of the newly designed end plates (CN0510, CN10) are slightly lower than those of the conventional end plates. The cell strain is higher at both ends of the stack with all kinds of end plates.

Conclusions
Stress and deformation analysis and topology optimization were performed in this paper to solve the deterioration of PEMWE performance caused by deformation-a problem for the end plate-and reduce the weight of the two types of conventional circular and square end plates. Thus, light end plates were designed using the derived parameters. The weights of the light circular and square end plates were reduced compared with conventional end plates by 22.9% and 20.1%, respectively. Furthermore, strain analysis was performed to confirm the uniformity of the clamping pressure between cells. The stacks with the light circular and square end plates had confirmed strains similar to the stack applied with the conventional end plates.  Figure 8 confirms the strain tendencies for each cell. In Figure 8, the stack applied with the conventional circular and CN0510 end plates had less strain at both ends of the cell compared with the stack with the conventional and CN10 end plates. The strains of the newly designed end plates (CN0510, CN10) are slightly lower than those of the conventional end plates. The cell strain is higher at both ends of the stack with all kinds of end plates.  Figure 8 confirms the strain tendencies for each cell. In Figure 8, the stack applied with the conventional circular and CN0510 end plates had less strain at both ends of the cell compared with the stack with the conventional and CN10 end plates. The strains of the newly designed end plates (CN0510, CN10) are slightly lower than those of the conventional end plates. The cell strain is higher at both ends of the stack with all kinds of end plates.

Conclusions
Stress and deformation analysis and topology optimization were performed in this paper to solve the deterioration of PEMWE performance caused by deformation-a problem for the end plate-and reduce the weight of the two types of conventional circular and square end plates. Thus, light end plates were designed using the derived parameters. The weights of the light circular and square end plates were reduced compared with conventional end plates by 22.9% and 20.1%, respectively. Furthermore, strain analysis was performed to confirm the uniformity of the clamping pressure between cells. The stacks with the light circular and square end plates had confirmed strains similar to the stack applied with the conventional end plates.

Conclusions
Stress and deformation analysis and topology optimization were performed in this paper to solve the deterioration of PEMWE performance caused by deformation-a problem for the end plateand reduce the weight of the two types of conventional circular and square end plates. Thus, light end plates were designed using the derived parameters. The weights of the light circular and square end plates were reduced compared with conventional end plates by 22.9% and 23.3%, respectively. Furthermore, strain analysis was performed to confirm the uniformity of the clamping pressure between cells. The stacks with the light circular and square end plates had confirmed strains similar to the stack applied with the conventional end plates. Furthermore, even if the square end plates have large stress distributions compared with the circular end plates, the cell clamping pressure was distributed uniformly in each cell because of the nonlinearity of the square end plate pressure distribution. The results verified that structural strength was required and that the square end plates exhibited reduced strain due to the large stress concentration compared with the circular end plates. Thus, FEA was performed to examine the end plate weight reduction and the uniformity of the clamping pressure between the stack cells. The pressure sensing experiments validated simulation results qualitatively. The comparative analysis of the circular and the square end plates with dummy cell simulation can improve the performance of the high-pressure PEMWE by using end plates to provide gas-tight sealing and uniform clamping pressure.