## 1 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]. [PERSON] 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, [PERSON] 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. [PERSON] et al. [5] conducted an experimental study on clamping pressure distribution with performance tests and pressure-sensitive films. Newly designed end plates provide uniform stress to MEA. The new design was convenient to use in the laboratory for the uniform clamping pressure, but not in practice because of its bulky system with the built-in hydraulically pressurizing devices. [PERSON] et al. [8] applied an endplate with center holes and hex-head screws in single-cell and 16-cell stacks. Simulation and experimental analyses of single-cell and 16-cell stacks and components of the stack were performed by finite element analysis (FEA) and pressure-sensitive film. The stress on the GDL is simulated at 1.6 MPa for the 16-cell stack and 4 MPa in single-cell. Experimental results demonstrated nearly zero pressure at the center of the stack, regardless of the clamping pressure. Pushing pins through center holes compensate for the deficient clamping pressure of end plates, which needs additional devices for the stacks. [PERSON] et al. [9] investigated the multi-objective topology optimization of end plates with nonlinear contact boundary conditions. The 5-cell and 10-cell stacks have different response forces to end plates, which optimize the different shapes of end plates. The stiff end plates press the cells uniformly, but the parametric study of various end plates was not investigated further. [PERSON] et al. [10] used FEA and a pressure film test to study end plate assembly pressure distribution. The quantitative comparison of simulation and experimental results are essential for obtaining consistent fuel cell performance with stacking parameters such as stacking design, BP thickness, sealing size, and assembly pressure. [PERSON] et al. [11] designed and manufactured end plates for a 5 kW PEMFC that provided uniform pressure distribution between the fuel cell components (e.g., BPs, GDLs, and current collectors) and, consequently, reduced the contact resistance, which was measured by electrochemical impedance spectroscopy. The thickness of the end plates was optimized, minimizing deflections. The clamping torque, end plate thickness, and number of bolts were optimally combined for the appropriate assembly pressure distribution. [PERSON] et al.