# Research on Out-of-Plane Bending Test of PVB Laminated Glass Plate with Different Number of Layers
## 1 Introduction
This method facilitates the application of classical analytical solutions, devised for single-layer plates, to laminated plates. Owing to its simplicity, this approach has been adopted in glass plate specifications across many countries [10; 11; 12; 13]. However, these specifications differ in the methodology used to determine the equivalent thickness of laminated glass plates. Additionally, variations in the equivalent principle lead to discrepancies in measured equivalent thickness [14; 15; 16; 17]. Theoretical studies have mainly focused on the bending calculations of two-layer PVB LG, with limited research on three-layer PVB LG. Furthermore, these studies typically assume the elastic modulus of PVB to be a constant value for calculations, ignoring the material's nonlinearity [17]. The validity of such an assumption remains in question and requires verification. Due to the high complexity involved in achieving a closed-form solution using lamination theory, finite element numerical analysis has become another popular method for studying the mechanical response of laminated glass plates. Typically, the finite element analysis of a laminated glass plate involves multi-layer plate elements for numerical simulation, introducing the constitutive model of PVB to simulate the relative slip between the plates. This finite element model is suitable for analyzing how various factors, such as the number of glass layers, temperature, and adhesive thickness, affect the mechanical properties of laminated glass plates. [PERSON] et al. [18] performed numerical analyses to investigate the effects of plate size, interlayer thickness, glass thickness, and the number of glass layers on bending behavior, indicating that plate size significantly influences the analytical results. Through finite element parametric analysis, [PERSON] et al. [19] assessed the impact of temperature, load duration, and laminate thickness on the deflection of the entire plate and the stress distribution within it, leading to the proposal of an approximate method for calculating the bending stiffness of the plate. [PERSON] et al. [20] used the improved zig-zag theory to develop numerical methods suitable for general working conditions and presented an analytical solution for statically determinate beams by treating the glass plate as an Euler beam and considering the adhesive layer as solely providing shear stiffness for coupling the glass layers. [PERSON] et al. [21] created a 3D modeling approach for bending laminated glass plates using a 2D planar grid and completed a visualization post-processing program. They utilized this method to compute the bending of laminated glass with two, three, and four layers of glass and analyzed the accuracy of the calculated results. [PERSON] et al. [22] employed ANSYS for numerical simulations of laminated glass, unveiling a strong correlation between bending stiffness and the type and thickness of the laminate material. [PERSON] et al. [23] developed a finite element model for PVB laminated glass supported at four points, examining the effect of load duration on maximum deflection and finding that prolonged loading can diminish the bending resistance of PVB laminated glass. [PERSON] et al. [24] carried out finite element analyses of PVB laminated glass with varying thicknesses for each glass layer, discovering that a significant discrepancy in layer thicknesses can increase deflection, thereby reducing load-bearing capacity. Bending stiffness is the physical quantity that most directly indicates a plate's ability to resist bending deformation. Although existing numerical simulations have explored the deformation of different layers of PVB LG, none have quantitatively analyzed the effect of the number of glass layers on bending stiffness. Moreover, the numerical simulation of three-layer PVB LG still lacks experimental validation.