**Abstract: **This article focuses on the numerical study of the dynamic test of the laminated tempered glass panel with four sides simply supported under shock wave load. The definition and definition of the element model and the material model under the dynamic load state are carried out. By simplifying the shock wave load, the application It is possible for ANSYS software to carry out numerical simulation and apply it to engineering practice. Finally, the comparative study of failure state, pressure, time history curve and test data confirms the scientific rationality of the design scheme in this paper. As a cutting-edge research on the anti-blast shock wave design of glass curtain walls, it provides an effective reference for future design, construction, and specification.

**Keywords:** finite element simulation; peak pressure value; elastoplasticity; element failure; impact load; PVB film

1. Introduction

Due to the increasingly serious consequences caused by the explosion, how to improve the comprehensive protection capability of the engineering structure is a problem that must be solved by the engineering structure. The impulse load generated by the explosion has a high degree of non-linearity, and it is usually completed in an instant from a few milliseconds to a dozen milliseconds, so the dynamic response of the structure to the explosion is very complicated [1]. At present, glass curtain walls are widely used in high-rise and super high-rise buildings as the outer protective structure of buildings. Such buildings have dense crowds. When the glass curtain wall is exposed to sudden outdoor explosions (including car bombs, human bombs, etc.) However, severe damage will cause great casualties and economic and property losses, and its safety should be considered.

Dynamics research is mainly carried out from three aspects: theoretical analysis, numerical calculation and experimental research. Experimental research occupies an important position and can be used to verify the results of theoretical analysis and numerical calculation. At the same time, the impact and explosion involved in material dynamics are all Completed in an instant, as well as the complexity and diversity of structural forms and the diversification of materials used make it difficult for theoretical research to meet the needs of engineering. Therefore, detailed observation of these phenomena must also rely on experimental research [2] and establish accurate numerical simulations based on experimental results. The model then lays the foundation for the accuracy of subsequent theoretical analysis and numerical simulation. This article uses ANSYS software to carry out a numerical simulation of the test model, and compares it with the explosion test of a simple-supported single-layer, laminated glass panel on four sides, and then a more accurate mechanical model is obtained.

2. The ANSYS

ANSYS is a world-renowned dynamic analysis finite element program, which can accurately and reliably handle various highly nonlinear problems, such as collision analysis, explosion analysis, stamping analysis, conventional weapon design, drop analysis, thermal analysis, fluid-structure coupling analysis, etc. . Since it was introduced into the country in the 1990s, it has been widely used in the automotive, national defense and military industry, electronics, manufacturing and construction industries. It is also a fully functional geometric nonlinearity (large displacement, large rotation and large strain), material nonlinearity (more than 140 dynamic material models) and contact nonlinearity (more than 50 contact modes) programs, mainly based on Lagrange algorithm. It has both A LE and Euler algorithms; it focuses on explicit solution, and it has implicit solution functions; it focuses on structural analysis, and it has thermal analysis and fluid-structure coupling functions; it focuses on nonlinear dynamic analysis, and it has static force. The analysis function is a general-purpose structural analysis nonlinear finite element program that combines military and civilian use [3].

The explosion dynamics process is very complicated and it is difficult to carry out accurate analytical analysis. Numerical analysis and model tests are currently the two most commonly used methods. The accuracy of numerical analysis depends on the model describing the material (such as material constitutive relationship, explosive state equation, etc.), boundary conditions, load conditions, etc. At present, the description of the material model under the effect of explosion is not perfect. The accuracy of numerical analysis is generally not higher than that of the approximate equation, but numerical simulation can provide a description of the phenomenon of the whole process, and the calculation result is made by the method of fitting parameters. It is consistent with the test results [4].

In this paper, the explicit dynamics software ANSYS is used to study the dynamic response of the glass panel under the action of the explosion shock wave, and the correctness of the model is verified through the test results.

3. Finite element model

The accuracy of the anti-explosion numerical simulation of glass panels is inseparable from reasonable material constitutive equations, accurate structural models and reasonable load distribution. According to test [5] specimens (glass size 1000 mm*1000 mm, single-layer tempered glass with a thickness of 8 mm and 6 mm+1.14 mm+6 mm laminated tempered glass) for modeling.

In the numerical simulation analysis, in order to reduce the calculation time and file size, 1/4 model of the panel is used for numerical calculation. Only for the analysis of laminated glass (the application of single-layer glass in engineering practice is of little significance), the symmetry plane is constrained by the symmetry axis, and the boundary is constrained by simple support.

The arrangement of measuring points is shown in Figure 1.

^{Figure 1 The arrangement of measuring points}

In the figure: d represents the displacement measuring point, and the distance between the measuring points is 200 mm; ε represents the strain measuring point corresponding to the stress σ, as shown by the above icon.

In the ANSYS element library, Shell163 thin shell elements and Solid164 solid elements can be selected to simulate glass panels and PVB laminated. Shell163 thin shell element is a 4-node element that can resist in-plane and normal stress. Each node has 12 degrees of freedom for translation, velocity, acceleration, and rotation in the X, Y, and Z directions. Solid164 is an 8-node solid element. Each node has 9 degrees of freedom in X, Y, and Z directions of translation, velocity, and acceleration. As shown in Figure 2, Figure 3.

^{Figure 2 Shell163 thin shell elements and Figure 3 Solid164 solid elements}

For a single piece of glass, in order to accurately describe the failure process of different layers of glass units, the Solid164 unit is used for simulation. For laminated glass, the interface between glass and PVB relies on heating and adhesion under high pressure, and its creep characteristics depend on temperature and time. Therefore, under dynamic load, PVB adhesion is relatively high. It can be assumed that the glass and the interlayer are fully bonded. The peeling of the film is not considered [6] [7], so the glass and laminated joints are used for finite element analysis.

There are three main types of models for numerical simulation of laminated glass: distributed model (smeared model), layered material model (layer ed material model) and 3D solid model (3D model). The 3D solid model can describe the constitutive relationship of the laminated material in more detail. Based on this model, Wei J. chooses the viscoelastic material model to consider the influence of the PVB strain rate, but compared with the shell element, the calculation of the solid element is more time-consuming.

Synthesizing the existing structure model, in order to obtain better mesh quality, obtain higher precision to reflect the interlayer interaction relationship of laminated glass, and obtain the failure process of different layers of glass, this paper uses the 3Dsolid model for numerical analysis.

Explosion is a physical or chemical energy release process in a very short time (usually within a few to tens of milliseconds). It has the characteristics of fast propagation speed, large peak value and short action time. Under the action of the explosive air shock wave load, the structural material is fast loaded in milliseconds, and its strain rate can reach 102~103/s, while the strain rate of conventional static load materials is about 10 -5/s. The material dynamic fast loading test shows As the strain rate increases, a series of physical and chemical changes occur in the material. Its mechanical properties are mainly reflected in the more complex stress-strain relationship. Some characteristic parameters, such as strength, ductility, elastic modulus, damping ratio, etc., have different degrees The change. A large number of test results show that under high-speed loading conditions, the yield strength of the material is significantly improved.

Glass is a brittle material, unlike metals and other materials that can be bent and deformed. When subjected to external force, especially when the external force exceeds the allowable stress of the glass itself, the glass will break. Its tensile strength depends on the crack defects on the surface (not necessarily visible to the naked eye), so although the theoretical tensile strength of glass (based on molecular force) is extremely high up to 32 GPa, this is only available when the glass is flawless, usually glass It is flawed, and the glass surface is particularly vulnerable to scratches, scratches or atmospheric erosion. Therefore, once the critical stress is exceeded in actual structural applications, the glass will be brittle and its tensile strength is much lower than theoretical. Figure 4 shows an overview of the tensile strength at different crack depths [8].

^{Figure 4 The overview of the tensile strength at different crack depths}

It can be seen from the figure above that the tensile strength of glass is not a constant. It depends on many factors, especially the condition of the glass surface, the size and thickness of the glass unit, the loading history (strength and duration), residual stress and environmental conditions. When the load is larger, the duration is longer, and the initial surface crack is deeper, the effective tensile strength of the glass is smaller.

The international industry standards "Glass Curtain Wall Engineering Technical Code" stipulates that under short-term load, the yield strength of tempered glass with a thickness of 5-12 mm is 84MPa[10]. Under the explosive impact load, the damage stress is increased corresponding to the static load. In the ANSYS material library [11], specific material models can be used to simulate the response of brittle materials such as glass and ceramics under impact loads. Due to the high-speed impact load, the material model undergoes large strain, large strain rate and high pressure process, so the parameters of the equation of state regarding strain, strain rate and pressure range need to be determined by experiments. For tempered glass, there is no response at home and abroad. Supported by the test data, this paper uses a material model with failure criteria to simulate glass failure [8].

Tests have shown that the mechanical properties of PVB laminated glue are greatly affected by the loading time. Under the action of longer load duration and small strain rate, PVB film has viscoelastic properties; under the action of shorter load duration and higher strain rate, the material exhibits elastoplastic properties, similar to other plastic materials, PVB It exhibits failure at large strains (about 300%). At the same time, under the condition of high strain rate, the elastic modulus of PVB film also increases exponentially [7]. Therefore, under the impact of the explosion load, the PVB film is taken as the elastoplastic material model. The glass and PVB laminated material parameters are shown in Table 1:

Glass material parameters | PVB laminated material parameters | ||

Parameter item | Parameter value | Parameter item | Parameter value |

Elastic modulus/MPa | 71000 | Elastic modulus/MPa | 220 |

Poisson's ratio | 0.22 | Poisson's ratio | 0.495 |

Density kg/cm | 0.00256 | Density kg/cm | 1.1 |

Plastic failure strain | 0.0013 | Elastic limit/MPa | 11 |

Yield strength/MPa | 120 | Ultimate stress/MPa | 28 |

^{Table 1 Tempered glass and PVB laminated material parameter table }

4. Mesh division

Grid division is an important part of the establishment of finite element model, and the divided grid form will directly affect the calculation accuracy and calculation scale. In this paper, it is necessary to simulate the damage of the glass panel under the action of explosive impact load, and to study the damage process such as cracks of the glass. In most general finite element software, there are two main methods for simulating the generation and propagation of cracks: one is to generate cracks in the structure through element failure; the other is to form cracks by defining node constraint failures. In the definition of the material model, the glass material defines the failure criterion. Therefore, the first method can be used to simulate the crack of the glass. However, in order to reduce the error of the result, the model needs to be divided into finer meshes. Otherwise, due to the large number of elements Failure will produce larger errors. In order to achieve the optimization and unity of calculation accuracy and calculation efficiency, this paper uses a quarter glass model for calculation, which is divided into 100 equal parts in the length direction and more than 3 units in the thickness direction of the single piece of glass. The grid division is shown in Figure 5.

^{Figure 5 The grid division}

5. Load simplification

The pressure parameters and duration of the explosion shock wave are important parameters that determine the response of the structure. For the simulation of explosive dynamic load, ANSYS provides two methods, one is to simplify the explosive load into a time-history curve of force applied to the structural surface element; the other is to use the equation of state to simulate the pressure and volume during the explosion process The relationship between the simulated explosive and the bombed structure. In this chapter, based on the pressure change with time after the explosion impact measured in experiment [5] (Figure 6), it is simplified as a triangular pressure time history curve applied to the glass panel (Figure 7).

^{Figure 6 Measured pressure time history curve Figure 7 Simplified stress time course}

Curve

It can be seen from the figure above that within a few milliseconds after the explosion, the pressure in the test section rose rapidly from zero to the predetermined peak pressure, and then gradually dropped to zero. Therefore, the time history curve of overpressure when the detonating cord explodes measured by the actual pressure time history curve can be simplified as a triangular load.

6. Comparative analysis of numerical results and test results of laminated glass

The finite element analysis is carried out according to the actual applied load (peak pressure value is 0.07MPa, duration is 50ms) in the test [5]. As shown in Figure 8, under the load applied by the test, the non-stressed surface of the glass panel is broken, and the broken cracks are evenly distributed from the center to the outside. In the numerical simulation, under the impact load, the back of the glass ( The unloaded surface) cracks first occurred in the middle of the span. As the load continues to increase, the cracks will quickly crack, but the glass panel remains intact. The PVB film is not damaged, and no fragments are splashed, which is consistent with the test results.

^{Figure 8 Destruction diagram of glass panel under impact load}

Figure 9 shows the stress cloud diagram on the back of the glass panel (unloaded surface) at different time periods. It can be seen from the figure that with the increase of the load duration, the stress of the panel continues to increase until the yield stress of the glass is reached, the glass is broken, and then the stress of the glass panel gradually decreases. This is consistent with the actual test results. The stress time history curve of the point is shown in Figure 10.

^{Figure 9 Stress cloud diagram of glass panel at different moments}

At about 6.65ms, cracks occurred first in the middle of the back of the glass (non-stressed surface), which was consistent with the test results. As the loading time increases, the panel cracks continue to expand, and the glass eventually breaks completely.

^{Figure 10 Corresponding to the stress time history curve of the measuring point 1}

It can be seen from the figure above that in the numerical simulation, the maximum stresses corresponding to the measured point stress σ1 (mid-span), σ2, and σ3 are 122.6MPa, 102.4MPa, and 99.3MPa respectively, and as the distance from the middle-span increases, the stress Gradually decrease, the finite element simulation is basically consistent with the test results. According to the international industry standard "Glass Curtain Wall Engineering Technical Code", under short-term load, the yield strength of tempered glass with a thickness of 5-12mm is 84MPa. Under the explosive impact load, its failure stress is increased corresponding to the static load. The relative errors with the test results (σ1=117.3MPa, σ2=80.1MPa, σ3=78.4MPa) are all within 25%, and the error is within the allowable error range.

Figure 11 is the finite element analysis of the displacement of the glass panel. It can be seen from the figure that the middle-span displacement of the panel is the largest, and the displacement gradually decreases with the increase of the distance between the middle-span distance, which is consistent with the test results. The displacement time history curve of the corresponding measuring point is shown in Figure 12.

^{Figure 11 Glass panel displacement graph}

^{Figure 12 Corresponding to the stress time history curve of the measuring point 2}

In the finite element analysis, when the mid-span stress of the glass panel reaches the maximum (6.65ms), the mid-span displacement reaches the maximum. The finite element simulation results show that the d1 (middle span), d2, d3 displacement changes with time are consistent, and the maximum displacement is 18.7mm, 14.2mm, and 6.1mm respectively; it is stipulated in the international industry standards "Glass Curtain Wall Engineering Technical Code" : Under such short-term load, the deflection limit of the four-sided simply supported glass panel should be adopted at 1/60 of the length of the short side. Therefore, it can be seen from the results of test [5]: Corresponding to the increase under static load. Compared with the actual measurement results (d1=21.5 mm, d2=16.9mm, d2=4.7mm), the maximum displacement differs by 25%, and the error is within the allowable error range.

7. Conclusion

Through the dynamic response test and numerical analysis of the glass curtain wall under the action of explosion impact load, the following conclusions can be drawn:

Laminated glass can resist a certain explosion shock wave, and the fragments will stick firmly in the PVB interlayer after damage, and will not cause secondary damage to personnel, so it can be used as safety glass in anti-explosive structures.

The pressure time history of the explosion shock wave measured in the test is simplified according to the triangular shock wave load, and the calculation result meets the accuracy requirements, indicating that the simplified load method is feasible and can be used as a reference for engineering design;

Based on the experiment, the dynamic response of the laminated glass curtain wall was studied, and the results consistent with the experimental results were obtained through the numerical simulation method, which proved the effectiveness of the numerical simulation method and provided a reference for solving practical engineering problems.

Both the test results and the numerical simulation results show that the yield stress and displacement of the glass panel when the glass panel fails under the action of explosive impact load are both greater than the value under the action of static load. When it is broken, it starts from the inner glass (unloaded surface) and gradually expands from the center to the outside. It provides a reference for the study of the failure form of the glass curtain wall under the action of explosive impact load.

**References**

[1] Timmel M., Kolling S., Osterrieder P., Du Bois P., A Finite Element Model for Imp act Simulation with Laminated Glass, International Journal of Impact Engineering Vol. 3 4, 2007, pp. 1465–1478.

[2] Martin Larcher, Norbert Gebbeken, Martien Teich, George Solomos. Simulation of Laminated Glass Loaded by Air Blast Waves. Applied Mechanics and Materials.Vol. 8 2(2011):69-74.

[3]Matthias Haldimann, Andreas Luible, Mauro Overend. Structural Use of Glass[M]. Switzerland: IABSE-AIPC-IVBH, 2008.

[4]Peter Rice, Hugh Dutton. Cable structure glass curtain wall [M]. Dalian: Dalian University of Technology Press, 2006, 2.

[5] JGJ 102-2003. Technical specifications for glass curtain wall engineering. 2003.

[6] www.Cadfamily.com. LS-DYNA Keyword User’s Manual[M]. California: Liverm oreSoftware Technology Corporation, 2006.

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