# Finite Element Analysis Model Design on the Mechanical Properties of Prefabricated Shear Wall Structure

Authors: Yuan Zhang
Journal: Scientific Programming
 (2022)

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## Abstract

At present, the mechanical properties analysis method of prefabricated shear wall structure based on static test is low overall simulation precision. In this paper, the finite element method is used to analyze the force performance of the prefabricated shear wall structure. Based on the shear of concrete material, elastic modulus, Poisson ratio, open fracture, the transfer coefficients of open and closed fracture, and tensile strength parameters, the finite element model is established by ANSYS. The vertical load and the horizontal load of the prefabricated shear wall structure are calculated, and the limit load value is obtained. The maximum stress change of the connector, the energy dissipation of the shear wall structure, and the change of the equivalent viscous damping coefficient are obtained by the way of loading and displacement change. The experimental results show that the simulated values of stiffness degradation, maximum displacement, maximum strain, and stress distribution obtained by this method are in good agreement with the actual values and are reliable.


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## Body

## 1. Introduction

Along with city development scale in China more and more big, the requirements of the government for environmental protection are higher, the requirements of real estate developers for time, cost, and quality are more strict, and the requirements of owners for the building product safety and comfort performance gradually increase, which have become the bottleneck restricting the development of the construction industry [1, 2]. The prefabricated shear wall structure has come into being. The fabricated building is a building constructed by precast components at the site. It has the advantages of short construction period, high construction quality, and environmental protection. It is catering to the national policies and development requirements of housing industrialization and building energy conservation and emission reduction. With the continuous development of prefabricated shear wall structure, the stress analysis has become a hot issue in structural engineering [3, 4].Zhang et al. [5] put forward an assembly scheme for the external wall panel for steel structure. In order to study the lateral resistance and seismic performance of steel frames with such wall panels, the ABAQUS finite element software was used to establish the overall model and comparison model of steel frames, and the finite element analysis of uniaxial loading and low cycle reciprocating loading was carried out. The results showed that the connection of the outer wall panel could guarantee the connection between the outer wall plate and the steel frame. When the structure had large deformation under lateral load, it could limit the transfer force between the wall panels and the frames, ensured that the wall panels were in an elastic state, and avoided wall panels from falling down. The enclosure system consisting of the external wall panel and the connection node significantly improved the mechanical performance of the steel frame, the initial stiffness of the structure was increased by 1.18 times, and the bearing capacity was increased by more than 30%. The scheme could enhance the seismic performance of the structure. When simulating the low cycle reciprocating loading, the total energy dissipation of the external wall panel’s steel frame model was increased by more than 90% compared with the pure frame model, but the overall simulation result was quite different from the actual value.In view of the large discrepancy between the simulation results in the literature and the actual values, a new finite element analysis method of prefabricated shear wall structure is put forward to improve the accuracy of mechanical properties of shear wall structure analysis.


## 2. Finite Element Analysis of the Mechanical Properties of Prefabricated Shear Wall Structure

The prefabricated shear wall structure is a new type of wallboard. The width of a single plate with a binding body part is selected as an analysis unit. Its size is the length of 3000 mm, the width of 600 mm, the thickness of 200 mm, and the concrete grade is C30. Because the integral modeling of ANSYS is used, the reinforcement ratio of the vertical bar in the plate is 1%, and the reinforcement ratio of the horizontal bar is 0.25%.The material parameters in finite element analysis are as follows: concrete C30, elastic modulus 3.0 GPa, Poisson’s ratio 0.2, steel bar HRB335, opening crack’s shear transfer coefficient 0.35, closed crack’s shear transfer coefficient 0.95, and the tensile strength 1.43 MPa.


### 2.1. The Model is Established

#### 2.1.1. Defining the Element Properties

The concrete is defined, the distribution unit type is SOLID65 unit, and the proper real constant and material model are selected. In considering the reinforced modeling, the internal structure of the structure is defined by the reinforcement ratio of the longitudinal reinforcement and the distribution of reinforcement in the real constant [6].


#### 2.1.2. The Division of Grid

The grid division is divided by swept grid and the source surface grid is divided by the mapped grid. The grid precision is controlled within 100 mm [7].


#### 2.1.3. Applying Constraint and Loads

This model is loaded by force mode. The rigid pad is added to the local compression position. The shell 63 element is adopted to prevent the stress concentration to cause that the calculation does not converge.A fixed end is applied at the bottom of the wallboard, and the top is the free end.


### 2.2. Solving and Postprocessing

The nonlinear analysis of the wall panel is carried out, and the mechanical properties of the components in the force process are obtained through the general postprocessing and the time postprocessing.In addition, the prefabricated shear wall model structure is shown in Figure1.Figure 1
Finite element model of prefabricated shear wall structure.The single axis strain-stress relation diagram of the concrete in Figure1 is shown in Figure 2(a), and the stress-strain curve of steel bar is shown in Figure 2(b).Figure 2
The stress-strain curve of material. (a)Single axis stress-strain relation diagram of concrete and (b) stress-strain curve of steel bar.
(a)(b)According to the provisions of the “Technical specification for concrete structure of high rise buildings,” under the action of representative value of neutral load, the axial pressure of the one, two, and three grade shear wall limbs is not suitable for the following restrictions: first class (9°): the limit of corresponding axial-compression ratio is 0.4, another level (6°, 7°, and 8°) the limit of corresponding axial-compression ratio is 0.5, and the limit of the axial compression ratio of second or third level is 0.6.In this paper, the axial compression ratio is 0.4, 0.5, and 0.6 [8], and the vertical load of the prefabricated shear wall structure is calculated according to formula (1).(1)μ=Nfc∗A,where A represents the area of the full section of the shear wall, N represents the axial pressure value of the section of shear wall, and μ represents the load value.According to the formula (1), there are(2)N1=0.4∗fc∗A=686kN,N2=0.5∗fc∗A=859kN,N3=0.6∗fc∗A=1030kN.Through the above calculation, the maximum bearing capacity of the vertical load of the prefabricated shear wall structure is 1030 kN. According to the provisions of the “Technical specification for concrete structure of high rise buildings,” the maximum horizontal displacement and height ratioΔμ/h of the floor layer between the floor layers under the stress load calculated by the elastic method conform to Table 1 [9, 10].Table 1
Ratio of maximum horizontal displacement to height.
Structural systemΔμ∕h limitFrame1/550Frame-shear wall, frame-core tube, and flat plate-column-shear wall1/800Tube in tube, shear wall1/1000The transformation layer other than the frame structure1/1000According to Table1, the calculated maximum displacement of the wall panel is 3 mm. When the vertex displacement of 3 mm can be obtained by using the formula (3), the horizontal load of the prefabricated shear wall structure is 36 kN, that is, the horizontal load under normal serviceability limit state.(3)wmax=FlEI,where F represents the load on the model, l represents the length of the model after the deformation, E represents the modulus of elasticity of the model, and I represents the I shaped section of the model.According to “The technical regulations of high building concrete structure,” there are as follows:(4)V≤1λ−10.5fy∗b∗h+0.13NAwsh,where V represents displacement, Aw represents the area of I shaped or T shaped cross-section shear wall, λ represents the shear span ratio of section, s represents the horizontal distribution of reinforcement spacing of shear wall, b represents the section width, and h represents the effective height of the model.According to formula (4), the shear capacity of the prefabricated shear wall structure is 123.8 kN; that is, the horizontal load under the ultimate bearing capacity of the prefabricated shear wall structure.Figure3 is the maximum stress change of the perforated rebar in the prefabricated shear wall structure, and Figure 4 is the maximum stress change of the connecting steel plate.Figure 3
The maximum stress change of perforated rebar.Figure 4
Maximum stress change of connecting steel plate.According to Figures3 and 4, it is known that at the initial stage of loading displacement, the connections are in the elastic deformation stage. When the displacement is loaded to 25 mm, the maximum stress of the connecting steel plate is 227 Mpa and enters the yield stage. Then, when the displacement is loaded to 45 mm, the perforated rebar enters the yield stage, and the maximum stress is 380 Mpa. When the displacement is loaded to 52 mm, the maximum stress of the steel plate begins to increase and enters the stage of plastic hardening. When the displacement is loaded to 55 mm, the perforated rebar enters the plastic hardening stage. When the displacement is loaded to 75 mm, the connecting steel plate reaches the limit stress 310 Mpa and enters the necking deformation stage. When the specimen is completely destroyed, the connecting steel plate is completely broken, but the reinforcing bar does not destroy.There are two main reasons for structural vibration energy dissipation: structural damping energy dissipation and elastoplastic energy dissipation.Damping and elasticity are one of the most important properties of the structure. When the structure is in the case of elastic vibration, the damping causes the dissipation of the structure energy. When the deformation of the structure exceeds the elastic limit, the structure will undergo plastic deformation. After unloading, the deformation of the structure cannot be completely recovered and there will be residual deformation and energy dissipation. According to “The technical specification for concrete structures of tall buildings,” the energy dissipation capacity of specimens should be measured by the area enclosed by the load-displacement curve [11–14]. Figure 5 is a schematic diagram for calculating the energy dissipation and equivalent viscous damping coefficients of specimens.Figure 5
Diagram for calculating energy dissipation and equivalent viscous damping coefficient for prefabricated shear wall structure.The energy dissipation factor is the ratio of the energy consumed by a hysteresis loop to load and unload for a circle to the total energy of loading and unloading. The energy dissipation factorE′ of the specimen [15–18] can be calculated by formula (5).(5)E′=SA′BC+SCDA′SΔBOE′+SΔDOF′.In the force response analysis of prefabricated shear wall structure [19–21], the equivalent viscous damping coefficient he is often used to carry out the pressure analysis. The equivalent viscous damping coefficient he can be calculated by using the formula (6).(6)he=E′2π.Figure6 is the energy dissipation diagram for each specimen of prefabricated shear wall structure:Figure 6
Energy dissipation diagram for each specimen of prefabricated shear wall structure.According to Figure6, it can see that with the increase of the displacement, the hysteretic curve of the specimen tends to be full and the energy consumption increases gradually. The energy dissipation capacity of the specimens under high axial compression ratio is relatively large, whether it is the connecting steel or the connecting steel plate in the prefabricated shear wall structure [22–24].Figure7 is the diagram of equivalent viscous damping coefficient of each specimen in a prefabricated shear wall structure.Figure 7
Equivalent viscous damping coefficient diagram of each specimen in prefabricated shear wall structure.As can be seen from Figure7, with the increase of displacement, the hysteresis loops of all the specimens in the prefabricated shear wall structure are gradually full, and the equivalent damping coefficient is increasing.


## 2.1. The Model is Established

### 2.1.1. Defining the Element Properties

The concrete is defined, the distribution unit type is SOLID65 unit, and the proper real constant and material model are selected. In considering the reinforced modeling, the internal structure of the structure is defined by the reinforcement ratio of the longitudinal reinforcement and the distribution of reinforcement in the real constant [6].


### 2.1.2. The Division of Grid

The grid division is divided by swept grid and the source surface grid is divided by the mapped grid. The grid precision is controlled within 100 mm [7].


### 2.1.3. Applying Constraint and Loads

This model is loaded by force mode. The rigid pad is added to the local compression position. The shell 63 element is adopted to prevent the stress concentration to cause that the calculation does not converge.A fixed end is applied at the bottom of the wallboard, and the top is the free end.


## 2.1.1. Defining the Element Properties

The concrete is defined, the distribution unit type is SOLID65 unit, and the proper real constant and material model are selected. In considering the reinforced modeling, the internal structure of the structure is defined by the reinforcement ratio of the longitudinal reinforcement and the distribution of reinforcement in the real constant [6].


## 2.1.2. The Division of Grid

The grid division is divided by swept grid and the source surface grid is divided by the mapped grid. The grid precision is controlled within 100 mm [7].


## 2.1.3. Applying Constraint and Loads

This model is loaded by force mode. The rigid pad is added to the local compression position. The shell 63 element is adopted to prevent the stress concentration to cause that the calculation does not converge.A fixed end is applied at the bottom of the wallboard, and the top is the free end.


## 2.2. Solving and Postprocessing

The nonlinear analysis of the wall panel is carried out, and the mechanical properties of the components in the force process are obtained through the general postprocessing and the time postprocessing.In addition, the prefabricated shear wall model structure is shown in Figure1.Figure 1
Finite element model of prefabricated shear wall structure.The single axis strain-stress relation diagram of the concrete in Figure1 is shown in Figure 2(a), and the stress-strain curve of steel bar is shown in Figure 2(b).Figure 2
The stress-strain curve of material. (a)Single axis stress-strain relation diagram of concrete and (b) stress-strain curve of steel bar.
(a)(b)According to the provisions of the “Technical specification for concrete structure of high rise buildings,” under the action of representative value of neutral load, the axial pressure of the one, two, and three grade shear wall limbs is not suitable for the following restrictions: first class (9°): the limit of corresponding axial-compression ratio is 0.4, another level (6°, 7°, and 8°) the limit of corresponding axial-compression ratio is 0.5, and the limit of the axial compression ratio of second or third level is 0.6.In this paper, the axial compression ratio is 0.4, 0.5, and 0.6 [8], and the vertical load of the prefabricated shear wall structure is calculated according to formula (1).(1)μ=Nfc∗A,where A represents the area of the full section of the shear wall, N represents the axial pressure value of the section of shear wall, and μ represents the load value.According to the formula (1), there are(2)N1=0.4∗fc∗A=686kN,N2=0.5∗fc∗A=859kN,N3=0.6∗fc∗A=1030kN.Through the above calculation, the maximum bearing capacity of the vertical load of the prefabricated shear wall structure is 1030 kN. According to the provisions of the “Technical specification for concrete structure of high rise buildings,” the maximum horizontal displacement and height ratioΔμ/h of the floor layer between the floor layers under the stress load calculated by the elastic method conform to Table 1 [9, 10].Table 1
Ratio of maximum horizontal displacement to height.
Structural systemΔμ∕h limitFrame1/550Frame-shear wall, frame-core tube, and flat plate-column-shear wall1/800Tube in tube, shear wall1/1000The transformation layer other than the frame structure1/1000According to Table1, the calculated maximum displacement of the wall panel is 3 mm. When the vertex displacement of 3 mm can be obtained by using the formula (3), the horizontal load of the prefabricated shear wall structure is 36 kN, that is, the horizontal load under normal serviceability limit state.(3)wmax=FlEI,where F represents the load on the model, l represents the length of the model after the deformation, E represents the modulus of elasticity of the model, and I represents the I shaped section of the model.According to “The technical regulations of high building concrete structure,” there are as follows:(4)V≤1λ−10.5fy∗b∗h+0.13NAwsh,where V represents displacement, Aw represents the area of I shaped or T shaped cross-section shear wall, λ represents the shear span ratio of section, s represents the horizontal distribution of reinforcement spacing of shear wall, b represents the section width, and h represents the effective height of the model.According to formula (4), the shear capacity of the prefabricated shear wall structure is 123.8 kN; that is, the horizontal load under the ultimate bearing capacity of the prefabricated shear wall structure.Figure3 is the maximum stress change of the perforated rebar in the prefabricated shear wall structure, and Figure 4 is the maximum stress change of the connecting steel plate.Figure 3
The maximum stress change of perforated rebar.Figure 4
Maximum stress change of connecting steel plate.According to Figures3 and 4, it is known that at the initial stage of loading displacement, the connections are in the elastic deformation stage. When the displacement is loaded to 25 mm, the maximum stress of the connecting steel plate is 227 Mpa and enters the yield stage. Then, when the displacement is loaded to 45 mm, the perforated rebar enters the yield stage, and the maximum stress is 380 Mpa. When the displacement is loaded to 52 mm, the maximum stress of the steel plate begins to increase and enters the stage of plastic hardening. When the displacement is loaded to 55 mm, the perforated rebar enters the plastic hardening stage. When the displacement is loaded to 75 mm, the connecting steel plate reaches the limit stress 310 Mpa and enters the necking deformation stage. When the specimen is completely destroyed, the connecting steel plate is completely broken, but the reinforcing bar does not destroy.There are two main reasons for structural vibration energy dissipation: structural damping energy dissipation and elastoplastic energy dissipation.Damping and elasticity are one of the most important properties of the structure. When the structure is in the case of elastic vibration, the damping causes the dissipation of the structure energy. When the deformation of the structure exceeds the elastic limit, the structure will undergo plastic deformation. After unloading, the deformation of the structure cannot be completely recovered and there will be residual deformation and energy dissipation. According to “The technical specification for concrete structures of tall buildings,” the energy dissipation capacity of specimens should be measured by the area enclosed by the load-displacement curve [11–14]. Figure 5 is a schematic diagram for calculating the energy dissipation and equivalent viscous damping coefficients of specimens.Figure 5
Diagram for calculating energy dissipation and equivalent viscous damping coefficient for prefabricated shear wall structure.The energy dissipation factor is the ratio of the energy consumed by a hysteresis loop to load and unload for a circle to the total energy of loading and unloading. The energy dissipation factorE′ of the specimen [15–18] can be calculated by formula (5).(5)E′=SA′BC+SCDA′SΔBOE′+SΔDOF′.In the force response analysis of prefabricated shear wall structure [19–21], the equivalent viscous damping coefficient he is often used to carry out the pressure analysis. The equivalent viscous damping coefficient he can be calculated by using the formula (6).(6)he=E′2π.Figure6 is the energy dissipation diagram for each specimen of prefabricated shear wall structure:Figure 6
Energy dissipation diagram for each specimen of prefabricated shear wall structure.According to Figure6, it can see that with the increase of the displacement, the hysteretic curve of the specimen tends to be full and the energy consumption increases gradually. The energy dissipation capacity of the specimens under high axial compression ratio is relatively large, whether it is the connecting steel or the connecting steel plate in the prefabricated shear wall structure [22–24].Figure7 is the diagram of equivalent viscous damping coefficient of each specimen in a prefabricated shear wall structure.Figure 7
Equivalent viscous damping coefficient diagram of each specimen in prefabricated shear wall structure.As can be seen from Figure7, with the increase of displacement, the hysteresis loops of all the specimens in the prefabricated shear wall structure are gradually full, and the equivalent damping coefficient is increasing.


## 3. Experimental Results and Analysis

In order to verify the correctness of finite element analysis results of prefabricated shear wall structures [25–27], an experiment is needed to verify the above results. The experimental platform is built on MATLAB.The prefabricated shear wall structure is taken as the experimental object, and the pressure is applied to record and track its bearing changes. The overall experimental results are as follows.From Figure8, we can see that the ultimate load of the shear wall finite element simulation is higher than the actual result, because the concrete vibration is not enough, and the specimen maintenance process is not up to standard, but the material in finite element simulation is not defective.Figure 8
Agreement between hysteretic curve of the shear wall structure by using the proposed method with the actual value. (a) Hysteretic curve of simulated prefabricated shear wall structure and (b) hysteretic curve of actual prefabricated shear wall structure.
(a)(b)However, the hysteretic curve of the finite element simulation of prefabricated shear wall is quite different from the actual result, and it can be found that the modeling of the finite element is correct.As shown in Figure9, the stiffness degradation values in the initial stage of the literature method and the proposed method are in high agreement with the actual values and are in a state of basic level. But with the changing value of displacement, the simulated value of the literature methods gradually deviated from the actual value curve. In the process of small displacement loading, the stiffness of all the specimens in the structure degenerates greatly and the loading continues to continue. The proposed method presents the advantages and is in a relatively consistent state with the actual stiffness degradation curve.Figure 9
Agreement between simulated values of the overall stiffness degradation of prefabricated shear walls by different methods and actual values.Figures10–13show the fitting degree of the maximum displacement and load relation between simulated values of different methods and actual values; the fitting degree of the maximum strain and displacement relationship between the simulated value of different methods and the actual value; the fitting degree of the simulated values of different methods and the actual values between the stress distribution and the load relation; the fitting degree of the displacement changes of different methods and the actual value under the different friction coefficients.Figure 10
The fitting degree of the maximum displacement and load relation between the simulated value of the different methods and the actual value.Figure 11
The fitting degree of the maximum strain and displacement relation between the simulated values of different methods and the actual values.Figure 12
The fitting degree of stress distribution and load relation between the simulated values of different methods and the actual values.Figure 13
The fitting degree of the displacement changes of different methods and the actual value under the different friction coefficients.The analysis of Figures10–13 shows that the simulated value of the maximum displacement and load relation of the proposed method are fitted to the actual value. The maximum strain and displacement relation between the simulated value and the actual value is fitted, and the relationship between stress distribution and load relation of the simulated value and the actual value is fitted. The fitting degree of the displacement changes of different methods and the actual value under the different friction coefficients is better than that of the literature method. This is because in the establishment of finite element model of prefabricated shear wall structure, the grid is divided by using sweep grid division, the control of grid precision is within 100 mm, and the force analysis of the model is always carried out according to “The technical specification for concrete structure of high rise buildings.” Moreover, the energy dissipation of shear wall structure and the equivalent viscous damping coefficient are analyzed in detail, and the overall analysis accuracy of the method is improved.


## 4. Conclusions

Prefabricated shear wall structure is a highly applied energy-saving building material. Its stress performance analysis is the key to promote the development of technology in this field. At present, there are various problems in the analysis of the force performance. Aiming at these problems, this paper puts forward a new research method, to construct the finite element model of prefabricated shear wall structure by using the ANSYS and prove the feasibility of the proposed method through experiments, which can provide a scientific basis for the development of this field.



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*Source: 4633128-2022-10-10.xml*