# Experiment and Simulation on the Anticollision Performance of a New Corrugated Steel Protection System for Bridge Piers

Authors: Guicheng Chen; Haidong Huang; Zhongfu Xiang
Journal: Shock and Vibration
 (2022)

---

## Abstract

To ensure the safety of ships and bridges at the same time during collisions, a new type of bridge pier protection system is proposed, in which one is composed of corrugated steel plates, bolts, and corrugated steel pipes (CSP), and the other is composed of ordinary steel plates, bolts, and corrugated steel pipes (OSP). To study their anticollision performance, a pendulum impact test and numerical simulation were carried out. Comparing the test results with the simulation results, it was shown that the simulation results are basically consistent with the test results. Then, the influence curves of the impact velocity, specimen thickness, weight, and frequency are analysed to evaluate the anticollision performance of CSP/OSP and optimize their structure. When the impact energy is low, the peak values of the lateral impact force and lateral displacement of the column equipped with OSP are all smaller than those of the column equipped with CSP. When the impact energy is high, the peak values of the lateral impact force and lateral displacement of the column equipped with OSP are larger than those of the column equipped with CSP. However, under the same impact energy, the total energy peak value of the CSP specimen is larger than that of the OSP specimen. Results can provide a certain numerical analysis basis for the structural design and research of new types of corrugated steel protection system for bridge pier.


---

## Body

## 1. Introduction

The accident of a ship hitting a bridge pier causes serious economic losses and casualties [1,2]. Especially with the increasing number of ships and their upsizing, the probability and risk of bridge piers being impacted have gradually increased. Therefore, bridges crossing inland waterways and coastal waterways must be designed to have anticollision properties. At present, two main ways are used to improve the impact resistance of bridges. One is to improve the impact resistance of the piers, and the other is to add anticollision facilities. During collisions, to ensure the safety of ships and bridges at the same time, adding anticollision facilities is feasible.AASHTO [3] provides some classic anticollision systems such as baffle systems, pile support systems, artificial island systems, and floating protection systems. Chen [4] proposed two new protection methods, namely, new materials and flexible energy consumption. Peng [5] summarized the development of anticollision facilities in 25 years, gave the application scenarios of 18 anticollision facilities in different regions, and compared the impact force changes before and after the addition. Chen [6] designed a new device to prevent ships from colliding with bridge piers called a flexible steel rope anticollision device. Jiang et al. [7] used a new material FRP to design an anticollision pontoon. Zhou et al. [8] proposed a steel-CFRP combined with an anticollision box. Shan and Huang [9] proposed a curve-shaped anticollision floating box of a bridge pier with a sandwich structure. These types of anticollision facilities have good anticollision effects and can effectively reduce the impact force during an impact. However, the cost is relatively high, the production process is complicated, they are difficult to industrialize, and the construction period is long. The honeycomb structure has good energy absorption and dissipation characteristics [10–12] and is an excellent type of anticollision facility structure. A new type of honeycomb pier anticollision facility with corrugated steel plates, bolts, and corrugated steel pipes (CSP) or ordinary steel plates, bolts, and corrugated steel pipes (OSP) as the structural element is proposed. It absorbs energy through the deformation of corrugated steel plates (or ordinary steel plates) and corrugated steel pipes, prolonging the impact time and reducing the impact force.Corrugated steel is widely used in engineering fields such as pipelines, culverts, buildings, and bridges. Fang et al. [13] analysed the axial mechanical behaviour of concrete-filled corrugated steel tube columns. Nassirnia et al. [14] proposed a hollow corrugated column by incorporating ultra-high-strength steel tubes and analysed its compression behaviour and buckling shape under axial load. Wojcik et al. [15] conducted full-scale filling and emptying tests on a medium-size steel cylindrical flat bottom silo with horizontally corrugated walls and columns composed of open-sectional thin-walled profiles, and the test results were different from those of Eurocode1. Kearns et al. [16] used simulated vehicle loads to conduct experimental research on corrugated steel ellipse culverts. The test results showed that the bending moment seriously affects the bearing capacity of corrugated steel ellipse culverts. Garcia and Moore [17] conducted laboratory tests on the joints in buried gravity flow pipelines to obtain the failure mode. Beben [18] studied the effect of backfill quality on corrugated steel plate culverts using three-dimensional numerical simulation and experimental comparison. Li et al. [19] used experimental methods to study an existing rehabilitated reinforced concrete rehabilitated with a grouted corrugated steel pipe. Regier et al. [20] conducted experimental research on deteriorated corrugated steel pipes, and the results showed that the corrosion level affects the bearing capacity of corrugated steel culverts. Yang et al. [21] used parametric numerical simulations to simulate the mechanical behaviour of helical corrugated steel pipes under axial tension, bending, and internal pressure loads and combined the simulations with a multiobjective optimization algorithm to propose an optimization method for the structural design of liquefied natural gas cryogenic helical corrugated pipes. Guo et al. [22] analysed the characteristic buckling of the concrete-infilled double steel corrugated-plate wall and studied its overall elastic buckling behaviour under axial load. Wang et al. [23] proposed a new type of shear wall with concrete-filled steel tubular frames and a corrugated steel plate and studied its seismic performance. Zhu et al. [24,25] conducted experiments and numerical studies on concrete-infilled double steel corrugated-plate walls, and the results showed that the walls had good seismic performance and bearing capacity. Wang et al. [26,27] used comparative experiments and numerical analysis methods to analyse the axial load-bearing characteristics and bending-torsion characteristics of concrete-infilled double steel corrugated-plate walls with T-section. Leblouba et al. [28,29] studied the shear characteristics of corrugated web steel beams. Zhou et al. [30] studied the torsion behaviour of prestressed composite box girders with corrugated steel webs. Zhou and An [31] studied the shear performance of nonprismatic beams with steel trapezoidal corrugated webs by numerical simulation and experiment. He et al. [32,33] conducted model tests on composite box girders with corrugated webs and steel tube slabs to study their structural damage mechanisms. Si et al. [34] analysed the difference in the dynamic response of deck pavement of two kinds of box girder bridges. Maslak et al. [35] used experimental and numerical analysis methods to study the steel corrugated arch sheets exposed to fire. Wu et al. [36] used numerical analysis and test methods to study the buckling behaviour and failure mode of steel circular closed supports with I-sections of sinusoidal corrugated webs. Fan et al. [37] used impact tests and finite element methods to study the anticollision performance of UHPFRC-based protective structures for bridge columns. Zhao et al. [38] conducted a combined test study of the axial and horizontal cyclic load on corrugated double-skin composite walls. Niknejad et al. [39] used quasi-static test methods to study the energy absorption characteristics of circular corrugated tubes under axial and lateral pressure. Studies have shown that corrugated steel plates or corrugated steel pipes have good characteristics such as shear resistance, bending resistance, torsion resistance, seismic resistance, and energy absorption, but the anticollision performance has not been studied in depth, so numerical simulation research on its anticollision performance has a major significance.In summary, this paper carries out numerical simulation research according to the pendulum impact test and studies the anticollision performance of CSP/OSP specimen. In addition, the relationship curve between the CSP/OSP specimen thickness and the peak value of the simulation results is analysed to evaluate the anticollision performance of CSP/OSP and its energy dissipation effect. The research results can provide a certain theoretical and experimental basis for the design and analysis of the two types of corrugated steel protection system for bridge pier.


## 2. Establishment and Verification of the Numerical Model of Pendulum Impact Test

In order to accurately evaluate the anticollision performance of the CSP/OSP specimens, a finite element model is established according to the geometric structure of the pendulum impact test for numerical simulation, and the entire pendulum impact test process is analysed in detail.


### 2.1. Pendulum Impact Test

The setting, data acquisition and processing, test phenomena, test results, and analysis of pendulum impact test have been introduced and discussed in detail in [40], which will not be repeated here.


### 2.2. Geometric Structure

The geometric structure of the CWACF-12.0 specimen is shown in Figure1(a). Waveform parameter of the corrugated steel plate (wave distance × wave depth) is 400 mm × 150 mm, and that of the corrugated steel pipe is 200 mm × 55 mm. The geometric structures of the CSP and OSP specimens are shown in Figures 1(b) and 1(c), respectively.Figure 1
Geometry of the specimen (unit: mm). (a) CWACF-12.0 specimen geometry. (b) OSP specimen geometry. (c) CSP specimen geometry.
(a)(b)(c)


### 2.3. Finite Element Model

Huang et al. [41] analysed the anticollision performance of flexible anticollision rings in different operating conditions through numerical simulation and experiments. Zhang et al. [42] used scale model tests and three-dimensional numerical models to analyse the failure modes of segmented precast columns under impact loads. Do et al. [43] used the pendulum impact test and numerical simulation to study the failure mode of a car hitting a bridge pier. Zhang and Hu [44] obtained the mechanical properties of bolt splicing through accurate finite element analysis and proposed a feasible simplified simulation method for bolts. Zhang et al. [42] used bolts to connect the impact test model to the bottom of the laboratory. Under the pretightening force of the bolts, the bottom of the model column did not move or rotate.ANSYS/LS-DYNA is a display dynamics program based on a display solution, suitable for solving impact and collision problems. The steel plate and the corrugated steel pipe are connected by high-strength bolts. In the numerical simulation, the high-strength bolts are simplified to the beam element, and the beam element algorithm SPOTWELD-BEAM is called in combination with the keyword∗INITIAL_AXIAL_FROCE_BEAM to apply pretightening force. The bolt pretightening force setting is assembled according to the impact test specimen. In the numerical simulation, the pretightening forces of M60 high-strength bolts and M12 high-strength bolts are set to 100 and 50 N, respectively. The connection between bolts and steel plates and steel pipes can be realized through the keyword ∗CONSTRAINED_NODAL_RIGID_BODY. The coefficients of static friction and dynamic friction between steels are 0.2 and 0.1, respectively. The static and dynamic friction coefficients of the base and the laboratory floor are set to 0.8 and 0.6, respectively, according to the friction coefficient [45] between iron and rubber to increase its relative sliding resistance. The contact between the pendulum and the steel plate, the contact between the steel plate and the column, and the contact between the base and the laboratory floor can be realized through the keyword ∗CONTACT_AUTOMATIC_SURFACE_TO_SURFACE. The self-contact between the steel plate and the corrugated steel pipe can be realized through the keyword ∗CONTACT_AUTOMATIC_SINGLE_SURFACE. The boundary condition is set as that one end of the connection between M60 bolt and laboratory floor is consolidation constraint. The laboratory floor is treated as a fixed rigid part. The element grid data is summarized in Table 1. CSP-2.75-4 field test model and its corresponding finite element model are shown in Figure 2.Table 1
Composition of the finite element model.
ComponentElementElement formulationSizeTotal numberBaseSolid212  mm × 12  mm × 12  mm58607ColumnSolid212  mm × 12  mm × 12  mm26795PendulumSolid212  mm × 12  mm × 12  mm6360M12Beam91.2  mm45M60Beam96  mm220Corrugated steel plateShell212  mm × 12  mm20248Corrugated steel pipeShell212  mm × 12  mm26229Ordinary steel plateShell212  mm × 12  mm10176FloorShell230  mm × 30  mm1593Approach slabShell210  mm × 10  mm567Figure 2
Description of model and case number. (a) Field test model of CSP-2.75-4; (b) finite element model of CSP-2.75-4; (c) description of the case number of the column without anticollision facilities; (d) description of the case number of the column equipped with CSP/OSP.
(a)(b)(c)(d)


### 2.4. Material Model

Zhi et al. [46], on the basis of the quasi-static tensile, high-temperature tensile, and dynamic tensile test data of Q235B, proposed that the Cowper-Symonds constitutive relationship in ANSYS/LS-DYNA is suitable for low-speed collisions in the engineering field. The material model ∗MAT_PLASTIC_KINEMATIC (MAT_003) in LS-DYNA can consider the influence of strain rate. Given that the corrugated steel plate and corrugated steel pipe are cold-formed [13], the yield strength is improved and the plasticity is reduced. The elastic-plastic material model ∗MAT_PIECEWISE_LINEAR_PLASTICITY (MAT_024) in ANSYS/LS-DYNA can consider the isotropic and kinematic hardening plasticity of the material, allowing the definition of any stress-strain relationship curve and the influence of strain rate. The influence of strain rate changes on the constitutive relationship of steel has been discussed by Kim et al. [47], Paik et al. [48], Park et al. [49], and Rokaya and Kim [50]. Figure 3 shows the stress-strain curve of the steel used in the numerical simulation based on the test measurement. The SPOTWELD-BEAM algorithm requires that it can only be used in conjunction with the material model ∗MAT_SPOTWELD (∗MAT_100) in ANSYS/LS-DYNA, so this material model can only be used to define the constitutive relationship of the bolt. The laboratory floor is very rigid. When using shell element simulation, it will be regarded as a rigid body, so its material model is defined by ∗MAT_RIGID (MAT_001). The material characteristic parameters are shown in Table 2.Figure 3
Stress-strain curve.Table 2
Material characteristic parameters.
MaterialLS-DYNA material modelDensityYoung’s modulusPoisson’s ratioYield stressCorrugated steel∗MAT_PIECEWISE_LINEAR_PLASTICITY7850 kg/m³176 GPa0.31390 MPaOrdinary steel∗MAT_PIECEWISE_LINEAR_PLASTICITY7850 kg/m³206 GPa0.31235 MPaHigh-strength bolts∗MAT_SPOTWELD7850 kg/m³206 GPa0.30640 MPaPendulum∗MAT_PLASTIC_KINEMATIC3000 kg/m³206 GPa0.311200 MPaLaboratory floor∗MAT_RIGID2600 kg/m³34.5 GPa0.2—


### 2.5. Model Calibration and Comparisons

The simulation results are verified by the impact test results provided in [40]. Taking CSP-2.75-4 and OSP-2.75-4 as examples, the deformation of the steel plate at the impact is shown in Figure 4. The experimental and simulation results of the deformation of the steel plate of CSP/OSP are basically consistent. When the specimen thickness is the same, the deformation of the outer steel plate increases with the increase of the impact velocity. When the impact velocity is the same, the deformation of the outer steel plate decreases with the increase of the specimen thickness.Figure 4
Deformation of steel plate at the impact. (a) CSP-2.75-4; (b) OSP-2.75-4.
(a)(b)Taking the direction balanced with the initial impact velocity as the positive direction of the lateral displacement, the lateral displacement field and the time history curves of the lateral displacement at the top of the column are shown in Figure5. Figure 5(c) shows that the trend of the time history curve of the lateral displacement at the top of the CSP-2.75-4 column is highly similar. The simulation and test results of the peak value of the lateral displacement of point D are 2.49 mm. The test results and simulation results of the lateral displacement field of the CSP-2.75-4 column at 10 ms are shown in Figures 5(a) and 5(b), respectively. The lateral displacement at the top position is 1.65 mm, that at the 3/4 position is 1.32 mm, that at the middle position is 0.986 mm, and that at the 1/4 position is 0.49 mm. It is shown that the test results of lateral displacement field of column are basically consistent with the simulation results.Figure 5
Comparison between experimental results and simulation results of lateral displacement field and lateral displacement time history curve of column (unit: mm). (a) The experimental result of CSP-2.75-4; (b) simulation result of CSP-2.75-4; (c) time history curve of CSP-2.75-4; (d) CSP; (e) OSP; (f) CWACF-12.0.Taking the impact velocity of 4 m/s as an example, the time history curves of the lateral displacement at the top of the column of CSP, OSP, and CWACF-12.0 obtained by the impact test and simulation are shown in Figures5(d)–5(f), respectively. It is shown that the time of CSP column returning to the initial position is greater than that of OSP, and CSP/OSP can effectively reduce the peak value of the lateral displacement at the top of the column. With the increase of impact velocity, the peak value of the lateral displacement at the top of the column also increases. The smaller the plate thickness of CSP/OSP specimen, the smaller the peak value of the lateral displacement at the top of the column.The comparison between the test results and simulation results of displacement and deformation fully shows that the established finite element model can accurately simulate the whole experimental process of pendulum impact.


## 2.1. Pendulum Impact Test

The setting, data acquisition and processing, test phenomena, test results, and analysis of pendulum impact test have been introduced and discussed in detail in [40], which will not be repeated here.


## 2.2. Geometric Structure

The geometric structure of the CWACF-12.0 specimen is shown in Figure1(a). Waveform parameter of the corrugated steel plate (wave distance × wave depth) is 400 mm × 150 mm, and that of the corrugated steel pipe is 200 mm × 55 mm. The geometric structures of the CSP and OSP specimens are shown in Figures 1(b) and 1(c), respectively.Figure 1
Geometry of the specimen (unit: mm). (a) CWACF-12.0 specimen geometry. (b) OSP specimen geometry. (c) CSP specimen geometry.
(a)(b)(c)


## 2.3. Finite Element Model

Huang et al. [41] analysed the anticollision performance of flexible anticollision rings in different operating conditions through numerical simulation and experiments. Zhang et al. [42] used scale model tests and three-dimensional numerical models to analyse the failure modes of segmented precast columns under impact loads. Do et al. [43] used the pendulum impact test and numerical simulation to study the failure mode of a car hitting a bridge pier. Zhang and Hu [44] obtained the mechanical properties of bolt splicing through accurate finite element analysis and proposed a feasible simplified simulation method for bolts. Zhang et al. [42] used bolts to connect the impact test model to the bottom of the laboratory. Under the pretightening force of the bolts, the bottom of the model column did not move or rotate.ANSYS/LS-DYNA is a display dynamics program based on a display solution, suitable for solving impact and collision problems. The steel plate and the corrugated steel pipe are connected by high-strength bolts. In the numerical simulation, the high-strength bolts are simplified to the beam element, and the beam element algorithm SPOTWELD-BEAM is called in combination with the keyword∗INITIAL_AXIAL_FROCE_BEAM to apply pretightening force. The bolt pretightening force setting is assembled according to the impact test specimen. In the numerical simulation, the pretightening forces of M60 high-strength bolts and M12 high-strength bolts are set to 100 and 50 N, respectively. The connection between bolts and steel plates and steel pipes can be realized through the keyword ∗CONSTRAINED_NODAL_RIGID_BODY. The coefficients of static friction and dynamic friction between steels are 0.2 and 0.1, respectively. The static and dynamic friction coefficients of the base and the laboratory floor are set to 0.8 and 0.6, respectively, according to the friction coefficient [45] between iron and rubber to increase its relative sliding resistance. The contact between the pendulum and the steel plate, the contact between the steel plate and the column, and the contact between the base and the laboratory floor can be realized through the keyword ∗CONTACT_AUTOMATIC_SURFACE_TO_SURFACE. The self-contact between the steel plate and the corrugated steel pipe can be realized through the keyword ∗CONTACT_AUTOMATIC_SINGLE_SURFACE. The boundary condition is set as that one end of the connection between M60 bolt and laboratory floor is consolidation constraint. The laboratory floor is treated as a fixed rigid part. The element grid data is summarized in Table 1. CSP-2.75-4 field test model and its corresponding finite element model are shown in Figure 2.Table 1
Composition of the finite element model.
ComponentElementElement formulationSizeTotal numberBaseSolid212  mm × 12  mm × 12  mm58607ColumnSolid212  mm × 12  mm × 12  mm26795PendulumSolid212  mm × 12  mm × 12  mm6360M12Beam91.2  mm45M60Beam96  mm220Corrugated steel plateShell212  mm × 12  mm20248Corrugated steel pipeShell212  mm × 12  mm26229Ordinary steel plateShell212  mm × 12  mm10176FloorShell230  mm × 30  mm1593Approach slabShell210  mm × 10  mm567Figure 2
Description of model and case number. (a) Field test model of CSP-2.75-4; (b) finite element model of CSP-2.75-4; (c) description of the case number of the column without anticollision facilities; (d) description of the case number of the column equipped with CSP/OSP.
(a)(b)(c)(d)


## 2.4. Material Model

Zhi et al. [46], on the basis of the quasi-static tensile, high-temperature tensile, and dynamic tensile test data of Q235B, proposed that the Cowper-Symonds constitutive relationship in ANSYS/LS-DYNA is suitable for low-speed collisions in the engineering field. The material model ∗MAT_PLASTIC_KINEMATIC (MAT_003) in LS-DYNA can consider the influence of strain rate. Given that the corrugated steel plate and corrugated steel pipe are cold-formed [13], the yield strength is improved and the plasticity is reduced. The elastic-plastic material model ∗MAT_PIECEWISE_LINEAR_PLASTICITY (MAT_024) in ANSYS/LS-DYNA can consider the isotropic and kinematic hardening plasticity of the material, allowing the definition of any stress-strain relationship curve and the influence of strain rate. The influence of strain rate changes on the constitutive relationship of steel has been discussed by Kim et al. [47], Paik et al. [48], Park et al. [49], and Rokaya and Kim [50]. Figure 3 shows the stress-strain curve of the steel used in the numerical simulation based on the test measurement. The SPOTWELD-BEAM algorithm requires that it can only be used in conjunction with the material model ∗MAT_SPOTWELD (∗MAT_100) in ANSYS/LS-DYNA, so this material model can only be used to define the constitutive relationship of the bolt. The laboratory floor is very rigid. When using shell element simulation, it will be regarded as a rigid body, so its material model is defined by ∗MAT_RIGID (MAT_001). The material characteristic parameters are shown in Table 2.Figure 3
Stress-strain curve.Table 2
Material characteristic parameters.
MaterialLS-DYNA material modelDensityYoung’s modulusPoisson’s ratioYield stressCorrugated steel∗MAT_PIECEWISE_LINEAR_PLASTICITY7850 kg/m³176 GPa0.31390 MPaOrdinary steel∗MAT_PIECEWISE_LINEAR_PLASTICITY7850 kg/m³206 GPa0.31235 MPaHigh-strength bolts∗MAT_SPOTWELD7850 kg/m³206 GPa0.30640 MPaPendulum∗MAT_PLASTIC_KINEMATIC3000 kg/m³206 GPa0.311200 MPaLaboratory floor∗MAT_RIGID2600 kg/m³34.5 GPa0.2—


## 2.5. Model Calibration and Comparisons

The simulation results are verified by the impact test results provided in [40]. Taking CSP-2.75-4 and OSP-2.75-4 as examples, the deformation of the steel plate at the impact is shown in Figure 4. The experimental and simulation results of the deformation of the steel plate of CSP/OSP are basically consistent. When the specimen thickness is the same, the deformation of the outer steel plate increases with the increase of the impact velocity. When the impact velocity is the same, the deformation of the outer steel plate decreases with the increase of the specimen thickness.Figure 4
Deformation of steel plate at the impact. (a) CSP-2.75-4; (b) OSP-2.75-4.
(a)(b)Taking the direction balanced with the initial impact velocity as the positive direction of the lateral displacement, the lateral displacement field and the time history curves of the lateral displacement at the top of the column are shown in Figure5. Figure 5(c) shows that the trend of the time history curve of the lateral displacement at the top of the CSP-2.75-4 column is highly similar. The simulation and test results of the peak value of the lateral displacement of point D are 2.49 mm. The test results and simulation results of the lateral displacement field of the CSP-2.75-4 column at 10 ms are shown in Figures 5(a) and 5(b), respectively. The lateral displacement at the top position is 1.65 mm, that at the 3/4 position is 1.32 mm, that at the middle position is 0.986 mm, and that at the 1/4 position is 0.49 mm. It is shown that the test results of lateral displacement field of column are basically consistent with the simulation results.Figure 5
Comparison between experimental results and simulation results of lateral displacement field and lateral displacement time history curve of column (unit: mm). (a) The experimental result of CSP-2.75-4; (b) simulation result of CSP-2.75-4; (c) time history curve of CSP-2.75-4; (d) CSP; (e) OSP; (f) CWACF-12.0.Taking the impact velocity of 4 m/s as an example, the time history curves of the lateral displacement at the top of the column of CSP, OSP, and CWACF-12.0 obtained by the impact test and simulation are shown in Figures5(d)–5(f), respectively. It is shown that the time of CSP column returning to the initial position is greater than that of OSP, and CSP/OSP can effectively reduce the peak value of the lateral displacement at the top of the column. With the increase of impact velocity, the peak value of the lateral displacement at the top of the column also increases. The smaller the plate thickness of CSP/OSP specimen, the smaller the peak value of the lateral displacement at the top of the column.The comparison between the test results and simulation results of displacement and deformation fully shows that the established finite element model can accurately simulate the whole experimental process of pendulum impact.


## 3. Simulation Results

The time history curves and peak values of the lateral impact force, energy, and lateral displacement were obtained by numerical simulation. The anticollision performance of CSP/OSP under impact load is analysed and evaluated by comparing the simulation results under different case.


### 3.1. The Characteristics of the Lateral Displacement

The time history curves of the lateral displacement at the top of the column with impact velocity of 4 m/s are introduced in Section2.5. The test results and simulation results of the lateral displacement peak values of each case are summarized in Table 3. The data shows that the experimental results are consistent with the numerical calculation results. As the impact velocity increases, the lateral displacement peak value at the top of the column also increases. The smaller the specimen thickness, the smaller the peak value of the lateral displacement at the top of column. When the impact velocity is 2 m/s, the lateral displacement peak value at the top of the column equipped with OSP is smaller than that of the column equipped with CSP. When the impact velocity is 3 and 4 m/s, the lateral displacement peak value of the top of the column equipped with OSP is larger than that of the column equipped with CSP.Table 3
Parameter study.
NumberH (mm)V (m/s)Weight (kg)Peak displacement (mm)Peak impact force (kN)Peak total energy (J)TestSimulationPendulum-CSP/OSPCSP/OSP-columnPendulum-columnCSP/OSPColumnCSP-2.75-22.752131.061.271.0738.2344.08—845.7016.49CSP-3.00-23.002145.901.411.1145.9050.87—827.9622.371CSP-3.50-23.502166.962.792.6659.8097.99—742.1564.57OSP-2.75-22.752118.04—1.0856.6433.8—762.8516.37OSP-3.00-23.002129.261.291.0459.4730.95—786.0616.90OSP-3.50-23.502145.402.082.2064.3733.51—748.6837.08CWACF-12.0-2—2—13.659.65——444.41—768.18CSP-2.75-32.753131.062.372.3943.6847.92—1859.1346.39CSP-3.00-33.003145.902.322.3452.9555.11—1873.3650.64CSP-3.50-33.503166.963.563.1266.06116.12—1811.0891.85OSP-2.75-32.753118.04—2.62123.5372.56—1569.01103.76OSP-3.00-33.003129.263.632.64131.5264.13—1567.23106.00OSP-3.50-33.503145.405.214.51111.6061.51—1501.16116.79CWACF-12.0-3—3—17.2813.97——644.64—1853.22CSP-2.75-42.754131.062.492.4948.0350.86—3326.8448.07CSP-3.00-43.004145.903.322.4756.7058.06—3335.8457.45CSP-3.50-43.504166.965.575.4373.10121.34—3213.86143.00OSP-2.75-42.754118.04—3.47158.5383.86—2859.94181.30OSP-3.00-43.004129.265.234.10177.5996.29—2653.40256.23OSP-3.50-43.504145.4010.837.61185.70397.38—2350.74330.11CWACF-12.0-4—4—23.4018.08——793.83—3307.93


### 3.2. Characteristics of the Lateral Impact Force

Taking the direction that is balanced with the initial impact velocity as the positive direction of the lateral impact force, after numerical simulation, the time history curve of the lateral impact force of each case is obtained. Taking the impact velocity of 4 m/s as an example, the time history curves of the lateral impact force are shown in Figure6. The peak values of time history curves of the lateral impact force of each case are summarized in Table 3. The results show that the assembly of CSP/OSP can prolong the impact time and reduces the peak value of the lateral impact force. The peak values of the lateral impact force between CSP and pendulum or column are similar, while the force between OSP and pendulum is larger than that of column. The data show that the peak value of lateral impact force of column equipped with OSP is not significantly affected by the change of specimen thickness, but the column equipped with CSP is significantly affected. The smaller the specimen thickness, the smaller the peak value of the lateral impact force of column. When the impact velocity is small, OSP is more effective than CSP in reducing the peak value of the lateral impact force of the column. When the impact velocity is high, CSP can effectively reduce the peak impact force on the column compared to OSP. CSP/OSP specimen can effectively reduce the peak value of lateral impact force of column. When the specimen thickness is constant, the peak value of the lateral impact force of column increases gradually with the increase of impact velocity.Figure 6
Time history curve of lateral impact force. (a) CSP; (b) OSP; (c) CWACF-12.0-4.
(a)(b)(c)


### 3.3. The Total Energy of CSP/OSP Specimen

The numerical analysis process follows the law of conservation of energy, and the time history curve of the total energy (kinetic energy + internal energy) of the CSP/OSP specimen is obtained by simulation. Taking the impact velocity of 4 m/s as an example, the time history curves of the total energy of the CSP/OSP specimen are shown in Figure7. The total energy peak value of CSP/OSP specimen decreases with the increase in the thickness of the specimen and finally it tends to a stable value. The total energy absorbed by CSP specimen is greater than that of OSP specimen. When the impact velocity is 2, 3, and 4 m/s, the total energy of the model system is 908.04, 2043.1, and 3632.16 J, respectively. The results show that the CSP/OSP specimens have obvious energy dissipation effects. With the increase of impact velocity, the total energy absorbed by CSP/OSP also increases, and CSP absorbs more total energy than OSP. Therefore, CSP/OSP specimens have obvious energy dissipation effect, and the of CSP specimen is stronger than the OSP one. The percentage of the total energy peak values of the CSP specimens is greater than that of the OSP specimens.Figure 7
The time history curves of the total energy of CSP/OSP specimen whenV = 4 m/s.


## 3.1. The Characteristics of the Lateral Displacement

The time history curves of the lateral displacement at the top of the column with impact velocity of 4 m/s are introduced in Section2.5. The test results and simulation results of the lateral displacement peak values of each case are summarized in Table 3. The data shows that the experimental results are consistent with the numerical calculation results. As the impact velocity increases, the lateral displacement peak value at the top of the column also increases. The smaller the specimen thickness, the smaller the peak value of the lateral displacement at the top of column. When the impact velocity is 2 m/s, the lateral displacement peak value at the top of the column equipped with OSP is smaller than that of the column equipped with CSP. When the impact velocity is 3 and 4 m/s, the lateral displacement peak value of the top of the column equipped with OSP is larger than that of the column equipped with CSP.Table 3
Parameter study.
NumberH (mm)V (m/s)Weight (kg)Peak displacement (mm)Peak impact force (kN)Peak total energy (J)TestSimulationPendulum-CSP/OSPCSP/OSP-columnPendulum-columnCSP/OSPColumnCSP-2.75-22.752131.061.271.0738.2344.08—845.7016.49CSP-3.00-23.002145.901.411.1145.9050.87—827.9622.371CSP-3.50-23.502166.962.792.6659.8097.99—742.1564.57OSP-2.75-22.752118.04—1.0856.6433.8—762.8516.37OSP-3.00-23.002129.261.291.0459.4730.95—786.0616.90OSP-3.50-23.502145.402.082.2064.3733.51—748.6837.08CWACF-12.0-2—2—13.659.65——444.41—768.18CSP-2.75-32.753131.062.372.3943.6847.92—1859.1346.39CSP-3.00-33.003145.902.322.3452.9555.11—1873.3650.64CSP-3.50-33.503166.963.563.1266.06116.12—1811.0891.85OSP-2.75-32.753118.04—2.62123.5372.56—1569.01103.76OSP-3.00-33.003129.263.632.64131.5264.13—1567.23106.00OSP-3.50-33.503145.405.214.51111.6061.51—1501.16116.79CWACF-12.0-3—3—17.2813.97——644.64—1853.22CSP-2.75-42.754131.062.492.4948.0350.86—3326.8448.07CSP-3.00-43.004145.903.322.4756.7058.06—3335.8457.45CSP-3.50-43.504166.965.575.4373.10121.34—3213.86143.00OSP-2.75-42.754118.04—3.47158.5383.86—2859.94181.30OSP-3.00-43.004129.265.234.10177.5996.29—2653.40256.23OSP-3.50-43.504145.4010.837.61185.70397.38—2350.74330.11CWACF-12.0-4—4—23.4018.08——793.83—3307.93


## 3.2. Characteristics of the Lateral Impact Force

Taking the direction that is balanced with the initial impact velocity as the positive direction of the lateral impact force, after numerical simulation, the time history curve of the lateral impact force of each case is obtained. Taking the impact velocity of 4 m/s as an example, the time history curves of the lateral impact force are shown in Figure6. The peak values of time history curves of the lateral impact force of each case are summarized in Table 3. The results show that the assembly of CSP/OSP can prolong the impact time and reduces the peak value of the lateral impact force. The peak values of the lateral impact force between CSP and pendulum or column are similar, while the force between OSP and pendulum is larger than that of column. The data show that the peak value of lateral impact force of column equipped with OSP is not significantly affected by the change of specimen thickness, but the column equipped with CSP is significantly affected. The smaller the specimen thickness, the smaller the peak value of the lateral impact force of column. When the impact velocity is small, OSP is more effective than CSP in reducing the peak value of the lateral impact force of the column. When the impact velocity is high, CSP can effectively reduce the peak impact force on the column compared to OSP. CSP/OSP specimen can effectively reduce the peak value of lateral impact force of column. When the specimen thickness is constant, the peak value of the lateral impact force of column increases gradually with the increase of impact velocity.Figure 6
Time history curve of lateral impact force. (a) CSP; (b) OSP; (c) CWACF-12.0-4.
(a)(b)(c)


## 3.3. The Total Energy of CSP/OSP Specimen

The numerical analysis process follows the law of conservation of energy, and the time history curve of the total energy (kinetic energy + internal energy) of the CSP/OSP specimen is obtained by simulation. Taking the impact velocity of 4 m/s as an example, the time history curves of the total energy of the CSP/OSP specimen are shown in Figure7. The total energy peak value of CSP/OSP specimen decreases with the increase in the thickness of the specimen and finally it tends to a stable value. The total energy absorbed by CSP specimen is greater than that of OSP specimen. When the impact velocity is 2, 3, and 4 m/s, the total energy of the model system is 908.04, 2043.1, and 3632.16 J, respectively. The results show that the CSP/OSP specimens have obvious energy dissipation effects. With the increase of impact velocity, the total energy absorbed by CSP/OSP also increases, and CSP absorbs more total energy than OSP. Therefore, CSP/OSP specimens have obvious energy dissipation effect, and the of CSP specimen is stronger than the OSP one. The percentage of the total energy peak values of the CSP specimens is greater than that of the OSP specimens.Figure 7
The time history curves of the total energy of CSP/OSP specimen whenV = 4 m/s.


## 4. Peak Analysis

To further investigate the anticollision performance of CSP/OSP, the impact velocity, specimen thickness, specimen weight, and specimen frequency effects on each peak values were studied, and the structure and energy dissipation effect of CSP/OSP are evaluated and optimized.


### 4.1. Impact Velocity

The curves of the ratio of the lateral displacement peak value at the top of the CSP/OSP column (DOSP(CSP)) to that of the CWACF column (DCWACF) are shown in Figure 8(a). When the impact velocity is small, the lateral displacement peak value ratio of CSP/OSP is basically close, but that of OSP-3.50 is less than that of CSP-3.50. When the impact velocity is large, the lateral displacement peak value ratio of CSP is small than that of OSP.Figure 8
Influence curves of impact velocity. (a) Ratio of lateral displacement peak value at the top of the column. (b) Ratio of total energy peak value of the CSP/OSP specimen. (c) Ratio of lateral impact force peak value.
(a)(b)(c)The curves of the ratio of the total energy peak value of CSP/OSP specimen (TEOSP(CSP)) to that of the model system (TESYS) are shown in Figure 8(b). The total energy peak value ratios of CSP-2.75 and CSP-3.00 are basically similar, but both are larger than those of CSP-3.50 and OSP. With the increase of impact velocity, the total energy peak value ratio of CSP tends to be stable, while that of OSP gradually decreases. Therefore, CSP/OSP can absorb most of the kinetic energy, and the proportion of CSP absorption is greater than that of OSP.The curves of the ratio of the lateral impact force peak value of the CSP/OSP column (PFOSP(CSP)) to that of the CWACF column (PFCWACF) are shown in Figure 8(c). The lateral impact force peak value ratio of CSP decreased with the increase of impact velocity, but that of the OSP increases with the increase of impact velocity. The ratio of CSP-3.50 is the largest. But when the impact velocity is small, the ratio of CSP is larger than that of OSP. When the impact velocity is large, the ratio of CSP is small than that of OSP.


### 4.2. Specimen Thickness

The curves of specimen thickness effect on the lateral displacement peak value, the total energy peak value of CSP/OSP specimen, and the lateral impact force peak value are shown in Figures9(a)–9(c), respectively. The influence curves of specimen thickness are all quadratic curves and have extreme points. With the increase of specimen thickness, the peak values of lateral impact force and lateral displacement first decrease and then increase, while the peak value of total energy first increases and then decreases.Figure 9
Influence curves of specimen thickness. (a) Lateral displacement peak value of the top of the column. (b) Total energy peak value of the CSP/OSP specimen. (c) Lateral impact force peak value.
(a)(b)(c)When the impact velocity is 2 m/s, the curve of the lateral displacement peak value of CSP intersects with that of OSP at (0, 9.65), (2.81, 1.00). Within [0, 2.81], the lateral displacement peak value of CSP is smaller than that of OSP, but within [2.81, 3.50], the lateral displacement peak value of CSP is larger than that of OSP. The curve of the total energy peak value of CSP specimen intersects with that of OSP at (0, 0), (3.00, 0.466). Within [0.00, 3.00], the total energy peak value of CSP specimen is larger than that of OSP, but, within [3.00, 3.5], the total energy peak value of CSP specimen is smaller than that of OSP. The curve of lateral impact force peak value of CSP intersects with that of OSP at (0,444.39), (2.61, 40.35). Within [0 2.61], the peak value of the lateral impact force of CSP is smaller than that of OSP, but, within [2.61 3.5], the peak value of the lateral impact force of CSP is larger than that of OSP.When the impact velocity is 3 m/s, the curve of the lateral displacement peak value of CSP intersects with that of OSP at (0, 13.97), (2.66, 2.37). Within [0.00 2.66], the lateral displacement peak value of CSP is larger than that of OSP, but, within [2.66, 3.50], the lateral displacement peak value of CSP is smaller than that of OSP. The curve of the total energy peak value of CSP specimen intersects with that of OSP specimen at (0, 0). Within [0 3.50], the total energy peak value of CSP specimen is larger than that of OSP specimen. The curve of the lateral impact force peak value of CSP intersects with that of OSP at (0,664.63), (3.05, 61.43). Within [0 3.05], the lateral impact force peak value of CSP is smaller than that of OSP, but, within [3.05 3.5], the lateral impact force peak value of CSP is larger than that of OSP.When the impact velocity is 4 m/s, the curve of the lateral displacement peak value of CSP intersects with that of OSP at (0, 18.08), (1.46, 4.28). Within [0.1.46], the lateral displacement peak value of CSP is slightly larger than that of OSP, but, within [1.46, 3.5], the lateral displacement peak value of CSP is smaller than that of OSP. The curve of total energy peak value of CSP specimen intersects with that of OSP at (0,0), (1.76, 2.31). Within [0, 1.76], the total energy peak value of CSP specimen is smaller than that of OSP, but, within [1.76, 3.50], the total energy peak value of CSP specimen is larger than that of OSP. The curve of the lateral impact force peak value of CSP intersects with that of OSP at (0,793.69), (3.31, 90.25). Within [0 3.31], the lateral impact force peak value of CSP is larger than that of OSP, but, within [3.31 3.5], the lateral impact force peak value of CSP is smaller than that of OSP.


### 4.3. Specimen Weight

The influence curves of specimen weight effect on the lateral displacement peak value at the top of the column, the total energy peak vale of CSP/OSP specimen, and the lateral impact force peak value are shown in Figures10(a)–10(c), respectively. The influence curves of specimen weight are all quadratic curves and have extreme points. With the increase of the specimen weight, the lateral displacement peak value at the top of the column and the lateral impact force first decreased and then increased, while the total energy peak value of CSP/OSP specimen first increased and then decreased.Figure 10
Influence curves of specimen weight. (a) Lateral displacement peak value of the top of the column. (b) Total energy peak value of the CSP/OSP specimen. (c) Lateral impact force peak value.
(a)(b)(c)When the impact velocity is 2 m/s, the curves of column lateral displacements of CSP and OSP intersect at (0, 9.64), (105.88, 0.78). Within [0.00, 105.88], the lateral displacement peak value of CSP is larger than that of OSP, but, within [105.88, 166.96], the lateral displacement peak value of CSP is smaller than that of OSP. The total energy peak value of CSP specimen intersects with that of OSP at (0, 0). Within [0.00 166.957], the total energy peak of CSP specimen is larger than that of OSP. The lateral impact force peak value of CSP intersects with that of OSP at (0, 444.46), (108.11, 43.58). Within [0.00, 108.11], the lateral impact force peak value of CSP is smaller than that of OSP. Within [108.11, 166.96], the lateral impact force peak value of CSP is larger than that of OSP.When the impact velocity is 3 m/s, the lateral displacement peak value of CSP intersects with that of OSP at (0, 13.97), (119.19, 2.45). Within [0, 119.19], the lateral displacement peak value of CSP is larger than that of OSP, but, within [119.19, 166.96], the lateral displacement peak value of CSP is smaller than that of OSP. The total energy peak value of the CSP specimen intersects with that of OSP specimen at (0, 0). Within [0, 166.81], the total energy peak value of CSP specimen is larger than that of OSP specimen. The lateral impact force peak value of CSP intersects with that of OSP at (0, 664.71), (145.39, 60.44). Within [0 145.39], the lateral impact force peak value of CSP is smaller than that of OSP, but, within [145.39, 166.96], the lateral impact force peak value of CSP is larger than that of OSP.When the impact velocity is 4 m/s, the lateral displacement peak value of CSP intersects with that of OSP at (0, 18.09), (100.71, 2.03). Within [0, 100.71], the lateral displacement peak value of CSP is larger than that of OSP, but, within [100.71, 166.96], the lateral displacement peak value of CSP is smaller than that of OSP. The curve of total energy peak value of the CSP specimen intersects with that of OSP specimen at (0, 0), (99.98, 2.49). Within [0 99.98], the total energy peak value of CSP specimen is smaller than that of OSP specimen, but, within [99.98, 166.96], the total energy peak value of CSP specimen is smaller than that of OSP specimen. The curve of lateral impact force peak value of CSP intersects with that of OSP at (0, 793.69). Within [0 166.96], the lateral impact force peak value of CSP is smaller than that of OSP.


### 4.4. Specimen Frequency

The influence curves of CSP/OSP specimen frequency [40] effect on the lateral displacement peak value at the top of the column, the total energy peak value of CSP/OSP specimen, and the lateral impact force peak value off the column are shown in Figures 11(a)–11(c), respectively. The influence curves of specimen frequency are all quadratic curves and have extreme points. With the increase of specimen frequency, the lateral displacement peak value at the top of the column and the lateral impact force peak value of the column decrease first and then increase. The total energy peak values of CSP and OSP specimens first increase and then decrease. The curves change rate of OSP is greater than that of CSP.Figure 11
Influence curves of specimen frequency. (a) Lateral displacement peak value of the top of the column. (b) Total energy peak value of the CSP/OSP specimen. (c) Lateral impact force peak value.
(a)(b)(c)


### 4.5. Structural Optimization

The influence curves of CSP/OSP specimens thickness, weight, and frequency are analysed in Sections4.2–4.4. However, each curve presents a quadratic curve with extreme points. Therefore, the technical route of CSP/OSP structure optimization is shown in Figure 12, and the optimization results are summarized in Table 4.Figure 12
Technical route of structural optimization.Table 4
Optimization results.
TypeParameterImpact velocity (m/s)Lateral displacement peak valueLateral impact force peak valueTotal energy peak value of CSP/OSP specimenTotal energy peak value of the columnCategoryOptimal valueCalculated valueRatioSimulation (mm)Percentage (%)Simulation (kN)Percentage (%)Simulation (J)Percentage (%)Simulation (J)Percentage (%)CSPThickness (mm)2.712.50.9221.8719.3831.807.16820.0090.3022.602.49Weight (kg)134.89119.410.8932.1015.0336.805.711870.0091.5329.001.42Frequency (Hz)42.5540.600.9542.1812.0639.404.963350.0092.2331.700.87OSPThickness (mm)2.832.50.8821.1211.6137.008.33768.0084.5817.701.95Weight (kg)122.09107.580.8832.8220.1965.2010.111600.0078.3192.704.54Frequency (Hz)13.8512.200.8843.3818.6991.9011.582960.0081.49122.003.36The results show that when the impact energy is low, the lateral displacement peak value of the top of the column, the lateral impact force peak value of the column, and the total energy peak value of the column equipped with OSP are smaller than those of the column equipped with CSP. When the impact energy is high, the lateral displacement peak value of the top of the column equipped with OSP, the lateral impact force peak value of the column equipped with OSP, and the total energy peak value of the column equipped with OSP are all larger than those of the column equipped with CSP. However, under the same impact energy, the total energy peak value of the CSP specimen is larger than that of the OSP specimen. The total energy peak value of the CSP specimen accounts for more than 90.30% of the total energy of the model system, whereas the total energy peak value of the OSP specimen accounts for more than 78.31% of the total energy of the model system. Therefore, using CSP is recommended.


## 4.1. Impact Velocity

The curves of the ratio of the lateral displacement peak value at the top of the CSP/OSP column (DOSP(CSP)) to that of the CWACF column (DCWACF) are shown in Figure 8(a). When the impact velocity is small, the lateral displacement peak value ratio of CSP/OSP is basically close, but that of OSP-3.50 is less than that of CSP-3.50. When the impact velocity is large, the lateral displacement peak value ratio of CSP is small than that of OSP.Figure 8
Influence curves of impact velocity. (a) Ratio of lateral displacement peak value at the top of the column. (b) Ratio of total energy peak value of the CSP/OSP specimen. (c) Ratio of lateral impact force peak value.
(a)(b)(c)The curves of the ratio of the total energy peak value of CSP/OSP specimen (TEOSP(CSP)) to that of the model system (TESYS) are shown in Figure 8(b). The total energy peak value ratios of CSP-2.75 and CSP-3.00 are basically similar, but both are larger than those of CSP-3.50 and OSP. With the increase of impact velocity, the total energy peak value ratio of CSP tends to be stable, while that of OSP gradually decreases. Therefore, CSP/OSP can absorb most of the kinetic energy, and the proportion of CSP absorption is greater than that of OSP.The curves of the ratio of the lateral impact force peak value of the CSP/OSP column (PFOSP(CSP)) to that of the CWACF column (PFCWACF) are shown in Figure 8(c). The lateral impact force peak value ratio of CSP decreased with the increase of impact velocity, but that of the OSP increases with the increase of impact velocity. The ratio of CSP-3.50 is the largest. But when the impact velocity is small, the ratio of CSP is larger than that of OSP. When the impact velocity is large, the ratio of CSP is small than that of OSP.


## 4.2. Specimen Thickness

The curves of specimen thickness effect on the lateral displacement peak value, the total energy peak value of CSP/OSP specimen, and the lateral impact force peak value are shown in Figures9(a)–9(c), respectively. The influence curves of specimen thickness are all quadratic curves and have extreme points. With the increase of specimen thickness, the peak values of lateral impact force and lateral displacement first decrease and then increase, while the peak value of total energy first increases and then decreases.Figure 9
Influence curves of specimen thickness. (a) Lateral displacement peak value of the top of the column. (b) Total energy peak value of the CSP/OSP specimen. (c) Lateral impact force peak value.
(a)(b)(c)When the impact velocity is 2 m/s, the curve of the lateral displacement peak value of CSP intersects with that of OSP at (0, 9.65), (2.81, 1.00). Within [0, 2.81], the lateral displacement peak value of CSP is smaller than that of OSP, but within [2.81, 3.50], the lateral displacement peak value of CSP is larger than that of OSP. The curve of the total energy peak value of CSP specimen intersects with that of OSP at (0, 0), (3.00, 0.466). Within [0.00, 3.00], the total energy peak value of CSP specimen is larger than that of OSP, but, within [3.00, 3.5], the total energy peak value of CSP specimen is smaller than that of OSP. The curve of lateral impact force peak value of CSP intersects with that of OSP at (0,444.39), (2.61, 40.35). Within [0 2.61], the peak value of the lateral impact force of CSP is smaller than that of OSP, but, within [2.61 3.5], the peak value of the lateral impact force of CSP is larger than that of OSP.When the impact velocity is 3 m/s, the curve of the lateral displacement peak value of CSP intersects with that of OSP at (0, 13.97), (2.66, 2.37). Within [0.00 2.66], the lateral displacement peak value of CSP is larger than that of OSP, but, within [2.66, 3.50], the lateral displacement peak value of CSP is smaller than that of OSP. The curve of the total energy peak value of CSP specimen intersects with that of OSP specimen at (0, 0). Within [0 3.50], the total energy peak value of CSP specimen is larger than that of OSP specimen. The curve of the lateral impact force peak value of CSP intersects with that of OSP at (0,664.63), (3.05, 61.43). Within [0 3.05], the lateral impact force peak value of CSP is smaller than that of OSP, but, within [3.05 3.5], the lateral impact force peak value of CSP is larger than that of OSP.When the impact velocity is 4 m/s, the curve of the lateral displacement peak value of CSP intersects with that of OSP at (0, 18.08), (1.46, 4.28). Within [0.1.46], the lateral displacement peak value of CSP is slightly larger than that of OSP, but, within [1.46, 3.5], the lateral displacement peak value of CSP is smaller than that of OSP. The curve of total energy peak value of CSP specimen intersects with that of OSP at (0,0), (1.76, 2.31). Within [0, 1.76], the total energy peak value of CSP specimen is smaller than that of OSP, but, within [1.76, 3.50], the total energy peak value of CSP specimen is larger than that of OSP. The curve of the lateral impact force peak value of CSP intersects with that of OSP at (0,793.69), (3.31, 90.25). Within [0 3.31], the lateral impact force peak value of CSP is larger than that of OSP, but, within [3.31 3.5], the lateral impact force peak value of CSP is smaller than that of OSP.


## 4.3. Specimen Weight

The influence curves of specimen weight effect on the lateral displacement peak value at the top of the column, the total energy peak vale of CSP/OSP specimen, and the lateral impact force peak value are shown in Figures10(a)–10(c), respectively. The influence curves of specimen weight are all quadratic curves and have extreme points. With the increase of the specimen weight, the lateral displacement peak value at the top of the column and the lateral impact force first decreased and then increased, while the total energy peak value of CSP/OSP specimen first increased and then decreased.Figure 10
Influence curves of specimen weight. (a) Lateral displacement peak value of the top of the column. (b) Total energy peak value of the CSP/OSP specimen. (c) Lateral impact force peak value.
(a)(b)(c)When the impact velocity is 2 m/s, the curves of column lateral displacements of CSP and OSP intersect at (0, 9.64), (105.88, 0.78). Within [0.00, 105.88], the lateral displacement peak value of CSP is larger than that of OSP, but, within [105.88, 166.96], the lateral displacement peak value of CSP is smaller than that of OSP. The total energy peak value of CSP specimen intersects with that of OSP at (0, 0). Within [0.00 166.957], the total energy peak of CSP specimen is larger than that of OSP. The lateral impact force peak value of CSP intersects with that of OSP at (0, 444.46), (108.11, 43.58). Within [0.00, 108.11], the lateral impact force peak value of CSP is smaller than that of OSP. Within [108.11, 166.96], the lateral impact force peak value of CSP is larger than that of OSP.When the impact velocity is 3 m/s, the lateral displacement peak value of CSP intersects with that of OSP at (0, 13.97), (119.19, 2.45). Within [0, 119.19], the lateral displacement peak value of CSP is larger than that of OSP, but, within [119.19, 166.96], the lateral displacement peak value of CSP is smaller than that of OSP. The total energy peak value of the CSP specimen intersects with that of OSP specimen at (0, 0). Within [0, 166.81], the total energy peak value of CSP specimen is larger than that of OSP specimen. The lateral impact force peak value of CSP intersects with that of OSP at (0, 664.71), (145.39, 60.44). Within [0 145.39], the lateral impact force peak value of CSP is smaller than that of OSP, but, within [145.39, 166.96], the lateral impact force peak value of CSP is larger than that of OSP.When the impact velocity is 4 m/s, the lateral displacement peak value of CSP intersects with that of OSP at (0, 18.09), (100.71, 2.03). Within [0, 100.71], the lateral displacement peak value of CSP is larger than that of OSP, but, within [100.71, 166.96], the lateral displacement peak value of CSP is smaller than that of OSP. The curve of total energy peak value of the CSP specimen intersects with that of OSP specimen at (0, 0), (99.98, 2.49). Within [0 99.98], the total energy peak value of CSP specimen is smaller than that of OSP specimen, but, within [99.98, 166.96], the total energy peak value of CSP specimen is smaller than that of OSP specimen. The curve of lateral impact force peak value of CSP intersects with that of OSP at (0, 793.69). Within [0 166.96], the lateral impact force peak value of CSP is smaller than that of OSP.


## 4.4. Specimen Frequency

The influence curves of CSP/OSP specimen frequency [40] effect on the lateral displacement peak value at the top of the column, the total energy peak value of CSP/OSP specimen, and the lateral impact force peak value off the column are shown in Figures 11(a)–11(c), respectively. The influence curves of specimen frequency are all quadratic curves and have extreme points. With the increase of specimen frequency, the lateral displacement peak value at the top of the column and the lateral impact force peak value of the column decrease first and then increase. The total energy peak values of CSP and OSP specimens first increase and then decrease. The curves change rate of OSP is greater than that of CSP.Figure 11
Influence curves of specimen frequency. (a) Lateral displacement peak value of the top of the column. (b) Total energy peak value of the CSP/OSP specimen. (c) Lateral impact force peak value.
(a)(b)(c)


## 4.5. Structural Optimization

The influence curves of CSP/OSP specimens thickness, weight, and frequency are analysed in Sections4.2–4.4. However, each curve presents a quadratic curve with extreme points. Therefore, the technical route of CSP/OSP structure optimization is shown in Figure 12, and the optimization results are summarized in Table 4.Figure 12
Technical route of structural optimization.Table 4
Optimization results.
TypeParameterImpact velocity (m/s)Lateral displacement peak valueLateral impact force peak valueTotal energy peak value of CSP/OSP specimenTotal energy peak value of the columnCategoryOptimal valueCalculated valueRatioSimulation (mm)Percentage (%)Simulation (kN)Percentage (%)Simulation (J)Percentage (%)Simulation (J)Percentage (%)CSPThickness (mm)2.712.50.9221.8719.3831.807.16820.0090.3022.602.49Weight (kg)134.89119.410.8932.1015.0336.805.711870.0091.5329.001.42Frequency (Hz)42.5540.600.9542.1812.0639.404.963350.0092.2331.700.87OSPThickness (mm)2.832.50.8821.1211.6137.008.33768.0084.5817.701.95Weight (kg)122.09107.580.8832.8220.1965.2010.111600.0078.3192.704.54Frequency (Hz)13.8512.200.8843.3818.6991.9011.582960.0081.49122.003.36The results show that when the impact energy is low, the lateral displacement peak value of the top of the column, the lateral impact force peak value of the column, and the total energy peak value of the column equipped with OSP are smaller than those of the column equipped with CSP. When the impact energy is high, the lateral displacement peak value of the top of the column equipped with OSP, the lateral impact force peak value of the column equipped with OSP, and the total energy peak value of the column equipped with OSP are all larger than those of the column equipped with CSP. However, under the same impact energy, the total energy peak value of the CSP specimen is larger than that of the OSP specimen. The total energy peak value of the CSP specimen accounts for more than 90.30% of the total energy of the model system, whereas the total energy peak value of the OSP specimen accounts for more than 78.31% of the total energy of the model system. Therefore, using CSP is recommended.


## 5. Conclusion

The numerical model verified by the pendulum impact test is used to simulate the whole process of the impact test, and the time history curve and its peak value of the simulation results are obtained. Then, the influence curves of the impact velocity, specimen thickness, weight, and frequency are analysed, and the following conclusions are obtained:(1)
According to the pendulum impact test, the corresponding simplified establishment method of numerical model is proposed, and the simulation results are basically consistent with the test results.(2)
The anticollision performance of CSP/OSP specimens is compared and analysed. Under the same impact energy, the energy absorbed by the CSP specimen is greater than that of the OSP specimen. Therefore, using CSP is recommended.(3)
The method of establishing the numerical model has been verified by the impact test. In the next step, the numerical simulation on the anticollision performance of the overall structure of the new corrugated steel protection system can be carried out.



---

*Source: 4718228-2022-07-22.xml*