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This paper investigates the dynamic performance of web frame structures under the impact of a conical hammer head. Compared with existing research on flat plates and stiffened panels, web frame structures exhibit significant differences in load-bearing mechanisms and design principles. To address these limitations, a series of drop-weight impact tests under different impact conditions are conducted, and the effects of drop heights on the dynamic responses of the web frame structure are systematically analyzed. By measuring the impact force responses and damage shapes, nonlinear dynamic characteristics and damage modes of the web frame structures under conical hammer head impacts can be revealed. The results indicate that higher drop heights lead to more severe damage areas, and damage area is more concentrated in the contact area of the indenter. Meanwhile, the peak impact force increases from 429.06 MN to 606.62 MN as the drop height increases from 1 m to 2.5 m, indicating a 41.38% rise. Additionally, the maximum energy absorbed by the structure reaches 62.89 KJ, and the energy loss ratio ranges from 18.58% to 30.73%. The findings offer critical theoretical insights and technical support for the optimization of impact resistant designs in web frame structures.
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1. Introduction
As computational power and finite element analysis (FEA) software rapidly advance, continued ship collisions pose a significant risk to maritime safety, leading to severe structural damage to the hull, as well as the potential loss of life and cargo. With the continuous growth of global shipping traffic and the increasing size of vessels, the frequency and likelihood of ship collisions are rising. Therefore, studying ship collision behavior is crucial for improving vessel safety [1,2], durability [3,4], and impact resistance [5,6]. A profound understanding of ship collision mechanics is essential for developing effective collision prevention measures, optimizing ship structure designs, and minimizing the damage caused by collision accidents.
In recent years, significant progress has been made in ship collision research. Scholars have employed a combination of experimental, numerical simulation, and theoretical methods to advance this field. For instance, Tengesdal et al. [7] and Lande et al. [8] conducted full-scale experiments to study real-world ship collision scenarios, proposing effective strategies for mitigating collision impacts. However, full-scale collision experiments present significant limitations, including the lengthy testing process, high costs, and the complexity of accurately replicating conditions [9,10]. As a result, researchers have increasingly turned to scaled-down collision tests, which offer a more efficient and cost-effective alternative while still providing valuable insights into the behavior of ship structures under collision scenarios [11]. Oshiro et al. [12] and Calle et al. [13] focused on the study of scale model structures in collisions to predict the performance of ship structures under impact conditions. Additionally, Gholipour et al. [14] examined the progressive damage and failure modes of cable-stayed bridge piers under ship collisions and proposed a two-degree-of-freedom finite element model to assess the impact response and damage. Liu et al.’s [15] research investigates the dynamic response of laser-welded corrugated sandwich panels under a plane blast wave, proposing a simplified analysis method for evaluating deformation. Gong et al. [16] develops a semi-analytical approach to predict the deflection and fracture of clamped plates under lateral indentation by a spherical indenter, with results matching experimental data. Liu et al. [17] presents an analytical method for evaluating the crushing force of girders with stiffened webs under local in-plane loads, introducing a new deformation model and comparing predictions with experimental results. These studies demonstrate that experimental and numerical approaches effectively reveal the damage mechanisms of ship structures, providing valuable insights for further investigation into their impact performance.
The performance of ship structures under various impact conditions has also been widely studied by experimental and numerical approaches [18,19]. Zhang et al. [20] conducted experimental and finite element analyses to examine the collision behavior of scaled double-hull side structures under conical and knife-edge impactors, revealing the effects of different impactor shapes on ship structure fracture and energy dissipation mechanisms. Liu et al. [21] studied the plastic behavior and failure of stiffened aluminum-alloy plates under indentation, comparing the effects of hemispherical and hemi-cylindrical indenters on deformation and collapse modes. The study highlights the importance of modeling welded joints, boundary conditions, and material degradation in heat-affected zones, and compares the impact behavior of aluminum and steel stiffened plates. Liu et al. [22] investigated the effects of conical and wedge-shaped impactors on small single-side ship structures, highlighting differences in deformation and fracture modes under various impact conditions. Moreover, researchers have focused on the influence of stiffener design on collision performance. Villavicencio et al. [23] and Park et al. [24] investigated the effects of drop-weight impacts on stiffened plates, while Cheng et al. [25] studied the dynamic response of U-shaped corrugated sandwich plates under low-velocity impacts, finding that transverse impact resistance was superior to longitudinal resistance. Despite recent advances in impact mechanics, most existing studies have focused on planar or folded plate structures, while investigations on the impact performance of web frame structures remain relatively scarce. Given the structural differences and practical relevance of web frames, a systematic study of their collision behavior is warranted. Compared to the existing studies that typically utilize flat or hemispherical indenters, the use of a conical indenter induces highly localized stress concentrations and prominent penetration effects. These features make conical impact particularly suitable for exposing the dynamic vulnerabilities and failure mechanisms of web frame structures. Unlike solid plates, web frames possess an open-frame configuration that results in distinct stress redistribution and deformation behaviors under impact. The interaction between the conical tip and the intersecting members leads to complex failure modes, such as localized buckling, member tearing, and joint collapse—underscoring the necessity for targeted investigations under this specific loading condition.
To address this gap, this paper presents a series of collision experiments to investigate the impact behavior of web frame structures under conical drop hammer impacts. By measuring the impact force and damage deformation of the web frame structure, the study analyzes the influence of different drop heights on structural responses. Finite element simulations are performed using LS-DYNA, and the numerical results show good agreement with experimental data, which validates the reliability of the simulation results. This research provides valuable guidance for the impact-resistant design optimization of ship hull frame structures and contributes to improving ship safety and the design of more resilient offshore structures.
2. Experimental Test
2.1. The Test Specimen
The stiffened plate structure consists of truss members and stiffeners, including 4 truss members and 8 stiffeners. Among the 8 stiffeners, 2 are T-shaped stiffeners (see specific parameters shown in Figure 1d, section A-A) and 6 are flat steel stiffeners (see specific parameters shown in Figure 1e, section B-B). The structure dimensions and specimen model are depicted in Figure 1 and Figure 2, respectively. The main dimensions of the model are 1520 mm × 1520 mm × 6 mm, and its specific structural parameters are listed in Table 1.
A conical shape was selected for the indenter. The diagram of the indenter is shown in Figure 3, and detailed parameters are summarized in Table 2. The bottom diameter of the conical hammer is 400 mm, the height is 311 mm, and the top is a sphere with a radius of 50 mm. The material is high-carbon chromium bearing steel with high hardness. It is assumed that the conical hammer head does not deform during the test.
The impact test was conducted in the drop-weight impact laboratory of the School of Ship and Marine Engineering at Jiangsu University of Science and Technology, as shown in Figure 4. The laboratory is spacious and features a reinforced concrete foundation, along with a 5 t/20 t truss car that can support the drop-weight impact tests while ensuring safety. To avoid interference with the strain gauge and lighting, the test was scheduled during daylight hours and in dry weather. During the test, the protective door of the drop-weight tester was kept closed, and personnel remained outside the safety line, which is 1.5 m away from the surrounding fence.
2.2. Drop-Weight Impact Test
The experimental device is shown in Figure 5. The system is mainly composed of an electrical operating system, a power drive system, a data acquisition system, a host frame, a hammer structure, and a specimen support device. The main body height is 6.3 m, and the maximum lifting height of hammer head is 3.9 m. The lifting mechanism can adjust the drop height in the range of 0~3.9 m, and therefore the maximum impact velocity of the equipment can reach 8.83 m/s. The maximum mass of the drop-weight system is 1400 kg, which contains 12 weight blocks of 12.5 kg. It can be used to adjust the impact mass of the drop-weight. Therefore, the maximum impact kinetic energy of the system is 54.6 kJ. A force sensor is set between the hammer head and the hammer body, which can record the reaction force during the impact process.
The support structure of the specimen is designed as shown in Figure 6. Openings at both ends are designed for bolt connection to the specimens. The support structure only restricts the two ends of the model with bolts, while the other two ends remain free and there is no contact with the model.
In this dynamic response test of the structure under impact load, the following key parameters are measured:
(1) Drop-weight displacement, velocity, and acceleration: These parameters characterize the external mechanism of the collision. In the experiment, a laser rangefinder (Jining Huiye Industrial and Mining Machinery Equipment Co. Ltd., Jining, Shandong, China). is used to track and measure the position of the reference point during the drop-weight’s fall and collision process, as shown in Figure 7.
(2) Structural damage deformation (damage, plastic deformation): The damage and plastic deformation of the plate frame structure are key focuses of this test, which can be judged by direct observation or tested using relevant flaw detection equipment. In this experiment, the plastic deformation is determined by measuring the distance from the reference plane to the grid line intersection before and after impact, as shown in Figure 8. The grid line spacing (both horizontal and vertical) is 50 mm, and the grid lines are represented by the dotted lines.
(3) Dynamic strain: The dynamic mechanical properties of the structure under impact load determine its performance. The dynamic strain during the experiment is measured by placing strain gauges on the model, as shown in Figure 9. The strain measurement points are arranged to cover the area shown in Figure 8. Five strain measuring points (A1~A5, B2~B5, C2~C5) are placed in the collision shadow area, at the center of the plate, and at the middle of each boundary. Points A2, A4, C2, and C4 are located at the longitudinal or transverse beam positions, facilitating strain distribution measurement of the frame material. To facilitate comparative analysis, each drop-weight stiffened plate test model adopts the same arrangement of measurement points.
(4) Damage of the impact structure model: This visually reflects the deformation and damage process of the local structure under the impact load. The deformation and failure processes are captured by a high-speed camera, as shown in Figure 10.
(5) Drop-weight impact force: The impact force is the cause of large displacement and deformation of the structure during the collision process. The collision process is clearly understood through the time history curve of impact force, which is obtained through force or acceleration sensors, as shown in Figure 11.
After preparing the specimen, the drop-weight test system and measuring equipment are installed and calibrated, as shown in Figure 12. This includes a dynamic strain test system, laser rangefinder, high-speed camera with light source, and a force sensor equipped with the drop-weight impact system. After adjusting and confirming the parameters, the test can be carried out, as shown in Figure 13.
To evaluate the specimen’s response under different conditions, four experimental setups were designed. In these tests, the weight of the drop-weight was kept constant at 1.35 tons (t), with the initial falling heights set at 1.0 m, 1.5 m, 2.0 m, and 2.5 m, respectively. The experimental conditions are summarized in Table 3, where each test is named based on the specific falling height used. This approach allows for a thorough analysis of the specimen’s behavior under varying impact forces, providing insights into different damage modes.
2.3. Experimental Results
During the experiment, the impact force was recorded by the force sensor, and the displacement of the impact head during the impact process is recorded by the laser range finder. The impact force–displacement relationship curves for the four experimental conditions are shown in Figure 14. The energy–displacement relationship curves for the four experimental conditions are shown in Figure 15. The peak impact force and failure displacement for each condition are listed in Table 4.
From Figure 14 and Table 4, it can be observed that the curves exhibit obvious nonlinear characteristics, and the overall trend shows a process of loading to the peak and then unloading. For the same impact location, as the drop height (i.e., initial impact velocity) increases, the peak impact force first gradually increases and then decreases. On the other hand, the failure displacement increases with the rise in drop height. Moreover, the higher the drop height, the faster the impact force rises and falls. This is primarily due to the constant mass of the drop-weight. With higher velocities, the impact kinetic energy increases, resulting in a larger impact force. Simultaneously, higher velocities lead to faster loading (force increase) and unloading (force decrease) rates.
As shown in Figure 15 and Table 4, the energy–displacement curves for different working conditions (SP-1 to SP-4) demonstrate distinct energy absorption capacities. SP-2 exhibits the highest peak impact force and energy absorption (62.89 KJ), followed by SP-1 and SP-3. In contrast, SP-4 shows the lowest values in both absorbed energy (16.44 KJ) and failure displacement (0.06 m), indicating significantly reduced impact resistance.
During the test, grid lines are drawn on the specimen to determine the damage area in two orthogonal directions. The plastic deformation of the specimen can be determined by measuring the distance difference between the measuring point and the reference plane before and after the test. Figure 16 shows the damage shape of the specimen under various impact conditions after the end of the test. Table 5 is the size of the damage shapes in the two orthogonal directions of the model.
The specimen under all four impact conditions fractured, displaying localized damage and deformation near the collision area, consistent with the expected outcomes of the collision. High-speed camera recordings reveal clear penetration in all conditions. Additionally, the deformation modes across all four conditions are similar. The specimen shows overall membrane tensile deformation and local bending, with fracture occurring due to shear force at the impact head’s edge. Stiffeners on both sides of the impact point exhibit lateral bending, while those at other positions remain largely unaffected. In all conditions, the outer plate undergoes membrane tensile deformation, with tear failure occurring at the impact location.
3. Numerical Simulation and Analysis
The finite element software LS-DYNA R14.0 is used to analyze the dynamic response of the specimen under impact load. By comparing it with the test results, the finite element modeling technology can be established, and the structural damage deformation mode and failure mechanism can be comprehensively analyzed.
3.1. Finite Element Model
According to the dimension of the web frame model, the finite element model of the drop-weight impact test is established, as shown in Figure 17. The model consists of a web frame structure and an impact head, with the impact point located between two stiffeners. The diameter of the top of the impact head is 100 mm, the plate truss is , the bone material is 1500 mm × 45 mm × 5 mm flat steel, and the rib plate is 1040 mm × 75 mm × 8 mm, as shown in Table 6.
The material input of the finite element model is based on the quasi-static tensile test of the material (Figure 18). The engineering stress–strain parameters obtained from the tensile test can be used to obtain the true stress–strain parameters as the input in the simulation. The engineering stress–strain curve and the true stress–strain curve are shown in Figure 19.
For dynamic problems such as collision and grounding, the influence of strain rate cannot be ignored. The common practice of considering strain rate is to adopt the material constitutive model, considering the influence of strain rate, such as the Cowper–Symonds model, the Johnson–Cook model, and so on. Here, the widely used Cowper–Symonds constitutive model is applied, and its constitutive model is expressed as
(1)
Here, is the dynamic real stress, is the corresponding static real stress, is the strain rate, and D and P are constant parameters. In this study, the parameters D and P in the Cowper–Symonds model were selected based on published experimental data to reflect the strain-rate sensitivity of the material. Specifically, for low-carbon steel, D is 40.4 and P is 5. For high-strength steel, D is 3200 and P is 5. These values were adopted following the recommendations of Jones (1989) [26] and are consistent with guidelines provided in the LS-DYNA Keyword User’s Manual.
A 4-node reduced integration shell element (SHELL163) is employed to model the specimen. SHELL163 is suitable for simulating thin to moderately thick shell structures and can handle large strain, large deflection, and complex nonlinear behaviors, making it ideal for impact simulations. To capture the structural damage and deformation patterns accurately, a mesh sensitivity analysis has been conducted. The results indicate that a mesh size of 10 mm × 10 mm offered the optimal balance between accuracy and computational efficiency. Therefore, a global element size of 10 mm was adopted in the final simulations, as illustrated in Figure 20.
The dynamic explicit analysis step is used in the impact process. In the analysis of the contact problem, the automatic surface–surface contact is selected and the friction coefficient is 0.3.
The constraint condition of the simulation model is based on the drop-weight impact test setup under realistic conditions. Specifically, the axial displacement of the two end plates is restricted, and the translational degrees of freedom of the nodes around the bolt holes are constrained. This configuration simulates the structural characteristics of ship web frames in actual service, where the ends are connected to adjacent components while other regions retain a certain degree of freedom, as shown in Figure 21. Although this boundary setting involves simplifications, it reasonably reflects the localized constraints present in real ship structures under impact. The simulation conditions are consistent with the experimental setup (refer to Table 3), and the mass of the conical hammer head is set to 1350 kg. In future work, more complex boundary conditions will be considered to further enhance the realism of the numerical model.
To provide a clearer understanding of the finite element model configuration, the number of nodes and degrees of freedom is summarized in Table 7. As shown, each node possesses six degrees of freedom (three translational and three rotational), and a uniform mesh size of 10 mm × 10 mm was adopted to ensure both accuracy and computational efficiency.
3.2. Comparison Results
3.2.1. Damage Deformation
Figure 22, Figure 23, Figure 24 and Figure 25 show the comparison of damage shapes of the specimen under four different collision conditions. Table 8 lists the sizes and areas of the breakages for the specimen under four conditions. It can be seen that the overall deformation characteristics, damage areas, and failure modes of the structure from the simulations are in close agreement with the experimental results. Moreover, the maximum error in the breakage area is 12.84%, which falls within the acceptable error range. Therefore, consistency can be achieved between the experimental and simulated results.
3.2.2. Impact Force–Displacement Responses
The impact force–displacement curves and peak force comparisons for different impact conditions are shown in Figure 26 and Table 9. It can be observed that the maximum error in peak impact force is 10.13%, which is within the acceptable range. The overall trend of the responses closely matches the experimental results. However, the experimentally obtained impact force curves exhibit more pronounced oscillations and slightly higher peaks compared to simulation results. This discrepancy is due to the presence of welds in the plate frame structure, which enhance the structural strength, a factor not considered in the simulation.
3.2.3. Energy–Time Responses
The energy absorption and loss ratios under different impact conditions are summarized in Figure 27 and Table 10. It can be observed that the total absorbed energy decreases progressively from SP-1 to SP-4, reflecting the reduced impact severity or structural capacity. The energy loss ratio, which accounts for energy dissipated through deformation and other mechanisms not captured by the simulation, ranges from 30.73% to 18.58%. These values indicate a relatively consistent pattern of energy dissipation across different conditions. However, higher loss ratios in SP-1 and SP-2 suggest that more energy is absorbed and dissipated through structural mechanisms not explicitly modeled, such as weld effects or minor material damage. This simplification may contribute to the deviation between simulation and experimental energy distributions. Further refinement of the model, including weld modeling and detailed fracture criteria, could improve simulation accuracy in future work.
3.2.4. Stress Triaxiality Analysis for Failure Mode Characterization
To further investigate the failure mechanism of the structure under impact loading, the stress triaxiality factor was extracted and visualized, as shown in Figure 28, Figure 29, Figure 30 and Figure 31. The triaxiality factor is a key indicator that characterizes the local stress state, providing insight into the dominant failure mode. A positive triaxiality value indicates a tensile-dominated stress state, often associated with ductile fracture, while a negative value corresponds to compressive or shear-dominated conditions, which may lead to shear band formation or material crushing. The spatial distribution of triaxiality reveals that the central region of the structure is predominantly under tensile stress, whereas the boundary zones exhibit localized compressive states, indicating potential areas of constraint-induced failure.
Figure 28 illustrates the distribution of the stress triaxiality factor at the moment when the drop-weight impacts the plate from a height of 2.5 m. The results show that a high positive triaxiality zone (red) is concentrated along the central vertical axis, indicating the presence of tensile-dominated stress states due to severe out-of-plane deformation. In contrast, the surrounding regions display lower triaxiality values, with localized negative zones (blue) on both sides of the impact center, suggesting compressive or shear-dominated stress states induced by lateral constraint and material flow. Notably, the area immediately surrounding the impact crater exhibits a rapid stress transition, which reflects the combined effect of bending, membrane stretching, and localized plastic deformation. This distribution provides critical insight into the failure initiation zone and potential fracture mode of the structure under dynamic impact.
Figure 29 presents the stress triaxiality distribution when the drop-weight impacts the plate from a height of 2.0 m. Compared to the 2.5 m case, the central high-triaxiality region (red) remains evident, indicating significant tensile stresses due to localized plastic stretching. However, the surrounding area exhibits a more moderate gradient of stress transition, with slightly reduced triaxiality peaks. The blue zones on both lateral sides still indicate compressive or shear-dominated conditions but appear slightly smaller in area and intensity, suggesting a relatively less severe material flow. The region around the impact crater shows a concentrated gradient of stress shift, reflecting strong stress concentration and potential damage nucleation. Overall, the results indicate that the structure experiences substantial tensile and shear interactions under 2.0 m impact, with failure modes likely to initiate from the crater boundary and propagate along the tensile axis.
Figure 30 illustrates the distribution of the stress triaxiality factor when the drop-weight impacts the plate from a height of 1.5 m. At this lower impact energy, the stress distribution appears more uniform, with the central tensile zone (red) still prominent along the vertical axis, indicating plastic stretching but of reduced intensity compared to higher drop heights. No significant crater is observed, suggesting that the deformation remains within the elastic–plastic range without local failure. The compressive zones (blue) on both sides are relatively small and scattered, implying limited lateral material flow and minimal structural instability. Overall, the results indicate that under a 1.5 m impact, the structure undergoes moderate tensile deformation while maintaining overall integrity, with a lower likelihood of crack initiation or severe damage at this stage.
Figure 31 shows the distribution of the stress triaxiality factor at the moment when the drop-weight impacts the plate from a height of 1.0 m. The central region still demonstrates a tensile-dominated stress state (highlighted in red), but its extent and intensity are significantly lower than in higher energy cases. The surrounding areas mainly exhibit green to yellow triaxiality levels, indicating a largely elastic or mildly plastic response. Compressive zones (blue) are minimal and dispersed, suggesting negligible lateral constraint or stress concentration. The absence of a crater and the smooth stress gradient imply that the plate undergoes low-level deformation without any indication of failure. This result confirms that at a 1.0 m drop height, the impact energy is insufficient to initiate damage, and the structure remains in a safe deformation state.
The comparative analysis of triaxiality factor distributions from SP1 to SP4 reveals a clear correlation between impact energy and the severity of the stress state in the target plate. As the drop height increases, the central region consistently exhibits higher positive triaxiality, indicating a shift toward tensile-dominated stress states and enhanced plastic deformation. In SP1 (2.5 m), intense triaxiality gradients and localized compressive zones suggest a high risk of ductile fracture initiation near the impact crater. SP2 and SP3 (2.0 m and 1.5 m) show similar stress patterns, with gradually reduced intensity, while SP4 (1.0 m) demonstrates a relatively mild and symmetric distribution, indicating that the structure remains within the elastic–plastic regime without failure. These findings highlight the progressive transition of stress modes and failure potential under increasing impact energy, providing a theoretical basis for the structural safety evaluation under dynamic loading conditions.
4. Conclusions
In this paper, a drop-weight test of a web frame structure under four working conditions is carried out. The impact force and damage deformation are analyzed, and the damage deformation mechanism of the structure is revealed. Based on this, numerical simulation is carried out, and the numerical techniques for the impact of web frame structures are developed. The main conclusions are as follows:
(1) Under four conditions with different drop heights (1.0 m, 1.5 m, 2.0 m, and 2.5 m), the web frame structure experience obvious plastic deformation. As the drop height increases, the damage and deformation become more severe. The damage and deformation are concentrated in the contact area. The outer plate primarily exhibits a membrane stretching deformation mode, with shear tearing failure at the rupture. The stiffeners close to the impact location experienced a certain degree of lateral bending, while the deformation of stiffeners at other locations was minimal.
(2) The impact force–displacement relationship has obvious nonlinear characteristics. For the same impact position, the peak value of the impact force increases gradually with the increase in the falling height (i.e., the initial impact velocity). The impact force curves for the same specimen at different heights show similar trends, with the oscillatory nonlinearity of the force–displacement relationship being lower for the stiffened plate specimen at lower drop heights compared to the higher drop heights.
5. Future Work
To further enhance the reliability and engineering applicability of the current research, future work will focus on three main aspects:
(1) More complex and realistic boundary conditions will be incorporated into the simulation models to better reflect actual constraints in ship structures;
(2) The effects of progressive and repeated impact loading will be investigated to evaluate structural durability under more representative service conditions;
(3) Advanced fracture modeling techniques, such as cohesive zone models or damage mechanics-based criteria, will be introduced to improve the accuracy of failure predictions.
These efforts will provide deeper insights into the dynamic behavior of web frame structures under impact and contribute to the development of more resilient structural designs.
Conceptualization, Z.L.; Methodology, C.J.; Software, G.W.; Validation, N.Z.; Investigation, K.L.; Writing—original draft, Z.L.; Writing—review & editing, Y.L. and K.L. All authors have read and agreed to the published version of the manuscript.
Data are contained within the article.
The authors declare no conflicts of interest.
Footnotes
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Figure 1 The dimension diagram of the specimen.
Figure 2 Sample model.
Figure 3 The object and dimension of the conical hammer head (unit: mm).
Figure 4 Test setup.
Figure 5 The composition and schematic diagram of drop-weight impact test system.
Figure 6 Schematic diagram of the test support.
Figure 7 Laser range finder and acquisition equipment.
Figure 8 Falling body collision grid line and strain measuring point arrangement.
Figure 9 Strain gauge cloth and data acquisition.
Figure 10 High speed camera.
Figure 11 Acceleration sensor.
Figure 12 The installation and debugging of test equipment.
Figure 13 Drop-weight test.
Figure 14 Impact force–displacement curves under different working conditions.
Figure 15 Energy–displacement curves under different working conditions.
Figure 16 Damage deformation under different working conditions.
Figure 17 The finite element model of drop-weight impact.
Figure 18 Quasi-static tensile test of material.
Figure 19 Material curve.
Figure 20 The grid division of the structure.
Figure 21 Boundary constraints.
Figure 22 Damage deformation under SP-1 working condition.
Figure 23 Damage deformation under SP-2 working condition.
Figure 24 Damage deformation under SP-3 working condition.
Figure 25 Damage deformation under SP-4 working condition.
Figure 26 Force–displacement comparison under various conditions.
Figure 27 Energy–time histories of total, plate, and truss components under various conditions.
Figure 28 Triaxiality distribution of specimen SP1.
Figure 29 Triaxiality distribution of specimen SP2.
Figure 30 Triaxiality distribution of specimen SP3.
Figure 31 Triaxiality distribution of specimen SP4.
Model parameters of stiffened plate structure.
| Principal Dimensions | Bone Spacing | Truss Spacing | Rib Plate | Materials | Quantities |
|---|---|---|---|---|---|
| 1520 mm × 1520 mm × 6 mm | 151 mm | 463 mm | 292 mm | Q235 | 7 |
Specific parameters of conical hammer head.
| Hammer Head Type | Base Diameter | Top Diameter | Altitude | Materials | Quantities |
|---|---|---|---|---|---|
| Conical hammer head | 400 mm | 50 mm | 311 mm | Q235 | 1 |
Test scheme and working conditions.
| Teat Conditions | Condition Name | Experimental Explanation |
|---|---|---|
| 1 | SP-1 | The impact mass is 1.35 t, and the initial falling height is 2.5 m |
| 2 | SP-2 | The impact mass is 1.35 t, and the initial falling height is 2.0 m |
| 3 | SP-3 | The impact mass is 1.35 t, and the initial falling height is 1.5 m |
| 4 | SP-4 | The impact mass is 1.35 t, and the initial falling height is 1.0 m |
Peak value of impact force, energy, and failure displacement under different working conditions.
| Teat Conditions | Peak Impact Force (KN) | Energy (KJ) | Failure Displacement (m) |
|---|---|---|---|
| SP-1 | 501.54 | 61.11 | 0.25 |
| SP-2 | 606.62 | 62.89 | 0.23 |
| SP-3 | 548.56 | 43.09 | 0.18 |
| SP-4 | 429.06 | 16.44 | 0.06 |
Dimensions of the damage shape under different working conditions.
| Test Conditions | SP-1 | SP-2 | SP-3 | SP-4 | |
|---|---|---|---|---|---|
| Dimensions of the damage shape (mm) | x | 225 | 198 | 153 | 141 |
| y | 152 | 151 | 148 | 102 | |
The dimension parameters of drop-weight impact model.
| Reinforcement Plate/mm | Head-Banging | ||||||
|---|---|---|---|---|---|---|---|
| Plate Length | Plate Width | Plate Thickness | Tendon Length | Truss Size | Bone Size/mm | Top Diameter/mm | Mass/kg |
| 1500 | 1040 | 6 | 1500 | | 1500 × 45 × 5 | 100 | 1350 |
Summary of model nodes and degrees of freedom.
| Description | Value |
|---|---|
| Total number of nodes | 64,879 |
| Total number of elements | 63,942 |
| Degrees of freedom per node | 6 |
| Total degrees of freedom | 38,9274 |
| Global element size | 10 mm × 10 mm |
Comparison of damage shapes between test and simulation results.
| Condition Number | The Size and Area of the Damage | ||||||
|---|---|---|---|---|---|---|---|
| Experiment | Simulation | Error of Break Area | |||||
| x (mm) | y (mm) | A (mm2) | x (mm) | y (mm) | A (mm2) | ||
| SP-1 | 225 | 152 | 34,200 | 240 | 160 | 38,400 | −10.94% |
| SP-2 | 198 | 151 | 29,898 | 210 | 158 | 33,180 | −9.89% |
| SP-3 | 153 | 148 | 22,644 | 159 | 157 | 24,963 | −9.29% |
| SP-4 | 141 | 102 | 14,382 | 150 | 110 | 16,500 | −12.84% |
Comparison of peak impact force between test and simulation.
| Condition Number | Impact Force Peak/kN | ||
|---|---|---|---|
| Experiment | Simulation | Error | |
| SP-1 | 501.54 | 534.98 | −6.25% |
| SP-2 | 606.62 | 593.01 | 2.30% |
| SP-3 | 548.56 | 525.32 | 4.42% |
| SP-4 | 429.06 | 389.58 | 10.13% |
Energy distribution and loss ratio under different impact conditions.
| Condition Number | Energy/kJ | |||
|---|---|---|---|---|
| Total | Plate | Truss | Energy Loss Ratio | |
| SP-1 | 77.06 | 31.05 | 22.33 | 30.73% |
| SP-2 | 61.65 | 24.71 | 17.73 | 31.16% |
| SP-3 | 46.23 | 17.47 | 17.25 | 24.89% |
| SP-4 | 30.82 | 11.37 | 13.64 | 18.58% |
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