Experimental and Numerical Study on Damage Characteristics of Web Frame Structure Under Conical Impact

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Editor,

Thank you for the opportunity to review the manuscript entitled "Experimental and numerical study on damage characteristics of web frame structure under conical impact." I have carefully evaluated the manuscript and would like to share the following comments and suggestions:

1. The abstract should conclude with the main findings of the study. It is highly recommended to include key numerical results, such as the percentage increase in load capacity or quantitative indicators of structural behavior like dissipated energy.
2. The number of references is limited (only 20), with just 4 sources published in the last three years. The authors are encouraged to enrich the literature review with more recent and relevant studies.
3. Figure 1: The quality of the figure is poor, and the numerical labels are pixelated. A clearer, higher-resolution version should be provided.
4. Figure 5: The experimental setup should include the instrumentation used. Specifically, the authors should clarify how displacement and impact force were measured during the tests.
5. Figures 7 and 18: These figures represent load-displacement curves under static loading. However, the manuscript lacks discussion on time-dependent effects. The dynamic nature of the impact loading must be reflected and discussed accordingly.
6. The manuscript does not provide the input parameters used in LS-DYNA, nor any discussion of the parameter selection process. There is no mesh sensitivity analysis, and the model dimensions or number of degrees of freedom are not specified. The authors should also mention and define the element types used in the simulations.
7. The results section is very limited and lacks in-depth analysis. A more comprehensive discussion and interpretation of the results is needed.
8. A major shortcoming of the manuscript is the absence of a parametric study. Variables such as progressive or repeated impact loading should be investigated. Otherwise, the benefit of the numerical validation efforts remains underutilized.

To enhance the manuscript, the authors may consider reviewing and referencing the following recent studies that may provide relevant insights and context:

• https://doi.org/10.3389/fmats.2024.1373292
• https://doi.org/10.12989/scs.2024.50.6.627

Overall, while the topic of the manuscript is relevant, the work requires significant improvements in both experimental detailing and numerical analysis to meet the journal’s publication standards.

Sincerely,

 

Author Response

Comment 1: The abstract should conclude with the main findings of the study. It is highly recommended to include key numerical results, such as the percentage increase in load capacity or quantitative indicators of structural behavior like dissipated energy.

Response1: We appreciate the reviewer’s valuable suggestion. In the revised manuscript, we have incorporated specific quantitative results at the end of the abstract to highlight the main findings of the study. This includes the peak impact force values under different drop heights, the corresponding percentage increase, the maximum energy absorbed by the structure, and the change in failure displacement. These additions aim to improve the clarity and informativeness of the abstract and to emphasize the practical significance of our results.

The revised abstract now reads (excerpt):

“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%”

Comment 2:The number of references is limited (only 20), with just 4 sources published in the last three years. The authors are encouraged to enrich the literature review with more recent and relevant studies.

Response2: Thank you for this constructive suggestion. We fully agree that incorporating more recent and relevant studies can strengthen the context and academic depth of the paper. In response, we have carefully revised the literature review section and added 5 new references (2022–2024). These additions provide updated insights into dynamic impact behavior, web/frame structures, and recent developments in material modeling under high strain rates. We believe these references help to contextualize our work more effectively within current research trends.

The following references have been newly added to enrich the manuscript:

9.Liu B, Soares C G. Recent developments in ship collision analysis and challenges to an accidental limit state design method. Ocean Engineering, 2023, 270: 113636.

10.Liu J, Yang F, Li S, et al. Testing and evaluation for intelligent navigation of ships: current status, possible solutions, and challenges. Ocean Engineering, 2024, 295: 116969.

11.Zhou H Y. Investigations on dynamic behaviors and similarity law of double hull ship structures under collisions. Yokohama National University, 2024.

18.Liu Y L, Wang P P, Wang S P, et al. Numerical analysis of transient fluid-structure interaction of warship impact damage caused by underwater explosion using the FSLAB. Journal of Ocean Engineering, 2022, 17(5): 1-15.

19.Liu K, Zong S, Li Y, et al. Structural response of the U-type corrugated core sandwich panel used in ship structures under the lateral quasi-static compression load. Marine structures, 2022, 84: 103198.

 

Comment 3: Figure 1: The quality of the figure is poor, and the numerical labels are pixelated. A clearer, higher-resolution version should be provided.

Response3: We thank the reviewer for pointing this out. In response, we have replaced Figure 1 with a high-resolution version to ensure improved clarity and readability. The numerical labels and graphical elements have been enhanced to eliminate pixelation and ensure consistent formatting. The updated figure has been embedded in the revised manuscript and rechecked for quality compliance with publication standards.

 

Comment 4: Figure 5: The experimental setup should include the instrumentation used. Specifically, the authors should clarify how displacement and impact force were measured during the tests.

Response 4: We appreciate the reviewer’s insightful comment. In the revised manuscript, we have updated Figure 5 to include the instrumentation used in the experimental setup. Specifically, we have indicated the locations of the load cell used to measure impact force and the high-speed camera and displacement sensor used to capture the deformation process and quantify the displacement. In addition, a brief description of the measurement methods has been added to the text (Section 3) to clarify how impact

force and displacement were obtained during the tests. This has been updated in Section 2.2 of the revised manuscript.

 

Comment 5: Figures 7 and 18: These figures represent load-displacement curves under static loading. However, the manuscript lacks discussion on time-dependent effects. The dynamic nature of the impact loading must be reflected and discussed accordingly.

Response 5: Thank you for this valuable comment. We acknowledge the importance of highlighting the dynamic characteristics of the impact process. In the revised manuscript, we have clarified that Figures 7 and 18 present quasi-static load–displacement curves, which are intended as baseline references for comparison with dynamic responses. To better reflect the time-dependent effects of impact loading, we have added a new figure (Figure 15) showing the energy–displacement curves under dynamic conditions. This allows for a clearer representation of energy absorption behavior during high-speed deformation.

Furthermore, the discussion in Section 2.3 has been expanded to emphasize key dynamic effects such as strain rate sensitivity, inertia-driven responses, and nonlinear energy dissipation, which are not captured in static tests. These additions strengthen the manuscript’s treatment of the dynamic nature of the problem and provide a more comprehensive analysis of the structural behavior under impact loading.

 

Comment 6: The manuscript does not provide the input parameters used in LS-DYNA, nor any discussion of the parameter selection process. There is no mesh sensitivity analysis, and the model dimensions or number of degrees of freedom are not specified. The authors should also mention and define the element types used in the simulations.

 

Response 6: We appreciate the reviewer’s thorough and constructive feedback. In the revised man Thank you for your valuable comments. In response to your suggestion, we have supplemented the relevant information in Section 3.1 of the manuscript. Specifically, we have provided detailed input parameters used in LS-DYNA, discussed the parameter selection process, and clarified that a mesh sensitivity analysis had already been conducted during the preliminary study. The comparison results showed that the mesh size of 10 mm × 10 mm provided the best balance between computational efficiency and accuracy. In addition, we have clearly described the model dimensions, the number of degrees of freedom, and the element types (SHELL163) used in the simulations. These additions aim to enhance the transparency and reproducibility of our simulation work.

 

Comment 7: The results section is very limited and lacks in-depth analysis. A more comprehensive discussion and interpretation of the results is needed.

Response 7: Thank you for your valuable comment regarding the need for a more comprehensive analysis of the results. In response, we have substantially expanded the Results section to provide a deeper discussion and interpretation. Specifically, in Section 3.2.3, we have added a detailed analysis of the time-history curves of various energy components (including kinetic energy, internal energy, and total energy), to better understand the dynamic response and energy dissipation mechanisms during the impact process. Furthermore, in Section 3.2.4, we have added a stress triaxiality analysis to characterize the failure modes, which offers additional insights into the damage initiation and evolution under different impact conditions. These additions significantly enhance the depth and completeness of the results interpretation. The newly added contents are highlighted in red for ease of review.

 

Comment 8: A major shortcoming of the manuscript is the absence of a parametric study. Variables such as progressive or repeated impact loading should be investigated. Otherwise, the benefit of the numerical validation efforts remains underutilized.

Response 8: We appreciate the reviewer’s insightful comment. While we acknowledge the value of an extended parametric study (such as progressive or repeated impacts) and will consider this in our future work, we have included a mesh sensitivity analysis in the revised manuscript to better utilize and validate the numerical model.

Specifically, three mesh sizes (15 mm, 10 mm, and 5 mm) have been tested in the simulation. The comparison results show that the 10 mm × 10 mm mesh provided the best balance between accuracy and computational efficiency, with minimal variation in peak force and energy absorption values when compared to the finer mesh.

Reviewer 2 Report

Comments and Suggestions for Authors

1. 

The abstract effectively summarizes the experimental and numerical components of the research, indicating the methodology (drop-weight impact test, finite element simulation), the key variables (drop height, impact force), and the main findings (damage concentration and increase in force with height). However, it could be improved by:

- Clearly stating the novelty of studying web frame structures as opposed to flat or stiffened panels.

-  Including quantitative results (e.g., peak force range, error between simulation and experiment).

• Explicitly mentioning the validated accuracy of the LS-DYNA model.

• Detailed Material Property Discussion:
  The paper lacks an in-depth explanation of material strain-rate sensitivity and fracture mechanisms. Consider elaborating on how material models (e.g., Cowper-Symonds) affect simulation accuracy.

• Fracture and Failure Mode Quantification:
  Although damage shapes are discussed visually, a more quantitative fracture analysis (e.g., strain localization zones or crack propagation) would enhance technical completeness.

• Mesh Convergence Study:
  The mesh size is selected without a convergence study. Including such a study would increase confidence in the simulation accuracy.

• Boundary Conditions and Realism:
  The support conditions in simulation (e.g., two ends bolted, others free) should be discussed in terms of how well they replicate real-world ship structures.

• Impact Energy vs. Absorbed Energy Analysis:
  The energy absorption capacity is central to impact studies, but this metric is not calculated. Including energy balance (input vs. absorbed vs. lost) would greatly improve the results section.

The differentiation from prior studies is addressed, particularly that most prior work focused on flat or stiffened plates, not web frame structures. However, the uniqueness of using conical impact on web frames should be emphasized more in both the introduction and abstract.

Consider adding a table or figure summarizing gaps in the literature and how this work fills them.

• Graphs (e.g., Figs. 7, 18) are clear but need:

  • Larger font sizes

  • More descriptive captions (e.g., “Experimental vs. Simulated Impact Force-Displacement Curves”)

  • Clear axis labeling with units

• Tables (e.g., Table 7) are informative, but:

  • Should include percentage errors directly in the table for clarity

  • Use consistent formatting (e.g., align decimals)

Recommendation: Align all visual elements to MDPI's graphic standards for clarity and reproducibility.

• The references are comprehensive and include both recent studies (2022–2024) and foundational work.

• However, more international studies from high-impact journals (e.g., Engineering Structures, Marine Structures, IJIE) should be included.

• Some relevant analytical or hybrid method studies are missing that could enrich the simulation framework.

The conclusions are well-structured, concise, and reflect the results accurately. However, the future work section is missing.

Comments on the Quality of English Language

• Original: “The pituitary gland can adjust the height drop…”
  Revised: “The lifting mechanism can adjust the drop height…”

• Original: “Meanwhile, finite element simulations of the drop hammer impact tests were performed using LS-DYNA software, and numerical results agree reasonably with the experimental data, which validates the reliability of the simulation method.”
  Revised: “Finite element simulations were performed using LS-DYNA, and the numerical results showed good agreement with experimental data, validating the simulation’s reliability.”

• Original: “The impact force curve obtained from the experiment shows more pronounced oscillations, with the peak slightly higher than the simulation results.”
  Revised: “The experimentally obtained impact force curves exhibit more pronounced oscillations and slightly higher peaks compared to simulation results.”

• Original: “The model is composed of a web frame structure and impact head, and the impact position of the model is between two stiffeners.”
  Revised: “The model consists of a web frame structure and an impact head, with the impact point located between two stiffeners.”

• Original: “The drop-weight impact test of web frame structure under four working conditions is carried out.”
  Revised: “Drop-weight impact tests on the web frame structure were conducted under four different conditions.”

Author Response

Comment 1: The abstract effectively summarizes the experimental and numerical components of the research, indicating the methodology (drop-weight impact test, finite element simulation), the key variables (drop height, impact force), and the main findings (damage concentration and increase in force with height). However, it could be improved by: Clearly stating the novelty of studying web frame structures as opposed to flat or stiffened panels. Including quantitative results (e.g., peak force range, error between simulation and experiment).

Response 1: We appreciate the reviewer’s valuable suggestion. In the revised manuscript, we have incorporated specific quantitative results at the end of the abstract to highlight the main findings of the study. This includes the peak impact force values under different drop heights, the corresponding percentage increase, the maximum energy absorbed by the structure, and the change in failure displacement. These additions aim to improve the clarity and informativeness of the abstract and to emphasize the practical significance of our results.

The revised abstract now reads (excerpt):

“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, representing a 41.38% rise. Additionally, the maximum energy absorbed by the structure reached 62.89 KJ, and the energy loss ratio ranged from 18.58% to 30.73%.”

We have also added the phrase 'Compared to the 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 ' in lines 2 to 4 of the abstract to clearly emphasize the novelty of investigating web frame structures, as opposed to flat or stiffened panels.

Comment 2: Explicitly mentioning the validated accuracy of the LS-DYNA model.

• Detailed Material Property Discussion:
  The paper lacks an in-depth explanation of material strain-rate sensitivity and fracture mechanisms. Consider elaborating on how material models (e.g., Cowper-Symonds) affect simulation accuracy.
• Fracture and Failure Mode Quantification:
  Although damage shapes are discussed visually, a more quantitative fracture analysis (e.g., strain localization zones or crack propagation) would enhance technical completeness.
• Mesh Convergence Study:
  The mesh size is selected without a convergence study. Including such a study would increase confidence in the simulation accuracy.
• Boundary Conditions and Realism:
  The support conditions in simulation (e.g., two ends bolted, others free) should be discussed in terms of how well they replicate real-world ship structures.
• Impact Energy vs. Absorbed Energy Analysis:
  The energy absorption capacity is central to impact studies, but this metric is not calculated. Including energy balance (input vs. absorbed vs. lost) would greatly improve the results section.

 

Response 2: We sincerely thank the reviewer for this comprehensive and constructive feedback.  Substantial revisions have been made to address each of these important points:

1. Detailed Material Property Discussion:

Thank you for pointing this out. We have revised the manuscript to include a more detailed discussion of the material strain-rate sensitivity and the influence of the Cowper-Symonds model on simulation accuracy. Specifically, we explain that the Cowper-Symonds model introduces strain-rate effects into the yield stress definition, which is particularly important in dynamic impact simulations. For the material used in this study, appropriate D and P parameters were selected based on relevant literature to ensure accurate representation of strain-rate sensitivity. These additions can be found in the revised Section 3.1.

2. Fracture and Failure Mode Quantification:

Thank you very much for your insightful suggestion. In response, we have incorporated a more quantitative fracture analysis into the revised manuscript by extracting strain localization zones and examining potential crack propagation paths based on the observed stress triaxiality distributions. This addition provides a more detailed understanding of the damage initiation and evolution mechanisms, thereby enhancing the technical rigor and completeness of the study. The relevant revisions have been made in Section 3.2.4.

3. Mesh Convergence Study:

A mesh sensitivity analysis has been conducted using 15 mm, 10 mm, and 5 mm element sizes.  The results show minimal variation between 10 mm and 5 mm meshes in terms of peak force and energy absorption, confirming that the selected 10 mm × 10 mm mesh is sufficiently accurate. Relevant explanations have been added in Section 3.1, with the specific modifications detailed as follows.

“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 was conducted. The results indicated 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 Fig. 20.”

4. Boundary Conditions and Realism:

We appreciate the reviewer’s insightful comment regarding the boundary conditions used in the simulation. In the revised manuscript, we have added a clarification in Section 3.1(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. 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 explain the rationale behind the selected support conditions. Specifically, the model assumes that the two ends of the structure are bolted (fixed), while the other edges are free, which aims to replicate the local response of web frame structures in ship hulls where the ends are connected to adjacent structural members, and lateral freedom reflects realistic load transmission in open compartments. Although this is a simplified representation, it captures the main constraints present in practical marine environments. Future work will consider more complex boundary conditions to further enhance simulation fidelity.

To support this approach, we refer to the study by Gao et al. (2014), which investigates the resistance of ship web girders under collision and grounding scenarios using finite element analysis. The study emphasizes the importance of accurately modeling boundary conditions to reflect real-world structural responses, particularly in the context of ship collisions and groundings.

5. Impact Energy vs. Absorbed Energy:

Thank you for your valuable suggestion. We fully agree that energy absorption is a key metric in evaluating impact resistance. In response to your comment, we have added a detailed energy analysis in Section 3.2.3 of the revised manuscript. This includes the calculation and comparison of input energy, absorbed energy (by plate and truss components), and energy loss ratios under different impact conditions. Table 10 was added to summarize these results, providing a clearer view of the energy balance and enhancing the discussion of structural performance during impact events.

 

Comment 3: The differentiation from prior studies is addressed, particularly that most prior work focused on flat or stiffened plates, not web frame structures. However, the uniqueness of using conical impact on web frames should be emphasized more in both the introduction and abstract.

Response 3: Specifically, in the third paragraph of the Introduction (lines 18 to the end), we have added the following content to highlight this point:

“Despite recent advances in impact mechanics, most existing studies have focused on planar or folded plate structures, while investigations into 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. In contrast to conventional 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.”

We believe this addition more clearly demonstrates the novelty and necessity of our study and addresses the reviewer’s suggestion effectively.

 

Comment 4:

Graphs (e.g., Figs. 7, 18) are clear but need:

• Larger font sizes
• More descriptive captions (e.g., “Experimental vs. Simulated Impact Force-Displacement Curves”)
• Clear axis labeling with units

Tables (e.g., Table 7) are informative, but:

• Should include percentage errors directly in the table for clarity
• Use consistent formatting (e.g., align decimals)

Recommendation: Align all visual elements to MDPI's graphic standards for clarity and reproducibility.

 

Response 4: We appreciate the reviewer’s detailed and constructive feedback on improving the quality of figures and tables.  In the revised manuscript:

• All graphs, including Figs. 7 and 18, have been updated with larger font sizes, clear axis labels with appropriate units, and more descriptive captions (e.g., “Comparison of Experimental and Simulated Impact Force–Displacement Curves”) to enhance clarity and understanding.
• Table 7 has been revised to include percentage errors between simulation and experimental results directly in the table, providing a clearer view of the comparison.
• We have also ensured consistent numerical formatting, including the alignment of decimals, across all tables.

All visual elements have been adjusted in accordance with MDPI’s graphic standards to improve visual clarity and reproducibility.

 

Comment 5: The references are comprehensive and include both recent studies (2022–2024) and foundational work. However, more international studies from high-impact journals (e.g., Engineering Structures, Marine Structures, IJIE) should be included. Some relevant analytical or hybrid method studies are missing that could enrich the simulation framework.

Response 5: Thank you for this constructive suggestion. We fully agree that incorporating more recent and relevant studies can strengthen the context and academic depth of the paper. In response, we have carefully revised the literature review section and added 5 new references (2022–2024). These additions provide updated insights into dynamic impact behavior, web/frame structures, and recent developments in material modeling under high strain rates. We believe these references help to contextualize our work more effectively within current research trends.

The following references have been newly added to enrich the manuscript:

9.Liu B, Soares C G. Recent developments in ship collision analysis and challenges to an accidental limit state design method. Ocean Engineering, 2023, 270: 113636.

10.Liu J, Yang F, Li S, et al. Testing and evaluation for intelligent navigation of ships: current status, possible solutions, and challenges. Ocean Engineering, 2024, 295: 116969.

11.Zhou H Y. Investigations on dynamic behaviors and similarity law of double hull ship structures under collisions. Yokohama National University, 2024.

18.Liu Y L, Wang P P, Wang S P, et al. Numerical analysis of transient fluid-structure interaction of warship impact damage caused by underwater explosion using the FSLAB. Journal of Ocean Engineering, 2022, 17(5): 1-15.

19.Liu K, Zong S, Li Y, et al. Structural response of the U-type corrugated core sandwich panel used in ship structures under the lateral quasi-static compression load. Marine structures, 2022, 84: 103198.

 

Comment 6: The conclusions are well-structured, concise, and reflect the results accurately. However, the future work section is missing.

Response 6: We sincerely appreciate the reviewer’s positive assessment of the conclusion section. In response to the suggestion, we have added a brief future work outlook at the end of the conclusion (session 5). This addition outlines the potential directions for further research, including the consideration of more complex boundary conditions, investigation of repeated or progressive impact scenarios, and incorporation of more advanced fracture modeling techniques. These efforts aim to further enhance the reliability and applicability of our findings.

 

Comment 7:Comments on the Quality of English Language

• Original: “The pituitary gland can adjust the height drop…”
  Revised: “The lifting mechanism can adjust the drop height…”
• Original: “Meanwhile, finite element simulations of the drop hammer impact tests were performed using LS-DYNA software, and numerical results agree reasonably with the experimental data, which validates the reliability of the simulation method.”
  Revised: “Finite element simulations were performed using LS-DYNA, and the numerical results showed good agreement with experimental data, validating the simulation’s reliability.”
• Original: “The impact force curve obtained from the experiment shows more pronounced oscillations, with the peak slightly higher than the simulation results.”
  Revised: “The experimentally obtained impact force curves exhibit more pronounced oscillations and slightly higher peaks compared to simulation results.”
• Original: “The model is composed of a web frame structure and impact head, and the impact position of the model is between two stiffeners.”
  Revised: “The model consists of a web frame structure and an impact head, with the impact point located between two stiffeners.”
• Original: “The drop-weight impact test of web frame structure under four working conditions is carried out.”
  Revised: “Drop-weight impact tests on the web frame structure were conducted under four different conditions.”

Response 7: We sincerely appreciate the reviewer’s comments regarding the language quality. The sentences pointed out have been revised based on the reviewer’s suggested improvements.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have made all required modifications satisfactorily.