Ultimate Buckling Limit State Assessments of Perforated Panels in Medium-Range Merchant Ships Based on Updated Classification Rules and Nonlinear Finite Element Analysis

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript addresses an important topic in ship structural design, particularly the buckling behavior of perforated panels in web frames. The use of updated CSR rules and nonlinear FEA is relevant. Please consider the following comments:

1. The novelty of the work could be better emphasized. Many similar studies have been conducted, and the manuscript would benefit from a clearer explanation of what distinguishes this work from previous research.
2. The study relies heavily on numerical simulations. The authors also acknowledged the importance of experimental validation. Is there any plan to perform experiments or validate the FE results against published experimental results?
3. The manuscript is quite long and dense. The authors can consider condensing some of the background literature (Section 1).
4. The mesh convergence study in Section 3.1 uses a square panel with four-edge support. Since most SUPs are three-edge supported, would the convergence behavior differ under those boundary conditions?
5. Section 4.4: The inelastic FEA assumes elastic-perfectly plastic behavior. Was any sensitivity analysis performed to assess the influence of strain hardening on the ultimate strength?
6. Section 4.5: The cost-saving analysis is a valuable addition. However, the assumptions (e.g., welding speed, material cost) should be more clearly justified or referenced.  Are these values based on actual shipyard data or literature estimates? Could the authors clarify whether a sensitivity analysis would strengthen this section?
7. The manuscript would benefit from a more explicit discussion of limitations. Could the authors comment on the applicability of their findings to larger vessels or offshore structures?

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This article aims to show a case study on how to reduce shipbuilding expenses by conducting a quantitative analysis of the buckling strength of such panels. The elastic buckling strength and ultimate buckling strength are evaluated according to the newly revised classification rules. For this purpose, perforated panels in transverse web frame were investigated on four actual built and operated merchant ships of a liquefied petroleum gas carrier, a container carrier, a product carrier, and a crude oil carrier. The stresses obtained from cargo hold analyses with loading conditions corresponding to the ultimate limit state, which had already been performed during the design phase of the four vessels, were used as the loads acting on the investigated perforated panels. The buckling strength of the perforated panels is then derived using the classification rule, eigenvalue FEA, and inelastic FEA. The importance of the buckling strength evaluation methodology is emphasized by analyzing the cost of construction based on the selective application of each methodology.
Following a suitable introduction, the paper presents the analytical calculation of perforated plates to illustrate the design strength requirements that must be satisfied (Load and boundary conditions, Ultimate buckling strength). The article includes a section focusing on the preparation steps for finite element analyses (FEAs), specifically addressing the determination of element size and the level of initial imperfections. The mesh size was optimized by analyzing how the elastic buckling strength varied with different element sizes, ensuring accurate and stable results. Additionally, the initial imperfection level was established by evaluating load–shortening behavior and comparing the ultimate compressive buckling strengths obtained from IACS rules and inelastic FEAs. This comparison helped define a representative initial deformation level to improve the reliability of the simulations. The article also examines the evaluation of the buckling limit state for the investigated perforated plates used in medium-sized merchant vessels. Several assessment methods are applied, including the IACS classification rules, eigenvalue finite element analyses (FEAs), and inelastic FEAs. The buckling performance of the plates is analyzed using each method, allowing for a comprehensive comparison of their predictive capabilities. This approach provides insight into the accuracy and conservativeness of the different evaluation techniques in determining the structural integrity of perforated panels under compressive loads. There are some cost calculations for reinforcement with carlings. It is demonstrated that the selective application of ultimate buckling strength evaluation methods in actual ship design can lead to significant cost savings. Future research is mentioned.
This research has important value. However, before publication, there are still some areas in the article that need to be improved. Below is my comment.
The research design has been appropriately structured to address the study objectives. The methods employed are described in sufficient detail, and the results are adequately explained. The findings are clearly presented and are supported by the analyses conducted. The results substantiate the conclusions drawn in the manuscript. Data have been effectively presented through well-constructed tables, informative figures, and properly formulated equations. These elements are correctly valued and interpreted within the context of the study, thereby enhancing the clarity and validity of the scientific communication.
The cost calculation section could be expanded by examining the size of the carlings. Is this size necessary for reinforcement in all cases?
Is the reference to Figure 1(b) correct on line 234?
Text is missing from the beginning of line 343.
The reference to Table 11 is missing.
In general, the article makes a good impression.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The authors assess the ultimate buckling strength of perforated web-frame panels, also known as Separated Unstiffened Panels (SUPs), that are used in commercial ships in this publication. They use both eigenvalue and inelastic (nonlinear) finite element analyses and the new IACS Common Structural Rules (CSR). I recommend minor revisions as:

Line 47: Sentence incomplete. Used for what? Please correct.

The description of Methods A and B is not clear. Please add more details.

Figure 2: The color (green) description needs to be explicitly explained in the Figure.

Preparation for FEA section: Eigenvalue of which mode? This should be specified. Can you present a graphical overview of the mode?

 

 

 

Reviewer 4 Report

Comments and Suggestions for Authors

The manuscript investigates the buckling analysis of unstiffened perforated panels for merchant ships with nonlinear finite element analysis.

After a literature review on the research topic where some significative previous papers are briefly commented, the main target of the research is declared, as well as the adopted methodology.

More specifically, the buckling modes are determined from finite element commercial software, and the effects of various parameters such as aspect ratios, and initial imperfections are checked. Then, a classification of these panels is conducted, based on Common Structural Rules. The results of the analysis are critically commented. The manuscript is well written and organized, and the topic is well explained. In order to improve the quality of the research work, the Reviewer suggests the hollowing hints:

• Please, do not adopt acronyms within titles and subtitles.
• The elements of novelty should be better explained.
• The terms “slight, average and severe” in Eq. 12 should be further commented.
• Have the Authors checked the validity of their finite element models against, for instance, 3D reference solution at least for one case?
• Referring to Fig. 11, subscript should be adopted for the label of y-axis.
• Please, add some comments at the beginning of each section before introducing the corresponding subsections.

The work is of scientific interest since it provides elements of novelty to the research field.

After these Minor Revisions, the manuscript may be considered for a possible publication in the Journal.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

All my comments were taken into account and necessary corrections were made. The paper can be accepted.