Buckling Knockdown Factors of Composite Cylinders under Both Compression and Internal Pressure

Round 1

Reviewer 1 Report

The paper describes buckling knockdown factors of composite cylinders under  both compression and internal pressure.

1. The analysis seems reasonable. Is there any experiments to verify the theory?

2. There are three figures from other references. There is one table from other reference. It is not good in an original paper. I suggest deleting them and add your own summary or analysis.

Author Response

The paper describes buckling knockdown factors of composite cylinders under both compression and internal pressure.

1. The analysis seems reasonable. Is there any experiments to verify the theory?

- We appreciate your comment. Unfortunately, there have been rarely experimental studies for thin-walled composite cylinders considering various thickness ratios and slenderness ratios when axial compression and internal pressure are applied to the cylinders simultaneously. At this time, the present authors’ research group are preparing the buckling tests for the thin-walled composite cylinders under both axial compression and internal pressure; therefore, in the near future, the numerical method used in this work may be validated against the experimental result. However, prior to the experimental work, it is important that the numerical analyses are conducted to study the modeling and analysis techniques; this is one of the goals of this paper.

- In addition a part of the present results is validated to the measured data from the buckling test. In Figure 6, the predicted global buckling load when the axial compression only is considered is compared with the measured data. As seen in the figure and description, the relative error between two results is 9.82%, which is reasonable.

- With above answer and considering your comment, we have added newly the following sentences in 4. Conclusions of the revised manuscript.

Furthermore, the buckling tests of thin-walled composite cylinders under both axial compression and internal pressure will be conducted in the near future; thus the buckling knockdown factors derived using the numerical methods applied in the present work will be compared with the experimental results.

 

2. There are three figures from other references. There is one table from other references. It is not good in an original paper. I suggest deleting them and add your own summary or analysis.

- Since the present cylinder model includes the internal pressure newly as compared to the original cylinder model, Z07 composite cylinder, given in the reference [13], Figure 2 has been modified in the revised manuscript, as your comment. However, Figures 1 and 5 and Table 1 in the manuscript are referred from the references [2, 13] for previous works. These figures and table are used to give the readers the basic information of knockdown factor, composite material properties, and analysis technique to the readers, not to show the results of the present authors’ original research results. The present work utilizes the previous modeling technique for the geometric initial imperfection of thin-walled cylinders; therefore, these should be referred from the previous works. We believe that the reviewer may understand this easily; therefore, the present authors have not revised or modified Figures 1 and 5 and Table 1 in the revised manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript systematically investigated the effect of internal pressure on the buckling knockdown factor for axially compressed thin-walled composite cylinders with different shell thickness ratios and slenderness ratios. This work is very interesting and useful. However, this manuscript also has some drawbacks.

 

1. Variables in this manuscript should be expressed in italic letters.
2. In this manuscript, the cylinder bears axial compression and internal pressure at the same time. The author should show both axial load and internal pressure in Fig. 2 instead of only axial pressure.
3. The last paragraph of the Chapter 1 introduced the finite element model and the numerical method adopted in this manuscript. The reviewer believes that this paragraph should be moved to Chapter 2, because the content of this paragraph is very similar to the content of Section 2.1.
4. Section 3.1 introduced the buckling load of the cylinder. This buckling load should be directly related to the radius R of the cylindrical shell. Please add the radius of the cylindrical shell in the Chapter 2 instead of just introducing the radius in Tab.1.
5. In this paper, the value of internal pressure of the shell is fixed at 10kPa. Please explain the reason for the value of this internal pressure. When the value of internal pressure changes, the imperfection sensitivity of the cylinder should be different. The conclusion of this article seems to be limited to a fixed value of external pressure. The author should change the value of the external pressure and obtain the knockdown factor of the cylinder.

Author Response

The manuscript systematically investigated the effect of internal pressure on the buckling knockdown factor for axially compressed thin-walled composite cylinders with different shell thickness ratios and slenderness ratios. This work is very interesting and useful. However, this manuscript also has some drawbacks.

 

1. Variables in this manuscript should be expressed in italic letters.

- As your comment, the letters to represent variables have been expressed using italic fonts in the revised manuscript.

 

2. In this manuscript, the cylinder bears axial compression and internal pressure at the same time. The author should show both axial load and internal pressure in Fig. 2 instead of only axial pressure.

- As your comment, Figure 2 has been modified to show both axial compression and internal pressure in the revised manuscript.

 

3. The last paragraph of the Chapter 1 introduced the finite element model and the numerical method adopted in this manuscript. The reviewer believes that this paragraph should be moved to Chapter 2, because the content of this paragraph is very similar to the content of Section 2.1.

- Considering your comment, some of the sentences in the last paragraph have been moved to the top of Section 2 of the revised manuscript.

 

4. Section 3.1 introduced the buckling load of the cylinder. This buckling load should be directly related to the radius R of the cylindrical shell. Please add the radius of the cylindrical shell in the Chapter 2 instead of just introducing the radius in Tab.1.

- In this study, the radius of a cylinder is fixed as the value of 0.25 m; however, the thickness and length are changed to consider various geometric properties. This is already described in the original manuscript below Table 1. Therefore, it may not be required that the value of a radius is written in all the results in Section 2. However, for clarity, the sentence has been modified on Page 4 of the revised manuscript as follows.

Based on the Z07 thin-walled composite cylinder model [13], the cylinder radius (R) is fixed for all the examples in this work, but the thickness (t) and length (L) are changed to design various R/t ratios and L/R ratios of the cylinders.

 

5. In this paper, the value of internal pressure of the shell is fixed at 10kPa. Please explain the reason for the value of this internal pressure. When the value of internal pressure changes, the imperfection sensitivity of the cylinder should be different. The conclusion of this article seems to be limited to a fixed value of external pressure. The author should change the value of the external pressure and obtain the knockdown factor of the cylinder.

- We appreciate your meaningful comment. The internal pressure’s magnitude in this work is selected to show clearly the increment of buckling knockdown factors when the internal pressure is applied to the cylinder, based on the trial and error method. However, various magnitudes of internal pressure are not considered in this work since this paper aims to investigate the amount of the increment in buckling knockdown factors, not to derive the empirical formula of buckling knockdown factors in terms of the internal pressure, when the internal pressure as well as the axial compression is considered. In spite of the above, as your comment, we will consider the different magnitudes of internal pressure at the buckling test which is in preparation at this time by the authors’ research group. This has been newly included in 4. Conclusion of the revised manuscript as follows.

 

Furthermore, the buckling tests of thin-walled composite cylinders under both axial compression and internal pressure with different magnitudes will be conducted in the near future; thus the buckling knockdown factors derived using the numerical methods applied in the present work will be compared with the experimental results.

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors present a FE numerical study during which they calculate the knockdown factors of laminated composite cylinder under combined axial compression and internal pressure.

Some comments :

1. It is known that for a shell under axial compression, an internal applied pressure would increase its capability to withstand the axial compression leading to higher knockdown factors.
2. The authors should discuss the innovation of their paper.  
3. The influence of the initial geometric imperfection is introduced using the SPLA method. However it is not quite clear if this method can be applied for the combined loading case.
4. The authors should introduce real initial geometric imperfections and calculate the reduction of the buckling load of the shells.
5. The main drawback of the present study, that it is based only on numerical results , without any experimental data. This should be discussed in the paper and and a comparison to existing experimental and/or numerical data available in the literature should be performed.

Author Response

The authors present a FE numerical study during which they calculate the knockdown factors of laminated composite cylinder under combined axial compression and internal pressure.

Some comments:

1. It is known that for a shell under axial compression, an internal applied pressure would increase its capability to withstand the axial compression leading to higher knockdown factors.

- As your comment, it is known that the internal pressure may improve the buckling stability of thin-walled structures under axial compression; however, there have not been studies which investigate the amount of increment in buckling knockdown factors of thin-walled composite cylinders when the internal pressure is considered. In addition, the present study considers various thickness ratios and slenderness ratios of thin-walled composite cylinders under both axial compression and internal pressure while the elastic coupling effect of composite laminates is maintained. The above is well described in 1. Introduction of the original manuscript.    

2. The authors should discuss the innovation of their paper.  

- The originality or innovation of the authors’ work is described fully and in detail in Page 3 of the original manuscript. However, as your comment, we have added the following sentences in 4. Conclusion of the revised manuscript to summarize the originality of this work.

This study investigated for the first time the amount of increase in buckling knockdown factors due to the internal pressure thoroughly for thin-walled composite cylinders with various geometric properties while the elastic coupling effect of composite laminates was maintained, and it demonstrated the possibility of improving the buckling knockdown factors when considering the internal pressure of axially compressed thin-walled composite cylinders;

 

3. The influence of the initial geometric imperfection is introduced using the SPLA method. However it is not quite clear if this method can be applied for the combined loading case.

- The SPLA is a method to model the geometric initial imperfection of a thin-walled shell structure. The geometric initial imperfection is independent of loading conditions since it means the geometric imperfection of a cylinder in an initial state, which is usually caused in the manufacturing process. Therefore, the SPLA can be used when the axial compression and internal pressure are applied to the cylinder simultaneously. Although it may not be guaranteed that the SPLA always provides a conservative buckling design criteria to thin-walled composite cylinders under both axial compression and internal pressure, it is believed that the SPLA is enough to show the trend of the amount of increment in buckling knockdown factors of thin-walled composite cylinders because of internal pressure. This has been newly explained in Page 6 of the revised manuscript as follows.

In addition, since the geometric initial imperfection of a thin-walled shell structure is independent of loading conditions, the SPLA is enough to study the trend of the amount of increment in the buckling knockdown factors due to internal pressure when the geometric initial imperfection only is considered.        

4. The authors should introduce real initial geometric imperfections and calculate the reduction of the buckling load of the shells.

- Unfortunately, it is impossible to obtain the measured imperfection data in the public domain for the Z07 composite cylinder used as the baseline model in this work. Therefore, this has not been considered in the revised manuscript. However, at this time, the present authors’ research group are preparing the buckling tests for the thin-walled composite cylinders under both axial compression and internal pressure; therefore, in the near future, the numerical results using SPLA will be compared with the postbuckling analyses using the measured imperfection data when both axial compression and internal pressure are applied to the cylinder, simultaneously. This has been described newly in 4. Conclusion of the revised manuscript as follows.   

Furthermore, the buckling tests of thin-walled composite cylinders under both axial compression and internal pressure will be conducted in the near future; thus the buckling knockdown factors derived using the numerical methods applied in the present work will be compared with the experimental results.

 

5. The main drawback of the present study, that it is based only on numerical results, without any experimental data. This should be discussed in the paper and a comparison to existing experimental and/or numerical data available in the literature should be performed.

 

• We appreciate your comment. Unfortunately, there have been rarely experimental studies for thin-walled composite cylinders considering various thickness ratios and slenderness ratios when axial compression and internal pressure are applied to the cylinders simultaneously. At this time, the present authors’ research group are preparing the buckling tests for the thin-walled composite cylinders under both axial compression and internal pressure; therefore, in the near future, the numerical method used in this work may be validated against the experimental result. However, prior to the experimental work, it is important that the numerical analyses are conducted to study the modeling and analysis techniques; this is one of the goals of this paper.
•  

- In addition a part of the present results is validated to the measured data from the buckling test. In Figure 6, the predicted global buckling load when the axial compression only is considered is compared with the measured data. As seen in the figure and description, the relative error between two results is 9.82%, which is reasonable.

 

- With the above answer and considering your comment, we have added newly the following sentences in 4. Conclusions of the revised manuscript.

 

Furthermore, the buckling tests of thin-walled composite cylinders under both axial compression and internal pressure will be conducted in the near future; thus the buckling knockdown factors derived using the numerical methods applied in the present work will be compared with the experimental results.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The authors are basing their solely on the SPLA method to simulate the worst case of initial geometric imperfections. Although claimed by the authors, that the method could simulate correctly the influence of the initial geometric imperfections on the buckling behavior of the shell, this is not sure a.

The authors should clearly state state in their conclusions, that the application of the SPLA was done, as no data regarding the measured imperfections of the shell calculated was not available to them. They should stress that their results only show the trend of the issue, and further calculations with measured initial imperfections in combination with real tests will give a better look at the problem .

Author Response

We appreciate your meaningful comments for our revised manuscript. Considering your comments, the present authors have revised the followings in the second revised manuscript. All the revisions have been expressed using blue color. 

As your comments, the present authors have added the following sentences in Page 6 of the second revised manuscript.

Since the geometric initial imperfection is unknown before measuring it and the measured imperfection data for the Z07 composite thin-walled composite cylinder are not available in the public domain, the SPLA [13] is applied to model the geometric initial imperfection of the thin-walled composite cylinder in this study.

 

In addition, as your comments, the following sentences have been newly included in 4. Conclusion of the second revised manuscript.

In Page 14,

The SPLA was applied to represent the geometric initial imperfection since the measured imperfection data of the present thin-walled composite cylinders were not available in the public domain.

 

In Page 15,

Furthermore, the buckling tests of thin-walled composite cylinders under both axial compression and internal pressure will be conducted in the near future. Using the measured imperfection data of the thin-walled composite cylinders and the global buckling loads obtained from the test, it will be investigated that the SPLA can be used to derive the buckling knockdown factor under both axial compression and internal pressure.

Author Response File: Author Response.pdf