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Peer-Review Record

Buckling of Rectangular Composite Pipes under Torsion

Appl. Sci. 2021, 11(3), 1342;
by Atsushi Takano 1,*, Ryo Mizukami 1 and Ryuta Kitamura 2
Reviewer 1: Anonymous
Reviewer 2: Anonymous
Reviewer 3: Anonymous
Appl. Sci. 2021, 11(3), 1342;
Submission received: 9 December 2020 / Revised: 24 January 2021 / Accepted: 30 January 2021 / Published: 2 February 2021
(This article belongs to the Special Issue Selected Papers from IMETI 2020)

Round 1

Reviewer 1 Report

The manuscript deals with the torsional buckling of composite plates. The Authors derived
a closed-form expression for determining the critical tangential stress for various
combination of the section geomtry and configuration/orientation of the plies.
Though the subject is of clear scientific interest, the manuscript requires a careful
revision process before publication.
In particular, the Authors are kindly invited to address the following comments.

Abstract. Line 14. The authors state that no previous studies have been conducted on the topic.
However, in reference [13] it seems that closed-form expression for torsional buckling of boxed sections
have been derived.
Moreover, other studies have been conducted on the torsional buckling of composite pipes,
proposing either closed-form expressions, either charts, see e.g.
[a] Marshall, I. H. (Ed.). (1981). Composite Structures. doi:10.1007/978-94-009-8120-1
[b] Loughlan, J. (1996). The buckling of composite stiffened box sections subjected to compression and bending. Composite structures, 35(1), 101-116.
[c] Vo, T. P., & Lee, J. (2007). Flexural–torsional buckling of thin-walled composite box beams. Thin-walled structures, 45(9), 790-798.
A comment on this, or better, a comparison between the here proposed solution and the literature formulas
may enrich the study and help highlighting the scientific contribution of the work.

Several equations appears badly formatted. Maybe this is due to the preprint template, but please
esnure that they are inserted in the proper way.

In Eqns. (3),(4) a coefficient appaears \Phi_{mn}, but it seems that it has not been defined elsewhere.
Consequently the assumption made through (5) is meaningless. Please give a detailed definition of
the introduced parameters and explain their role in the problem, otherwise the mathematical procedure
is hardly understandable.

It is not clear how the work of the torsional stress is defined. A more detailed explanation on
the derivation of Eqns. (16) and (21) is kindly requested.

Line 97-99. Please clarify the concept about the coefficient matrix. Still it has not been defined
and it is not possible to follow the procedure.

The numerical example at par. 2.2 considers a quasi-isotropic material: this is not a case of interest,
since the solution for torsional buckling of thin-walled boxed sections is very well-known in the literature.
Thus, if it is considered to valitdate the proposed approach, at least a comparison with literature solution
is required.

The results illustrated in Fig. 4 and the related comments are not clear. The critical tangential stress
is evaluated as a function of the aspect ratio l/b for different values of the number of adopted
shape functions. It is adopted as a validation for the convergence of the solution, but
the solution changes drastically between the case n=20 and n=100, thus
it is not possible to state that the case n=m=100 represents the exact solution.
Further comments are expected on the latter aspect: maybe plotting the case n=50, n=80 may help
in highiliting which is the best value for n, or better, a comparison with the FE solution
would solve the issue.

Please check all the unit measure of the paramters throughout the manuscript. Foe example,
they are missing at lines 115-116.

Line 126-127. It is not clear the meaning of the sentence, maybe a typo. Please check.

Figure 6 shows again the critical tangential stress is evaluated as a function of the aspect ratio l/b,
but here for different values of the aspect ratio h/b and a comaprison with the FE solution
is illustrated: the curve at h/b=1 derived via FE is missing.

In the mathematical modeling only the longitudinal and transver mechanical properties of the
composite appear, but no consideration is made about how the through-thickness properties
are evaluted is made. Of course, as stated at lines 140-145, an expensive numerical analysis
is required, but yet a summarized description would help in understanding the Authors contribution,
since for this purpose simplified closed-form expressions are available, see e.g.
[d] Jones, R. M. (1998). Mechanics of composite materials. CRC press.
[e] Ng, Y. C. (2005). Deriving composite lamina properties from laminate properties
using classical lamination theory and failure criteria. Journal of composite materials, 39(14), 1295-1306.
STIFFNESS PROPERTIES OF CLOSED COMPOSITE SECTIONS. Journal of Aeronautics & Space Technologies/Havacilik ve Uzay Teknolojileri Dergisi, 10(1).

In Fig. 10 a clear shift between the polynomial and numerical solution is observed. Though, the proposed
approach delivers a more conservative solution, an explanation why the polynomial solution
is affected by this almost constant shift should be given. Maybe n>100 may reduce the gap?

Please reformulate the final sentence in the conclusion. It appears the the verb is missing.
In addition, please, motivate the good agreement between theoretical and experimental buckling.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

The manuscript presents a numerical study on the buckling of rectangular composite pipes under torsion. The authors present an energy method to obtain the buckling load of the rectangular pipes. under torsion.

It is not clear why the authors did not include the warping of the cross section when calculating the total potential. Please explain.

The authors wrote :"The plate with a plane size a×b, in which m+n’ is even has a lower buckling load than the one in which  m+n’ is odd". Please explain and discuss this statement.

"Figure 5 shows the buckling mode and the changes in the angles of the pipe from 90°." Please explain in detail this figure as it is hard to understand the output.

Another problematic issue is lack of comparison of the present model with FE results or even for a simpler model (isotropic material instead of composite material). Without comparisons with existing results , the reliability of the present model is questionable.


Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

Dear Authors, 

The manuscript tilted "Buckling of Rectangular Composite Pipes" has been submitted to the Journal of Applied Sciences. The paper consider the buckling of composite thin walled composite pipes due to the torsion loading. The paper cover actual problem of buckling of composites. However the Reviewer has several objections which shall be respond to:

  1. The introduction shall be improved. The reader shall not be introduced into the scope of the current project but for the general problem related to the buckling of composite thin walled structures.    
  2. The title of the manuscript shall be change to the following: "Buckling of  Rectangular Pipes Due to the Torsion Loading" - the Authors consider only one type of loading. 
  3. The derivation of the energy method is not consistent. The authors shall provide the theoretical introduction in a lamina coordinate system, rather than in the global coordinate system (x,y,z). 
  4. The bending stiffnesses shall be given in lamina coordinate system and followed by a transformation matrix. 
  5. The authors state that they consider a symmetric lamination sequence in the form of  [(0/90)r,(±45)1-r], but this not a case for the symmetric laminate. 
  6. The paper is limited the one lamination sequence of the pipe, namely  [(0/90)r,(±45)1-r]. This not  is not justified by the Authors. 
  7. The Author claim that the buckling phenomenon appear prior any other failure of the composites. Please justify such assumption. How the Authors can be sure that a delamination would not appear prior the buckling.    
  8. The description of the numerical model is not sufficient. There is a lack of the material model assumed for the pipe. Please clarify which material model was used for numerical study.  
  9. There are many terms used by the authors that are not consistent with the mechanics of composite materials or theory of elasticity, such as "layups" instead of lamination sequence. Please explain what do the following terms mean: numerical buckling load; external torsional stress; the linked out-plane displacements;     
  10.  All the integers and variables used in the equations shall be clearly defined - the is a lack of such description in most case.

The Reviewer strongly suggest to improve the English grammar. 

To sum up, the paper can be consider for the publication after major revision. 

Yours Sincerely, 


Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors provided adequate reply to the comments given by the Reviewer and went through a careful revision of the manuscript.


Reviewer 2 Report

The authors introduced some explanations following the remarks of the reviewers.

In its present form, the manuscript can be published.

Reviewer 3 Report

The paper tilted "Buckling of Rectangular Composite Pipes" has been considerably revised. The Authors have responded to all of the the Reviewer's remarks accordingly. 

The only matter left is the formation of the equations and formulas. Please, contact the Editing section in this matter. 

The Reviewer suggests to publish the paper in the present form.  

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