Slope Deflection Method in Nonlocal Axially Functionally Graded Tapered Beams
Round 1
Reviewer 1 Report
In this paper, the slope-deflection method for AFG beams with the variable cross-section was presented in the frame of nonlocal elasticity. Detailed comments and suggestions are given below.
1）In the introduction, the authors can not simply list the work done by other researchers, they need to summarize the research work done by other researchers.
2) It would be useful to highlight the main contribution and difference between the present study and the previous studies done by other researchers.
3）If the basic equations of a non-local Euler beam are not derived by the authors, it would be better to cite the related references.
Author Response
Dear Editors,
Required revisions of the related article were made as follows.
- The introduction part has been expanded with the addition of previous studies related to the subject of the article at the request of the editors.
- Related references are made to equations with missing references.
- Abbreviations of equations and figure sections have been corrected identically throughout the article.
- Parameters that are not defined in the equations are explained.
- Long titles have been shortened at the request of the editors, and necessary explanations have been added to the sections.
- The abstract, introduction, and conclusion sections of the article have been modified to include the purpose of the study, the method used, and its innovative aspect.
- At the request of the editors, the accuracy of the study was validated using a widely used book reference in the world.
- Referring to the comment "Modify Fig. 12 so that the left hinged end rotates" by the relevant editor: Since the examples given in this article were intended by the authors to contain a high-order degree of hyperstaticity, relevant changes were not made.
- Referring to the comment “line 117 and 277: 0 ≤ ? < ?? → ?? ≤ ? ≤ ?
- " by the relevant editor: Since the z length in the relevant interval is accepted as the point where the p2 load starts, the range of 0 ≤ ? < ?? has not been changed.
- The title of the article was changed to "Static Analysis of nonlocal axially functionally graded tapered beams" considering the editor's suggestion.
Along with the major revisions made above, the valuable comments of all editors have been taken into account in detail.
Please address all correspondence concerning this manuscript to me at [[email protected]].
Thank you for your consideration of this manuscript.
Sincerely,
Dr. Murat Çelik
Reviewer 2 Report
See comments attached.
Comments for author File: 
Comments.pdf
Author Response
Dear Editors,
Required revisions of the related article were made as follows.
- The introduction part has been expanded with the addition of previous studies related to the subject of the article at the request of the editors.
- Related references are made to equations with missing references.
- Abbreviations of equations and figure sections have been corrected identically throughout the article.
- Parameters that are not defined in the equations are explained.
- Long titles have been shortened at the request of the editors, and necessary explanations have been added to the sections.
- The abstract, introduction, and conclusion sections of the article have been modified to include the purpose of the study, the method used, and its innovative aspect.
- At the request of the editors, the accuracy of the study was validated using a widely used book reference in the world.
- Referring to the comment "Modify Fig. 12 so that the left hinged end rotates" by the relevant editor: Since the examples given in this article were intended by the authors to contain a high-order degree of hyperstaticity, relevant changes were not made.
- Referring to the comment “line 117 and 277: 0 ≤ ? < ?? → ?? ≤ ? ≤ ?
- " by the relevant editor: Since the z length in the relevant interval is accepted as the point where the p2 load starts, the range of 0 ≤ ? < ?? has not been changed.
- The title of the article was changed to "Static Analysis of nonlocal axially functionally graded tapered beams" considering the editor's suggestion.
Along with the major revisions made above, the valuable comments of all editors have been taken into account in detail.
Please address all correspondence concerning this manuscript to me at [[email protected]].
Thank you for your consideration of this manuscript.
Sincerely,
Dr. Murat Çelik
Reviewer 3 Report
In this paper, the slope-deflection method for axially functionally graded beams with the variable cross section was presented in the frame of nonlocal elasticity. Generally speaking, this paper is somewhat interesting. Therefore, this reviewer suggests the acceptance after major revisions according to the following comments.
1. Many cases concerning axially functionally graded beams are analyzed and discussed, however, there is no corresponding validation. Although authors stated in the conclusion “the accuracy of this theoretical work should be supported with the help of finite element software and experimental studies”, it is still recommended that authors try to conduct a simple and feasible validation, for example, try to compare the solutions obtained in this study with others, even if the solutions are degraded solutions.
2. The abstract part should be re-organized to clearly show the research background, the main work, results and conclusions.
3. The Introduction section should be strengthened and divided into several parts (but not a very long paragraph), including the problem proposed, the method used, the existed works review and lastly, the innovation of this work.
4. Equation (1) should be indicated where it comes from. It is obvious that the equation is not derived by authors themselves.
5. If there is no Section 4.1.2, Section 4.1.1 cannot be listed as a separate title. Also, there are the same problem for Section 5.1.1, Section 5.2.1, …., please check them all.
6. The titles for Sections 5.1, 5.2, 5.3 and 5.4 are too long, please shorten them and move redundant descriptions into the main text.
7. Given that some equations are very long, authors should reasonably arrange their structural forms, otherwise, otherwise, to understand them in the present form would be very difficult. For example, Equations (37), (38), (47), (48), (52) and (53).
8. The conclusion section should be given point by point, thus the potential readers may understand the main conclusions obtained in this study.
9. The style of the References should agree well with the standard of MDPI, for example, the journal name should be abbreviated and italic, the number for publication year is bold and the number for the volume is italic. In addition, Ref. [42] is problematic, please check it.
10. At line 458, there is a typo, figure 25?
Author Response
Dear Editors,
Required revisions of the related article were made as follows.
- The introduction part has been expanded with the addition of previous studies related to the subject of the article at the request of the editors.
- Related references are made to equations with missing references.
- Abbreviations of equations and figure sections have been corrected identically throughout the article.
- Parameters that are not defined in the equations are explained.
- Long titles have been shortened at the request of the editors, and necessary explanations have been added to the sections.
- The abstract, introduction, and conclusion sections of the article have been modified to include the purpose of the study, the method used, and its innovative aspect.
- At the request of the editors, the accuracy of the study was validated using a widely used book reference in the world.
- Referring to the comment "Modify Fig. 12 so that the left hinged end rotates" by the relevant editor: Since the examples given in this article were intended by the authors to contain a high-order degree of hyperstaticity, relevant changes were not made.
- Referring to the comment “line 117 and 277: 0 ≤ ? < ?? → ?? ≤ ? ≤ ?
- " by the relevant editor: Since the z length in the relevant interval is accepted as the point where the p2 load starts, the range of 0 ≤ ? < ?? has not been changed.
- The title of the article was changed to "Static Analysis of nonlocal axially functionally graded tapered beams" considering the editor's suggestion.
Along with the major revisions made above, the valuable comments of all editors have been taken into account in detail.
Please address all correspondence concerning this manuscript to me at [[email protected]].
Thank you for your consideration of this manuscript.
Sincerely,
Dr. Murat Çelik
Round 2
Reviewer 2 Report
None.
Reviewer 3 Report
This paper may be accepted for publication in present form.
