Round 1

Reviewer 1 Report

This is a review of manuscript applsci-2281305 “Multi-domain substructure synthesis with normalized interpolating technique for non-matching interfaces” sent by Z.-Y. Chen, L. Liu and S.-L. Chen to Applied Science.

I have carefully read the manuscript and found the subject interesting, pertinent and, to my knowledge, original. The literature review is well exposed, the methodology is clearly described and the numerical example are convincing. Globally, the manuscript is well written but I find that the grammar could be improved in lots of places (I give some advices right after). I also feel the display of equations could be improved, notably with being more rigorous on the use of bold for vector and regular for scalar. To take this into account, I recommend a major review in the MDPI journals sense (as minor reviews are not validated by reviewers). Here are precise remarks:

-        Page 1, line 35: “expose the shortcomings” => “expose their shortcomings”, or simply “expose shortcomings”

-        Page 1, line 38: “in dealing transient problems” => “in dealing with transient problems”

-        Page 2, line 56: “when IRFs generated” => “are generated”

-        Page 2, line 60: “In history” => “Historically”

-        Page 2, line 62: “One class of methods to coupling” => “for coupling”, “to couple” or “one class of coupling methods”

-        Page 2, line 74: “Because after derivation…”, there is not verb in this sentence

-        Page 3, line 104: “the IRFs can be regard” => “regarded”

-        Page 3, line 111: “efficacious” => “efficient”

-        Page 3, equation 2: n and delta_t should be formally defined

-        Page 3, line 143 : “comply the Newton’s third law” => comply with

-        Page 4, equation 5: I feel that Eq. 5 is not exactly a substitution of 4 into 2. Formally an additional step or explanation may be required although I understand what is written

-        Page 5, line 176 : “are not coincided” => “are not coincident” ?

-        Page 7, line 260 : “can be rewrote” => “rewritten”

-        Page 7, equation 35 : surely M, C and K should be in bold font

-        Page 7, line 264 : “And” => generally, as the equation is part of a sentence, the usage is to put a comma after the equation, and not to start the next word with a capital letter. I found it in some other places in the manuscript. Please check.

-        Page 8, equation 37: I feel that here in second line u_n^(s), the n should not be bold as it is a subscript. In the same vein, in dt, the t should not be bold.

-        Page 8, line 280: “Then u_n’ and u_n’’ “ => these should be written in bold fonts, same in equation 42.

-        Page 9, line 316: “eigen-frequencies” => “eigenfrequencies” is more common these days.

-        Page 10, line 353 “no-matching” should be “non-matching” as in the title.

-        Page 11, line 376, “coincide” => “to coincide” to make the sentence grammatically correct

-        Page 11, equation 56: is it really equal to scalar 1 ?

-        Page 11, line 402, “two interpolation method is introduced” => “methods are introduced”

-        Page 11, subsection B : variable is surely a vector, and should be displayed in bold, as it is in equation 63 later

-        Page 12, line 429, “MK” is not introduced as far as I’ve looked.

-        Page 13, equation 70: add units

-        Page 18, line 573: “no-matching” should be “non-matching” as in the title.

-        Page 19, is figure 11 taken from reference 13 ?

-        Page 20, line 620: “for al” => “for all”

-        Page 20, line 621: “spend” => “spends”

-        Page 20, line 623: “doesn’t need” => “do not need”

-        Page 20, line 645, “its precision influence” => “precise”

-        Page 25, but a more general advice for the references, to make the authors presentation homogeneous: [31] is L. Gu, [32] is T. PLAN, [33] is Belytschko, T.

 

Author Response

Response to reviewer1

Thanks to the suggestion of reviewer. The grammar of paper has been check and improved. The equation has been checked carefully, especially for the use of vector and scalar. I made a modification according to the comment of reviewer. Following is some response to comment.

Comment1: Page 4, equation 5: I feel that Eq. 5 is not exactly a substitution of 4 into 2. Formally an additional step or explanation may be required although I understand what is written.

Response: Thanks to the advice of reviewer. Eq. 2 only consider the external force. So we add interface force into it.

Comment2: Page 7, line 264 : “And” => generally, as the equation is part of a sentence, the usage is to put a comma after the equation, and not to start the next word with a capital letter. I found it in some other places in the manuscript. Please check.

Response: We have change it according to the reviewer.

Comment3: Page 11, equation 56: is it really equal to scalar 1 ?

Response: Yes, according to definition, it must equal to 1.

Comment4: Page 12, line 429, “MK” is not introduced as far as I’ve looked.

Response: We add a definition before,see line 409

Comment5: Page 13, equation 70: add units单位

Response: We add units

Comment6:  I also feel the display of equations could be improved, notably with being more rigorous on the use of bold for vector and regular for scalar

(a)Page 8, equation 37: I feel that here in second line u_n^(s), the n should not be bold as it is a subscript. In the same vein, in dt, the t should not be bold.

(b)Page 8, line 280: “Then u_n’ and u_n’’ “ => these should be written in bold fonts, same in equation 42.

(c) Page 11, subsection B : variable is surely a vector, and should be displayed in bold, as it is in equation 63 later

Response: We check all equation to make sure all vector is written in bold fonts.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Dear Authors, 

the manuscript you propose for publication on Applied Sciences regards a topic of high interest in the field of structural engineering, especially in the context of aerospace applications. Substructuring methods provide for efficient ways of connecting multiple structural models in a coherent manner. 

In my view, the manuscript needs two important modifications before it can be published on AS:

  1. a thorough grammar check, with some parts that need to be rewritten entirely and many others that need smaller adjustments;

  2. the innovative contribution of the authors has to be underlined with more emphasis and critical analysis with respect to the current state of the art. 

Regarding the second point, I suggest the authors to dedicate a specific section in the introduction to highlight where the proposed approach differ from the state of the art.

Other minor issues and questions I have about the manuscript are found below. 

1. In section 3, lines 164-165: when you state that your proposed method is "based on the work of Aminpour", can you please elaborate on what specifically you drew from that reference, and what is original in your formulation?

2. In section 4, lines 347-348: which is the meaning of 'transforms' in this context? I think that the meaning of the sentence is generally clear, inasmuch as there is not a single configuration of forces that guarantees equilibrium between the substructures at the interface, but I don't get the meaning of 'transforms'. Can you please explain this a bit better, maybe rephrasing the sentence?

3. Section 4, lines 352-354: The meaning of the sentence "For a discrete problem ... have a relationship" is not clear to me. I'm really struggling to understand what you mean: can you please explain it better and maybe rephrase?

4. Section 4, line 390: I think that the reference to equation (68) is not correct, here;

5. Section 4, line 419: there is an equation reference missing;

6.Section 4, line 448: I suggest you to plot the external force against time;

7. Figure 6,7,8,12: the font in the figures' text is really small, I suggest you to increase the size in order to better match the font size of the rest of the paper;

8. Section 5, lines 578-580: can you please clarify the sentence "Since H(t) ... need to be considered."? Do you mean that since in the IBS method the representation of the substructure dynamics is delegated to its impulse response, the substructure is only modeled through the input-output behavior between applied loads at specific points and the response at other points, while no other dof contribution is directly available in the reduced model? 

9. Section 5, lines 614-616: more details about the implementation are needed, in my opinion, to give sense to the computation times. Is the proposed method implemented by the authors in some existing FE code, or the entire code (preprocessor with interfacing methods + solver) developed by the authors? If the latter is true, it would be very interesting if the authors could open source their implementation, or distribute an example implementation in the additional material attached to the manuscript.

 

Other generic comments: 

a) I would suggest the authors to avoid using the same symbol for the interface forces and the intepolating functions (g). While it is generally quite clear which symbol refers to which term, using different symbols will enhance the readability of the mathematical expressions;

b) Seems to me that the superscript (s), used throughout the manuscript to indicate the substructure 'index', is unnecessary and can removed without any loss of information, again gaining instead in readability of the math;

 

Author Response

Response to reviewer 2

Comment1: In section 3, lines 164-165: when you state that your proposed method is "based on the work of Aminpour", can you please elaborate on what specifically you drew from that reference, and what is original in your formulation?

Response: According to the comment of reviewer, we add an explanation of Aminpour and elaborate original in my formulation. See line 166

Comment2:  In section 4, lines 347-348: which is the meaning of 'transforms' in this context? I think that the meaning of the sentence is generally clear, inasmuch as there is not a single configuration of forces that guarantees equilibrium between the substructures at the interface, but I don't get the meaning of 'transforms'. Can you please explain this a bit better, maybe rephrasing the sentence?

Response: To explain it better, This sentence has been rephrased.

Comment3: Section 4, lines 352-354: The meaning of the sentence "For a discrete problem ... have a relationship" is not clear to me. I'm really struggling to understand what you mean: can you please explain it better and maybe rephrase?

Response: To explain it better, This sentence has been rephrased.

Comment4:  Section 4, line 390: I think that the reference to equation (68) is not correct, here;

Response: Thank you, we made a mistake here

Comment5:  Section 4, line 419: there is an equation reference missing;

Response: Thank you, we made a mistake here

Comment6:  Section 4, line 448: I suggest you to plot the external force against time;

Response:：We have add a picture of external force, see figure 3

Comment7:  Figure 6,7,8,12: the font in the figures' text is really small, I suggest you to increase the size in order to better match the font size of the rest of the paper;

Response:：We have updated figure.

Comment8:  Section 5, lines 578-580: can you please clarify the sentence "Since H(t) ... need to be considered."? Do you mean that since in the IBS method the representation of the substructure dynamics is delegated to its impulse response, the substructure is only modeled through the input-output behavior between applied loads at specific points and the response at other points, while no other dof contribution is directly available in the reduced model? 

Response:：It means by using H(t), the dof of substructure have been reduced. Since this sentence have no relation with previous sentence, I removed it.

Comment8:  9. Section 5, lines 614-616: more details about the implementation are needed, in my opinion, to give sense to the computation times. Is the proposed method implemented by the authors in some existing FE code, or the entire code (preprocessor with interfacing methods + solver) developed by the authors? If the latter is true, it would be very interesting if the authors could open source their implementation, or distribute an example implementation in the additional material attached to the manuscript.

Response: All of three methods is based on FE code, so computation times can represent the efficiency of methods.

Comment9: I would suggest the authors to avoid using the same symbol for the interface forces and the interpolating functions (g). While it is generally quite clear which symbol refers to which term, using different symbols will enhance the readability of the mathematical expressions;

Response: Thanks to the advice of reviewer, we have check all equation and make sure they have explained clearly.

Comment10: Seems to me that the superscript (s), used throughout the manuscript to indicate the substructure 'index', is unnecessary and can removed without any loss of information, again gaining instead in readability of the math;

Response: Thanks to the advice of reviewer,. The ordinary IBS method was proposed by Daniel Rixen On 2010 (A Substructuring Technique Based on Measured and Computed Impulse Response Functions of Components). In this paper the superscript (s) was used to indicate the substructure 'index'. In his later published paper and other researcher’s paper, they all used superscript (s). So in this paper, I have to obey the rule.

Author Response File: Author Response.docx

Reviewer 3 Report

This manuscript applied the multi-domain substructures including IBS, FEM and modal substructure with non-matching interfaces to deal with a lunar lander with a rover. The manuscript can be accepted for publication after a minor revision based on the following suggestions:

1. The motivation and contribution of the study should be highlighted in Introduction.

2. The reasons of the differences in Figure 7 should be given.

3. The total CPU time of different method should be listed in Table 5.

4. The Conclusion should be discussed the main contribution of paper. There should be more discussion on the novel findings of the paper.

Author Response

Response to reviewer 3

Comment1: The motivation and contribution of the study should be highlighted in Introduction.

Response: Thanks to the advice of reviewer. We make it clear in Introduction.

Comment2: The reasons of the differences in Figure 7 should be given.

Response: Thanks to the advice of reviewer. We have added a short discussion on Figure 7.

Comment3: The total CPU time of different method should be listed in Table 5.

Response: Thanks to the advice of reviewer. We have discuss the CPU time of different method on line 618. To clearly explain, We add a table to compare the total CPU time of different method, see Table 6.

Comment3: The Conclusion should be discussed the main contribution of paper. There should be more discussion on the novel findings of the paper.

Response: Thanks to the advice of reviewer. We add a discussion of main contribution of paper on The Conclusion.

Author Response File: Author Response.docx

Reviewer 4 Report

This manuscript extends ordinary IBS method and presents a method for coupling multi-domain substructures including IBS, FEM and modal substructure with non-matching interfaces. The major revision can be found below:

(1) There are similar works that have been published in the literature, see for example: Chen, Shulin, et al. "Multi-domain substructures synthesis with general joints for the dynamics of large structures." Aip Advances 7.10 (2017): 105007.; Wang, Binbin, et al. "A multiple and multi-level substructure method for the dynamics of complex structures." Applied Sciences 11.12 (2021): 5570. Please explain the differences; what is the contribution of your paper?

(2) What is the motivation of the work? The problem considered does not have a sound motivation. The authors should clearly demonstrate the scientific interest of the objectives and results.

(3) Section 2, Numerical methodology and data process, contains many well know equations, which are already published. The methodology sections should be reduced and appropriate references should be added. The authors should keep only their new contributions.

(4) The authors should check typing errors throughout the manuscript. English style should also be improved.

 

Author Response

Response to reviewer 4

Comment1：There are similar works that have been published in the literature, see for example: Chen, Shulin, et al. "Multi-domain substructures synthesis with general joints for the dynamics of large structures." Aip Advances 7.10 (2017): 105007.; " Applied Sciences 11.12 (2021): 5570. Please explain the differences; what is the contribution of your paper?

Response: Thanks to the comment of reviewer. It is very important to explain the difference.       (1) Chen, Shulin, et al. "Multi-domain substructures synthesis with general joints for the dynamics of large structures." Aip Advances 7.10 (2017): 105007. I am the co-author of this paper. This paper mainly discuss the a “JOINT” type interface between substructures. The type of interface is rather special. This paper extend his work and can solve all type of interface between substructures.       (2) Wang, Binbin, et al. "A multiple and multi-level substructure method for the dynamics of complex structures.  This paper proposed a multiple and multi-level substructure method for the modeling of complex structures. In this paper, the part is modeled as full scale FEM substructure and the interface between substructure is matched. However, our manuscript consider FEM, CB and IBS three type of substructure and focus on solving the non-matched interface.

Comment2：What is the motivation of the work? The problem considered does not have a sound motivation. The authors should clearly demonstrate the scientific interest of the objectives and results.

Response: The motivation of the work is to extend IBS method. In engineering applications, a complex structures are usually divided into several substructures, which are designed independently by each unit. The interface of each substructure is non-matching. This problem limit the application of substructure method. This work want to solve this problem.

Comment3：Section 2, Numerical methodology and data process, contains many well know equations, which are already published. The methodology sections should be reduced and appropriate references should be added. The authors should keep only their new contributions.

Response: Thanks to the suggestion of reviewer. I have reduced the methodology sections.

Comment3：The authors should check typing errors throughout the manuscript. English style should also be improved.

Response: Thanks to the suggestion of reviewer. We have done an English revision

 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The manuscript has been edited in accordance with my suggestions, therefore I feel it can be published. Thank you.

Reviewer 4 Report

It can be accepted.