Direct Evaluation of the Stress Intensity Factors for the Single and Multiple Crack Problems Using the P-Version Finite Element Method and Contour Integral Method
Round 1
Reviewer 1 Report
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Comments for author File: 
Comments.pdf
Author Response
Thank you very much for your valuable comments and very carefully work.
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Recommendations attached.
Comments for author File: 
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Author Response
Thank you very much for your valuable comments.
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
-
Comments for author File: Comments.pdf
Author Response
Response to Reviewer 1
All symbols appearing in the paper must be defined. Reply: We have defined all
symbols appearing in the paper.
Some of the symbols are not yet defined in the paper.
Reply: Sorry, we check again all symbols appearing in the paper and we find some of the symbols in Eq. (11) -Eq. (14) are not defined, here we only cite the formulae from CIM to extract the SIFs, and we mentioned Ref. [31,35], interested readers can refer to the literature. If all of symbols are defined and explained clearly, it will need to add more content. Hence, we add an explanation “Definitions of symbols in Eq. (11)-Eq. (14) refer to [31]”.
The dimensions and material properties used in the different case studies (H, W, E…) sometimes have units and sometimes does not. Why? Reply: We use international unit in calculation for those cases which have not units.
Even if international units are used, they must also appear in the paper.
Reply: We have added units for those cases which have not units in the paper.
Why is a different material used for each calculation? Reply: For different examples, we used different material properties to keep under the same conditions in comparison with the results obtained using other methods.
The SIF does not depend on the material properties.
Reply: For the ease of comparison, all of conditions are as same as the corresponding papers no matter what. We would not like to compare the results under different conditions even if it is seemingly different.
In all cases, the normalized SIF should be used in the results instead of the SIF, with a general definition for the whole paper. Reply: For the convenient comparisons with references, we used the SIF or the normalized SIF to keep the same as corresponding papers in the literature.
Using the normalized SIF instead of the SIF provides generality.
Reply: We have added the normalized SIF, but for the ease of comparison, we keep the SIFs because only SIFs were given out in the corresponding published papers.
What is the energy norm? Reply:…
An explanation of what the energy norm is should be added to the paper.
Reply: An explanation of what the energy norm is can be found in many books, for example, in Ref. [30]. Perhaps，it will be better not to add the explanation to the paper because the energy norm is a basic concept in the analysis of finite element. We note that it is not so explained to the energy norm in most published papers. Anyway, we have added the explanation of the energy norm in the paper.
Why is the Chen and Hasebe solution [39] taken as the reference solution?
This question has not been answered.
Reply: Sorry, we had omitted this question. For this model, we do not find the analytical solution in the literature, Chen and Hasebe solution [39] is taken as the reference solution in Ref. [40, 41], and we note that Chen and Hasebe solution [39] often was used as the reference solution for this model in the literature, for example:
- Christophe Daux, Nicolas Moës, John Dolbow, Natarajan Sukumar and Ted Belytschko, Arbitrary branched and intersecting cracks with the extended finite element method, Int. J. Numer. Meth. Engng 2000; 48:1741-1760.
- G. W. Ma, X. M. An, H. H. Zhang, L. X. Li, Modeling complex crack problems using the numerical manifold method, Int J Fract (2009) 156:21–35,
DOI 10.1007/s10704-009-9342-7.
Hence we also use Chen and Hasebe solution [39] as the reference solution.
Conclusions are general and do not present any novelty in relation to the Ref. [10].
This question has not been answered.
Reply: The novelties of this paper are as follows:
- Although using the same method (P-FEM and CIM), Ref. [10] focus on hole-edge cracks in a rectangular plate, a square plate with an inclined centered crack and a pipeline crack problems. This manuscript studies different numerical examples (A central straight crack plate and a slanted single edge crack plate), and compares the numerical results with recently published papers in Ref. [6, 37], especially results of SIFsin NMM [37] were compared with the present results. It can be seen from Table 1 and Table 2 that the improvement in accuracy of SIFsis obvious.
- We find the present method (P-FEM and CIM) can not only be used to analyze the single crack problems, but also can be used to evaluate the SIFs of multiple crack problems. (See Section 4.3, 4.4 and 4.5), and it only need less number of meshes (less preprocessing), has higher accuracy and better stability compared with other numerical methods in the literature.
Above statements have been written in Abstract and Conclusion Section (Line
283-292).
Thank you very much for the reviewer’s valuable comments and very carefully work.
Author Response File: Author Response.pdf
