Mesh-Free MLS-Based Error-Recovery Technique for Finite Element Incompressible Elastic Computations
Round 1
Reviewer 1 Report
The problem is timely and interesting. I recommend the publication of the manuscript after the following revisions are properly made:
1) The authors should define the novelty of the problem at the end of the introduction.
2) English of the paper should be polished carefully.
3) The abstract is too long. Shortened the abstract if it is possible.
4) The basic governing equations should be discussed term by term and also supported by past studies.
5) For general readers, authors are encouraged to discuss other kind of works on FEM such as: [(a) “Microstructural/geometric imperfection sensitivity on the vibration response of geometrically discontinuous bi-directional functionally graded plates (2D-FGPs) with partial supports by using FEM”, Steel and Composite Structures, 45(5), 621-640.; (b) “Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM”, European Journal of Mechanics - A/Solids, 96, 104743.].
6) Add some physical applications of current study in the introduction section.
7) What is author own contribution what is focus of the study and motivation.
8) Tables 7 and 8 should be more discussed.
9) In conclusion, give only main findings of your research with an appropriate value.
Author Response
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Reviewer 2 Report
The present study explores the effectiveness and applicability of mesh-free MLS in- 415 terpolation approach-based displacement/stress error recovery for incompressible elastic 416 finite element analysis. The moving least squares (MLS) interpolation technique consid- 417 ering radial weights over circular support domains are employed for the recovery of so- 418 lution errors and errors are quantified in energy norms. The incompressible elastic plate 419 problems, with 6-node triangular and 4-node quadrilateral discretization schemes, is 420 solved to investigate the order of errors, error convergence rate, effectivity and updated 421 meshes for desired accuracy. It is very interesting technique paper. However, here is something to be considered carefully.
1. Only 4-node and 6-node elements are studied, how about other types of elements?
2.Is this method suitable for solid elements? If not, how could it be used in engineering structures?
3.The simulated results should be compared with the experimental data.
Author Response
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Reviewer 3 Report
In this paper, a mesh-free error recovery technique based on moving least squares interpolation is investigated for incompressible elastic finite element analysis. Several numerical examples are given to verify the effectiveness and applicability of the mesh-free MLS interpolation error recovery technique.
The paper is generally well-written but still needs some improvements. The following points require further explanation:
1. The language and logic need to be improved and polished significantly, especially in the introduction of this manuscript.
2. Could the method proposed in this paper be applied to complex boundary problems or dynamics problems?
Author Response
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Reviewer 4 Report
This paper proposes a mesh-free error recovery technique based on moving least squares (MLS) interpolation for incompressible elastic finite element analysis. The MLS interpolation is used to create an approximate continuous field variable based on the finite element analysis field variable/field variable derivatives solution in a weighted sense, and errors are estimated in energy norms. The paper also evaluates the effect of element types and patch formation on MLS-based interpolation error quantification and compares MLS-based interpolation error quantification with least square-based interpolation. The numerical examples of incompressible elasticity, including problems with singularity, demonstrate the effectiveness and applicability of the proposed mesh-free MLS interpolation error recovery technique. The paper uses a mixed formulation (displacement and pressure) for finite element analysis of incompressible problems, and the rate of convergence, effectivity of error estimation, and modified meshes for desired accuracy are used to assess the effectiveness of error estimators. The paper concludes that displacement-based recovery is more effective in finite element incompressible elastic analysis than stress-based recovery considering mesh-free and mesh-dependent patches. The error convergence rates are computed in the original FEM solution and post-processed solution using mesh-free MLS-based displacement and stress recovery and mesh-dependent patch-based least square-based displacement and stress recovery for 4-node quadrilateral and 6-node triangular meshes. Overall, the paper provides a thorough analysis of the proposed mesh-free error recovery technique and its effectiveness for incompressible elastic finite element analysis. The evaluation of different interpolation methods and patch formations provides valuable insights into their impact on error quantification. However, it should be noted that the paper may be difficult to understand for those without a strong background in finite element analysis and numerical methods. Turnitin report is 29%. Therefore, author is strongly advised to reduce the similarity to 24% and below.
Author Response
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