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Analytical Buckling Solutions of Functionally Graded Plates With Complex Boundary Conditions Using the Finite Integral Transform Method.

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Title: Analytical Buckling Solutions of Functionally Graded Plates With Complex Boundary Conditions Using the Finite Integral Transform Method.
Authors: Du, Yu1 (AUTHOR), Ji, Chen2 (AUTHOR), Wang, Liuqi1 (AUTHOR), Li, Shuang1 (AUTHOR), Liu, Heng3 (AUTHOR), Zhang, Jinghui1 (AUTHOR) zhangjinghui653@ysu.edu.cn
Source: ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. May2026, Vol. 106 Issue 5, p1-19. 19p.
Subjects: Mechanical buckling, Analytical solutions, Mechanical loads, Functionally gradient materials, Boundary value problems, Structural plates, Integral transforms
Abstract: This study derives analytical solutions for the biaxial buckling of functionally graded material (FGM) rectangular thin plates subjected to complex boundary conditions (BCs), particularly focusing on rotationally‐restrained BCs, employing the finite integral transform (FIT) approach. Obtaining these solutions analytically through traditional semi‐inverse methods is challenging, primarily due to the complex BCs and graded material properties of FGM plates, which significantly complicate the application of such methods. In the solution procedure, utilizing the FIT method, the fundamental high‐order partial differential equations (PDEs) for FGM rectangular thin plates' buckling analysis are converted to four sets of linear algebraic equations. This transformation facilitates the derivation of analytical solutions without pre‐determined deflection functions, thereby enhancing the efficiency of the solving process. To validate the results, this study systematically compares them with ABAQUS simulations and existing analytical solutions. The comparison demonstrates strong agreement, confirming the precision of the proposed technique. The approach is straightforward and versatile, applicable to both thick and moderately thick plates, and suitable for analyzing bending and vibration under diverse BCs. Furthermore, the effects of aspect ratio, rotational constraint coefficient, FGM distribution models, porosity distributions, and biaxial load ratio of the FGM plates are systematically investigated. The results establish reliable benchmarks for validating the accuracy of other analytical and numerical methods. [ABSTRACT FROM AUTHOR]
Copyright of ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 194139267
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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Items – Name: Title
  Label: Title
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  Data: Analytical Buckling Solutions of Functionally Graded Plates With Complex Boundary Conditions Using the Finite Integral Transform Method.
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  Data: <searchLink fieldCode="AR" term="%22Du%2C+Yu%22">Du, Yu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ji%2C+Chen%22">Ji, Chen</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wang%2C+Liuqi%22">Wang, Liuqi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Li%2C+Shuang%22">Li, Shuang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Heng%22">Liu, Heng</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Jinghui%22">Zhang, Jinghui</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhangjinghui653@ysu.edu.cn</i>
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– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Mechanical+buckling%22">Mechanical buckling</searchLink><br /><searchLink fieldCode="DE" term="%22Analytical+solutions%22">Analytical solutions</searchLink><br /><searchLink fieldCode="DE" term="%22Mechanical+loads%22">Mechanical loads</searchLink><br /><searchLink fieldCode="DE" term="%22Functionally+gradient+materials%22">Functionally gradient materials</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Structural+plates%22">Structural plates</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+transforms%22">Integral transforms</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study derives analytical solutions for the biaxial buckling of functionally graded material (FGM) rectangular thin plates subjected to complex boundary conditions (BCs), particularly focusing on rotationally‐restrained BCs, employing the finite integral transform (FIT) approach. Obtaining these solutions analytically through traditional semi‐inverse methods is challenging, primarily due to the complex BCs and graded material properties of FGM plates, which significantly complicate the application of such methods. In the solution procedure, utilizing the FIT method, the fundamental high‐order partial differential equations (PDEs) for FGM rectangular thin plates' buckling analysis are converted to four sets of linear algebraic equations. This transformation facilitates the derivation of analytical solutions without pre‐determined deflection functions, thereby enhancing the efficiency of the solving process. To validate the results, this study systematically compares them with ABAQUS simulations and existing analytical solutions. The comparison demonstrates strong agreement, confirming the precision of the proposed technique. The approach is straightforward and versatile, applicable to both thick and moderately thick plates, and suitable for analyzing bending and vibration under diverse BCs. Furthermore, the effects of aspect ratio, rotational constraint coefficient, FGM distribution models, porosity distributions, and biaxial load ratio of the FGM plates are systematically investigated. The results establish reliable benchmarks for validating the accuracy of other analytical and numerical methods. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1002/zamm.70441
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 19
        StartPage: 1
    Subjects:
      – SubjectFull: Mechanical buckling
        Type: general
      – SubjectFull: Analytical solutions
        Type: general
      – SubjectFull: Mechanical loads
        Type: general
      – SubjectFull: Functionally gradient materials
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Structural plates
        Type: general
      – SubjectFull: Integral transforms
        Type: general
    Titles:
      – TitleFull: Analytical Buckling Solutions of Functionally Graded Plates With Complex Boundary Conditions Using the Finite Integral Transform Method.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Du, Yu
      – PersonEntity:
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            NameFull: Ji, Chen
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            NameFull: Wang, Liuqi
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            NameFull: Li, Shuang
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            NameFull: Liu, Heng
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            NameFull: Zhang, Jinghui
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          Dates:
            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 00442267
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              Value: 106
            – Type: issue
              Value: 5
          Titles:
            – TitleFull: ZAMM -- Journal of Applied Mathematics & Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
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