3D elasticity solution for uniformly loaded elliptical plates of functionally graded materials using complex variables method
Based on the generalized England’s method, the three-dimensional elastic response in a transversely isotropic functionally graded elliptical plate with clamped edge subject to uniform load is investigated. The material properties can arbitrarily vary along the thickness direction of the plate. The e...
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| Published in | Archive of applied mechanics (1991) Vol. 88; no. 10; pp. 1829 - 1841 |
|---|---|
| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2018
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0939-1533 1432-0681 |
| DOI | 10.1007/s00419-018-1407-5 |
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| Abstract | Based on the generalized England’s method, the three-dimensional elastic response in a transversely isotropic functionally graded elliptical plate with clamped edge subject to uniform load is investigated. The material properties can arbitrarily vary along the thickness direction of the plate. The expressions of the mid-plane displacements of the plate are constructed to meet the clamped boundary conditions in which the unknown constants are determined from the governing equations. The expressions of four analytic functions
α
(
ζ
)
,
β
(
ζ
)
,
ϕ
(
ζ
)
and
ψ
(
ζ
)
corresponding to this problem are then obtained using the complex variables method. As a result, the three-dimensional elasticity solution of a functionally graded elliptical plate with clamped boundary subject to uniform load is derived. Finally, numerical examples are presented to verify the proposed method and discuss the effects of different factors on the deformation and stresses in the plate. |
|---|---|
| AbstractList | Based on the generalized England’s method, the three-dimensional elastic response in a transversely isotropic functionally graded elliptical plate with clamped edge subject to uniform load is investigated. The material properties can arbitrarily vary along the thickness direction of the plate. The expressions of the mid-plane displacements of the plate are constructed to meet the clamped boundary conditions in which the unknown constants are determined from the governing equations. The expressions of four analytic functions α(ζ), β(ζ), ϕ(ζ) and ψ(ζ) corresponding to this problem are then obtained using the complex variables method. As a result, the three-dimensional elasticity solution of a functionally graded elliptical plate with clamped boundary subject to uniform load is derived. Finally, numerical examples are presented to verify the proposed method and discuss the effects of different factors on the deformation and stresses in the plate. Based on the generalized England’s method, the three-dimensional elastic response in a transversely isotropic functionally graded elliptical plate with clamped edge subject to uniform load is investigated. The material properties can arbitrarily vary along the thickness direction of the plate. The expressions of the mid-plane displacements of the plate are constructed to meet the clamped boundary conditions in which the unknown constants are determined from the governing equations. The expressions of four analytic functions α ( ζ ) , β ( ζ ) , ϕ ( ζ ) and ψ ( ζ ) corresponding to this problem are then obtained using the complex variables method. As a result, the three-dimensional elasticity solution of a functionally graded elliptical plate with clamped boundary subject to uniform load is derived. Finally, numerical examples are presented to verify the proposed method and discuss the effects of different factors on the deformation and stresses in the plate. |
| Author | Yang, Y. W. Chen, W. Q. Yang, B. Yang, Q. Q. Zhang, Y. |
| Author_xml | – sequence: 1 givenname: Y. W. surname: Yang fullname: Yang, Y. W. organization: Department of Civil Engineering, Zhejiang Agriculture and Forestry University – sequence: 2 givenname: Y. surname: Zhang fullname: Zhang, Y. organization: Department of Civil Engineering, Zhejiang Sci-Tech University – sequence: 3 givenname: W. Q. surname: Chen fullname: Chen, W. Q. organization: Department of Engineering Mechanics, Zhejiang University – sequence: 4 givenname: B. surname: Yang fullname: Yang, B. email: bo.young@163.com organization: Department of Civil Engineering, Zhejiang Sci-Tech University – sequence: 5 givenname: Q. Q. surname: Yang fullname: Yang, Q. Q. organization: Jiangsu Province Key Laboratory of Advanced Manufacturing Technology, Huaiyin Institute of Technology |
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| Keywords | Elasticity solutions Elliptical plates Functionally graded materials Complex variables method |
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| References_xml | – reference: ChengZQBatraRCThree-dimensional thermoelastic deformations of a functionally graded elliptic platesCompos. Part B Eng.20003129710610.1016/S1359-8368(99)00069-4 – reference: JiangJLHuangDJYangBChenWQDingHJElasticity solutions for a transversely isotropic functionally graded annular sector plateActa Mech.2017228726032621366731310.1007/s00707-017-1839-y – reference: WangYXuRQDingHJThree-dimensional solution of axisymmetric bending of functionally graded circular platesCompos. Struct.2010921683169310.1016/j.compstruct.2009.12.002 – reference: HuangDJYangBChenWQDingHJAnalytical solution for a transversely isotropic functionally graded sectorial plate subjected to a concentrated force or couple at the tipActa Mech.20162272495506345641410.1007/s00707-015-1460-x – reference: YangBDingHJChenWQElasticity solutions for functionally graded rectangular plates with two opposite edges simply supportedAppl. Math. Model.201236488503283502610.1016/j.apm.2011.07.020 – reference: LiXYDingHJChenWQAxisymmetric elasticity solutions for a uniformly loaded annular plate of transversely isotropic functionally graded materialsActa Mech.200819613915910.1007/s00707-007-0498-9 – reference: LiXYDingHJChenWQElasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$qr^{k}$$\end{document}Int. J. Solids Struct.20084519121010.1016/j.ijsolstr.2007.07.023 – reference: YangBChenWQDingHJ3D elasticity solutions for equilibrium problems of transversely isotropic FGM plates with holesActa Mech.201522615711590332326510.1007/s00707-014-1270-6 – reference: FallahFKhakbazAOn an extended Kantorovich method for the mechanical behavior of functionally graded solid/annular sector plates with various boundary conditionsActa Mech.201722826552674366731610.1007/s00707-017-1851-2 – reference: ReddyJNWangCMKitipornchaiSAxisymmetric bending of functionally graded circular and annular platesEur. J. Mech. A/Solids199918218519910.1016/S0997-7538(99)80011-4 – reference: AdinehMKadkhodayanMThree-dimensional thermos-elastic analysis of multi-directional functionally graded rectangular plates on elastic foundationActa Mech.2017228881899361506310.1007/s00707-016-1743-x – reference: ThaiH-TKimS-EA review of theories for the modeling and analysis of functionally graded plates and shellsCompos. Struct.2015128708610.1016/j.compstruct.2015.03.010 – reference: LiXYDingHJChenWQPure bending of simply supported circular plate of transversely isotropic functionally graded materialJ. Zhejiang Univ. (Sci)2006781324132810.1631/jzus.2006.A1324 – reference: LiXYDingHJChenWQLiPDThree-dimensional piezoelectricity solutions for uniformly loaded circular plates of functionally graded piezoelectric materials with transverse isotropyJ. Appl. Mech.2013800410071210.1115/1.4007968 – reference: DingHJChenWQZhangLCElasticity of Transversely Isotropic Materials2006DordrechtSpringer1101.74001 – reference: XiangSKangGWStatic analysis of functionally graded plates by the various shear deformation theoryCompos. Struct.20139922423010.1016/j.compstruct.2012.11.021 – reference: AlibeiglooAThree-dimensional thermo-elasticity solution of sandwich cylindrical panel with functionally graded coreCompos. Struct.201410745846810.1016/j.compstruct.2013.08.009 – reference: AghdamMMShahmansouriNMohammadiMExtended Kantorovich method for static analysis of moderately thick functionally graded sector platesMath. Comput. Simul.201286118130303840810.1016/j.matcom.2010.07.029 – reference: YangBChenWQDingHJEquilibrium of transversely isotropic FGM plates with elliptical holes: 3D elasticity solutionsArch. Appl. Mech.20168681391141410.1007/s00419-016-1124-x – reference: TimoshenkoSPWoinowsky-KriegerSTheory of Plates and Shells19592New YorkMcGraw-Hill0114.40801 – reference: TimoshenkoSPGoodierJNTheory of Elasticity19703New YorkMcGraw-Hill0266.73008 – volume: 36 start-page: 488 year: 2012 ident: 1407_CR12 publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2011.07.020 – volume: 227 start-page: 495 issue: 2 year: 2016 ident: 1407_CR15 publication-title: Acta Mech. doi: 10.1007/s00707-015-1460-x – volume: 18 start-page: 185 issue: 2 year: 1999 ident: 1407_CR3 publication-title: Eur. J. Mech. 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| SubjectTerms | Analytic functions Boundary conditions Classical Mechanics Complex variables Deformation effects Elasticity Elliptical plates Engineering Functionally gradient materials Material properties Original Theoretical and Applied Mechanics |
| Title | 3D elasticity solution for uniformly loaded elliptical plates of functionally graded materials using complex variables method |
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