Nonlinear bending analysis of nanoplates made of FGMs based on the most general strain gradient model and 3D elasticity theory
. In this article, the nonlinear bending behavior of rectangular nanoplates made of functionally graded materials (FGMs) is studied in the context of a variational formulation. To capture size effects, the most general form of strain gradient theory is employed. The three-dimensional (3D) elasticity...
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| Published in | European physical journal plus Vol. 134; no. 4; p. 167 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.04.2019
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 2190-5444 2190-5444 |
| DOI | 10.1140/epjp/i2019-12501-x |
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| Abstract | .
In this article, the nonlinear bending behavior of rectangular nanoplates made of functionally graded materials (FGMs) is studied in the context of a variational formulation. To capture size effects, the most general form of strain gradient theory is employed. The three-dimensional (3D) elasticity theory is used for modeling the nanoplate. The governing equations are also derived in the discretized weak form using the variational differential quadrature (VDQ) method. Finally, the solution of the nonlinear bending problem is obtained by the pseudo arc-length continuation algorithm. In the numerical results, the effects of thickness-to-length scale ratio, side length-to-thickness ratio and material gradient index on the nonlinear bending response of nanoplates subject to different types of boundary conditions are analyzed. Moreover, a comparison is provided between the predictions of various strain gradient-based theories. |
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| AbstractList | .
In this article, the nonlinear bending behavior of rectangular nanoplates made of functionally graded materials (FGMs) is studied in the context of a variational formulation. To capture size effects, the most general form of strain gradient theory is employed. The three-dimensional (3D) elasticity theory is used for modeling the nanoplate. The governing equations are also derived in the discretized weak form using the variational differential quadrature (VDQ) method. Finally, the solution of the nonlinear bending problem is obtained by the pseudo arc-length continuation algorithm. In the numerical results, the effects of thickness-to-length scale ratio, side length-to-thickness ratio and material gradient index on the nonlinear bending response of nanoplates subject to different types of boundary conditions are analyzed. Moreover, a comparison is provided between the predictions of various strain gradient-based theories. In this article, the nonlinear bending behavior of rectangular nanoplates made of functionally graded materials (FGMs) is studied in the context of a variational formulation. To capture size effects, the most general form of strain gradient theory is employed. The three-dimensional (3D) elasticity theory is used for modeling the nanoplate. The governing equations are also derived in the discretized weak form using the variational differential quadrature (VDQ) method. Finally, the solution of the nonlinear bending problem is obtained by the pseudo arc-length continuation algorithm. In the numerical results, the effects of thickness-to-length scale ratio, side length-to-thickness ratio and material gradient index on the nonlinear bending response of nanoplates subject to different types of boundary conditions are analyzed. Moreover, a comparison is provided between the predictions of various strain gradient-based theories. |
| ArticleNumber | 167 |
| Author | Gholami, R. Rouhi, H. Ansari, R. Gholami, Y. |
| Author_xml | – sequence: 1 givenname: Y. surname: Gholami fullname: Gholami, Y. organization: Department of Mechanical Engineering, University of Guilan – sequence: 2 givenname: R. surname: Ansari fullname: Ansari, R. email: r_ansari@guilan.ac.ir organization: Department of Mechanical Engineering, University of Guilan – sequence: 3 givenname: R. surname: Gholami fullname: Gholami, R. organization: Department of Mechanical Engineering, Lahijan Branch, Islamic Azad University – sequence: 4 givenname: H. surname: Rouhi fullname: Rouhi, H. organization: Department of Engineering Science, Faculty of Technology and Engineering, East of Guilan, University of Guilan |
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| References_xml | – reference: BarrettaR.BrčićM.ČanadijaM.LucianoR.de SciarraF.M.Eur. J. Mech. A-Solid20176512017EJMS...65....1B10.1016/j.euromechsol.2017.03.002 – reference: AnsariR.ShojaeiM.F.EbrahimiF.RouhiH.Arch. Appl. Mech.2015859372015AAM....85..937A10.1007/s00419-015-1002-y – reference: MatsunagaH.Compos. Struct.20088249910.1016/j.compstruct.2007.01.030 – reference: BunchJ.S.Van Der ZandeA.M.VerbridgeS.S.FrankI.W.TanenbaumD.M.ParpiaJ.M.Science20073154902007Sci...315..490B10.1126/science.1136836 – reference: KoiterW.T.Nederl. Akad. Wetensch. Proc. Ser. B19646717163469 – reference: H.B. Keller, Numerical solution of bifurcation and nonlinear eigenvalue problems, in Applications of Bifurcation Theory, Proc. Advanced Sem., Univ. Wisconsin, Madison (Academic Press, New York, 1977) pp. 359--384 – reference: YangF.ChongA.C.M.LamD.C.C.TongP.Int. J. Solids Struct.200239273110.1016/S0020-7683(02)00152-X – reference: MindlinR.D.TierstenH.F.Arch. Ration. Mech. 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In this article, the nonlinear bending behavior of rectangular nanoplates made of functionally graded materials (FGMs) is studied in the context of a... In this article, the nonlinear bending behavior of rectangular nanoplates made of functionally graded materials (FGMs) is studied in the context of a... |
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| SubjectTerms | Algorithms Applied and Technical Physics Atomic Bending Boundary conditions Complex Systems Condensed Matter Physics Elasticity Functionally gradient materials Mathematical and Computational Physics Mechanical engineering Molecular Nonlinear response Optical and Plasma Physics Physics Physics and Astronomy Quadratures Regular Article Size effects Strain Theoretical Thickness ratio Three dimensional models |
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| Title | Nonlinear bending analysis of nanoplates made of FGMs based on the most general strain gradient model and 3D elasticity theory |
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