A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates

Hosseini-Hashemi, Shahrokh; Fadaee, M.; Atashipour, Seyed Rasoul

doi:10.1016/j.ijmecsci.2010.10.002

Cited by 206 publications

(87 citation statements)

References 39 publications

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“…The following features are evident: (1) results based on the CPT neu and FSDT match well with the analytical solutions [17,21]; (2) as the CPT, natural frequencies obtained by the CPT neu are larger than the analytical solutions; (3) the accuracy of the CPT neu is higher than that of the FSDT when the number of control points is small, whereas the accuracy of the CPT neu is almost the same as that of the FSDT with increasing number of control points. The computational time versus the number of control points is plotted in Figure 5.…”

Section: A Simply Supported Al/alsupporting

confidence: 53%

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Free Vibration Analyses of FGM Thin Plates by Isogeometric Analysis Based on Classical Plate Theory and Physical Neutral Surface

Yin

Liu

2013

Advances in Mechanical Engineering

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The isogeometric analysis with nonuniform rational B-spline (NURBS) based on the classical plate theory (CPT) is developed for free vibration analyses of functionally graded material (FGM) thin plates. The objective of this work is to provide an efficient and accurate numerical simulation approach for the nonhomogeneous thin plates and shells. Higher order basis functions can be easily obtained in IGA, thus the formulation of CPT based on the IGA can be simplified. For the FGM thin plates, material property gradient in the thickness direction is unsymmetrical about the midplane, so effects of midplane displacements cannot be ignored, whereas the CPT neglects midplane displacements. To eliminate the effects of midplane displacements without introducing new unknown variables, the physical neutral surface is introduced into the CPT. The approximation of the deflection field and the geometric description are performed by using the NURBS basis functions. Compared with the first-order shear deformation theory, the present method has lower memory consumption and higher efficiency. Several numerical results show that the present method yields highly accurate solutions.

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Section: A Simply Supported Al/alsupporting

confidence: 53%

“…The same Al/Al 2 O 3 material considered in the previous section is employed. [17,21]. Figure 4 shows the comparison of the first normalized natural frequencies from the proposed method and the reference solutions with different control points.…”

Section: Numerical Resultsmentioning

confidence: 99%

Free Vibration Analyses of FGM Thin Plates by Isogeometric Analysis Based on Classical Plate Theory and Physical Neutral Surface

Yin

Liu

2013

Advances in Mechanical Engineering

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“…The classical plate theory (CPT) (Feldman and Aboudi 1997, Javaheri and Eslami 2002, Mahdavian 2009, Mohammadi et al 2010, Chen et al 2006, Baferani et al 2011) yields acceptable results only for the thin plates, whereas accuracy of the first-order shear deformation theory (FSDT) (Mohammadi et al 2010, Croce and Venini 2004, Efraim and Eisenberger 2007, Zhao et al 2009a, b, Lee et al 2009, Hosseini-Hashemi et al 2011, Naderi and Saidi 2010, Nguyen-Xuan et al 2012, Thai and Choi 2013a) depends on the shear correction factor. Higherorder shear deformation theories with five unknown functions, which are included third-order shear deformation plate theory (TSDT), sinusoidal shear deformation plate theory (SSDT), hyperbolic shear deformable plate theory (HSDT), exponential shear deformation plate theory (ESDT), predict more accurate the response of moderate and thick FG plates (Reddy 2000, Zenkour 2006, Matsunaga 2008, Chen et al 2009, Pradyumna and Bandyopadhyay 2008, Gilhooley et al 2007, Talha and Singh 2010, Mantari and Soares 2012, 2013, Neves et al 2012a, b, Jha et al 2013, Thai and Kim 2013, Thai and Choi 2013b, Zenkour 2013.…”

Section: Introductionmentioning

confidence: 99%

A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates

Nguyen¹,

Thai²,

Vo³

2015

Steel Compos. Struct.

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Thuc (2015) A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates. Steel and Composite Structures, 18 (1 Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University's research output. Copyright © and moral rights for items on NRL are retained by the individual author(s) and/or other copyright owners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata page. The content must not be changed in any way. Full items must not be sold commercially in any format or medium without formal permission of the copyright holder. The full policy is available online: http://nrl.northumbria.ac.uk/policies.html This document may differ from the final, published version of the research and has been made available online in accordance with publisher policies. To read and/or cite from the published version of the research, please visit the publisher's website (a subscription may be required.)A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates Abstract. A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates is presented in this paper. It contains only four unknowns, accounts for a hyperbolic distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion are derived from Hamilton's principle. The Navier-type and finite element solutions are derived for plate with simply-supported and various boundary conditions, respectively. Numerical examples are presented for functionally graded sandwich plates with homogeneous hardcore and softcore to verify the validity of the developed theory. It is observed that the present theory with four unknowns predicts the response accurately and efficiently.

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“…The FSDT [1][2][3][4][5][6][7][8][9] gives acceptable prediction, but requires a shear correction factor which is hard to find out consistently because of dependent on many parameters including geometry, boundary conditions, and loading conditions. The HSDTs [10][11][12][13][14][15][16][17] do not require a shear correction factor, but their equations of motion are more complicated than those of the FSDT.…”

Section: Introductionmentioning

confidence: 99%

A quasi-3D hyperbolic shear deformation theory for functionally graded plates

Thai

Bui

et al. 2013

Acta Mech

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Northumbria University has developed Northumbria Research Link (NRL) to enable users to access the University's research output. Copyright © and moral rights for items on NRL are retained by the individual author(s) and/or other copyright owners. Single copies of full items can be reproduced, displayed or performed, and given to third parties in any format or medium for personal research or study, educational, or not-for-profit purposes without prior permission or charge, provided the authors, title and full bibliographic details are given, as well as a hyperlink and/or URL to the original metadata page. The content must not be changed in any way. Full items must not be sold commercially in any format or medium without formal permission of the copyright holder. The full policy is available online: http://nrl.northumbria.ac.uk/policies.html This document may differ from the final, published version of the research and has been made available online in accordance with publisher policies. To read and/or cite from the published version of the research, please visit the publisher's website (a subscription may be required.)

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A new exact analytical approach for free vibration of Reissner–Mindlin functionally graded rectangular plates

Cited by 206 publications

References 39 publications

Free Vibration Analyses of FGM Thin Plates by Isogeometric Analysis Based on Classical Plate Theory and Physical Neutral Surface

Free Vibration Analyses of FGM Thin Plates by Isogeometric Analysis Based on Classical Plate Theory and Physical Neutral Surface

A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates

A quasi-3D hyperbolic shear deformation theory for functionally graded plates

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