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Tytuł artykułu

Analysis of cross-ply laminated plates using isogeometric analysis and unified formulation

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we study the static bending and free vibration of cross-ply laminated composite plates using sinusoidal deformation theory. The plate kinematics is based on the recently proposed Carrera Unified Formulation (CUF), and the field variables are discretized with the non-uniform rational B-splines within the framework of isogeometric analysis (IGA). The proposed approach allows the construction of higher-order smooth functions with less computational effort.Moreover, within the framework of IGA, the geometry is represented exactly by the Non-Uniform Rational B-Splines (NURBS) and the isoparametric concept is used to define the field variables. On the other hand, the CUF allows for a systematic study of two dimensional plate formulations. The combination of the IGA with the CUF allows for a very accurate prediction of the field variables. The static bending and free vibration of thin and moderately thick laminated plates are studied. The present approach also suffers fromshear locking when lower order functions are employed and shear locking is suppressed by introducing a modification factor. The effectiveness of the formulation is demonstrated through numerical examples.
Wydawca
Rocznik
Tom
1
Numer
1
Opis fizyczny
Daty
otrzymano
2014-07-30
zaakceptowano
2014-09-03
online
2014-12-10
Twórcy
autor
  • Department of Mechanical
    Engineering, Indian Institute of Technology, Madras, Chennai -
    600036, India
  • Faculdade de Engenharia da Universidade do
    Porto, Porto, Portugal
  • Department of Mechanics, Faculty of Mathematics
    and Computer Science, University of Science, HCMC, Vietnam
Bibliografia
  • [1] H. Man, C. Song, T. Xiang, W. Gao, F. Tin-Loi, High-order platebending analysis based on the scaled boundary finite elementmethod, International Journal for Numerical Methods in Engineering95 (2013) 331–360.
  • [2] T. Xiang, S. Natarajan, H. Man, C. Song, W. Gao, Free vibrationand mechanical buckling of plates with in-plane material inhomogeneity- a three dimensional consistent approach, CompositeStructures.
  • [3] R. Khandan, S. Noroozi, P. Sewell, J. Vinney, The development oflaminated composite plate theories: a review, J. Mater. Sci. 47(2012) 5901–5910.[Crossref]
  • [4] Mallikarjuna, T. Kant, A critical review and some results of recentlydeveloped refined theories of fibre reinforced laminatedcomposites and sandwiches, Composite Structures 23 (1993)293–312.[Crossref]
  • [5] J. Reddy, A simple higher order theory for laminated compositeplates, ASME J Appl Mech 51 (1984) 745–752.[Crossref]
  • [6] Y. Guo, A. P. Nagy, Z. Gürdal, A layerwise theory for laminatedcomposites in the framework of isogeometric analysis, CompositeStructures 107 (2014) 447–457.[Crossref][WoS]
  • [7] L. Demasi, 16 Mixed plate theories based on the GeneralizedUnified Formulation Part I: Governing equations, CompositeStructures 87 (2009) 1–11.[WoS]
  • [8] R. Rolfes, K. Rohwer, Improved transverse shear stresses incomposite finite elements based on first order shear formationtheory, International Journal for Numerical Methods in Engineering40 (1997) 51–60.
  • [9] T. Kant, K. Swaminathan, Analytical solutions for free vibrationof laminated composite and sandwich plates based on a higherorderrefined theory, Composite Structures 53 (1) (2001) 73–85.[Crossref]
  • [10] E. Carrera, Developments, ideas and evaluations based uponthe Reissner’s mixed variational theorem in the modelling ofmultilayered plates and shells, Appl. Mech. Rev. 54 (2001) 301–329.[Crossref]
  • [11] E. Carrera, L. Demasi, Classical and advancedmultilayered plateelements based upon PVD and RMVT. Part 1: derivation of finiteelement matrices, International Journal for Numerical Methodsin Engineering 55 (2002) 191–231.
  • [12] A. Ferreira, E. Viola, F. Tornabene, N. Fantuzzi, A. Zenkour, Analysisof sandwich plates by generalized differential quadraturemethod, Mathematical Problems in Engineering 964367 (2013)1–12.[WoS]
  • [13] A. Ferreira, E. Carrera, M. Cinefra, E. Viola, F. Tornabene, N. Fantuzzi,A. Zenkour, Analysis of thick isotropic and cross-ply laminatedplates by generalized differential quadrature method anda unified formulation, Composite Part B: Engineering 58 (2014)544–552.[WoS]
  • [14] C. Shu,W.Wu, H. Ding, C.Wang, Free vibration analysis of platesusing least-square finite difference method, Computer Methodsin Applied Mechanics and Engineering 196 (2007) 1330–1343.[Crossref]
  • [15] O. Civalek, B. Ozturk, Vibration analysis of plates with curvilinearquadrilateral domains by discrete singular convolutionmethod, Structural Engineering and Mechanics 36 (2010) 279–299.[WoS][Crossref]
  • [16] M. Ganapathi,O. Polit, M. Touratier, A Co eight-node membraneshear-bending element for geometrically nonlinear (static anddynamic) analysis of laminates, International Journal for NumericalMethods in Engineering 39 (1996) 3453–3474.
  • [17] H. Kapoor, R. Kapania, Geometrically nonlinear NURBS isogeometricfinite element analysis of laminated composite plates,Composite Structures 94 (2012) 3434–3447.[Crossref]
  • [18] T. Q. Bui, M. N. Nguyen, C. Zhang, An efficient meshfree methodfor vibration analysis of laminated composite plates, ComputationalMechanics 48 (2011) 175–193.[WoS][Crossref]
  • [19] K. Liew, X. Zhao, A. J. Ferreira, A review of meshless methods forlaminated and functionally graded plates and shells, Composite Structures 93 (2011) 2031–2041.[WoS][Crossref]
  • [20] Y. Xing, B. Liu, High-accuracy differential quadrature finite elementmethod and its application to free vibration of thin platewith curvilinear domain, International Journal for NumericalMethods in Engineering 80 (2009) 1718–1742.[WoS]
  • [21] X. Wang, Y. Wang, Z. Yuan, Accurate vibration analysis of skewplates by the new version of the differential quadrature method,Applied Mathematical Modelling 38 (2014) 926–937.[WoS][Crossref]
  • [22] E. Carrera, M. Cinefra, P. Nali, MITC technique extended to variablekinematic multilayered plate elements, Composite Structures92 (2010) 1888–1895.[WoS][Crossref]
  • [23] S. Natarajan, A. Ferreira, S. Bordas, E. Carrera, M. Cinefra, Analysisof composite plates by a unified formulation-cell basedsmoothed finite element method and field consistent elements,Composite Structures 105 (2013) 75–81.[Crossref]
  • [24] T. Hughes, M. Cohen, M. Haroun, Reduced and selective integrationtechniques in finite element method of plates, NuclearEngineering Design 46 (1978) 203–222.[Crossref]
  • [25] H. Nguyen-Xuan, T. Rabczuk, S. Bordas, J. Debongnie, Asmoothed finite element method for plate analysis, ComputerMethods in Applied Mechanics and Engineering 197 (2008)1184–1203.[Crossref]
  • [26] B. R. Somashekar, G. Prathap, C. R. Babu, A field-consistentfour-noded laminated anisotropic plate/shell element, Computersand Structures 25 (1987) 345–353.
  • [27] K. Bathe, E. Dvorkin, A four-node plate bending element basedon Mindlin/Reissner plate theory and a mixed interpolation,International Journal for Numerical Methods in Engineering 21(1985) 367–383.
  • [28] H. Santos, J. Evans, T. Hughes, Generalization of the twist-Kirchhoff theory of plate elements to arbitrary quadrilateralsand assessment of convergence, Computer Methods in AppliedMechanics and Engineering 209–212 (2012) 101–114.[WoS]
  • [29] C. H. Thai, H. Nguyen-Xuan, N. Nguyen-Thanh, T.-H. Le,T. Nguyen-Thoi, T. Rabczuk, Static, free vibration, and bucklinganalysis of laminated composite Reissner-Mindlin plates usingNURBS-based isogeometric approach, International Journal forNumerical Methods in Engineering 91 (2012) 571–603.
  • [30] L. de Veiga, A. Buffa, C. Lovadina, M. Martinelli, G. Sangalli,An isogeometric method for the Reissner-Mindlin plate bendingproblem, Computer Methods in Applied Mechanics and Engineering45–53 (2012) 209–212.[WoS]
  • [31] E. Carrera, L. Demasi, Classical and advancedmultilayered plateelements based upon PVD and RMVT. Part 2: Numerical implementations,International Journal for Numerical Methods in Engineering55 (2002) 253–291.
  • [32] J. Cottrell, T. Hughes, Y. Bazilevs, Isogeometric analysis: towardintegration of CAD and FEA, John Wiley, 2009.
  • [33] N. Valizadeh, S. Natarajan, O. A. Gonzalez-Estrada, T. Rabczuk,T. Q. Bui, S. P. Bordas, NURBS-based finite element analysisof functionally graded elastic plates: Static bending, vibration,buckling and flutter, Composite Structures 99 (2013) 309–326.[Crossref]
  • [34] F. Kikuchi, K. Ishii, An improved 4-node quadrilateral platebending element of the Reissner-Mindlin type, CompuationalMechanics 23 (1999) 240–249.
  • [35] M. Touratier, An eficient standard plate theory, InternationalJournal of Engineering Science 29 (1991) 901–916.[Crossref]
  • [36] N. Pagano, Exact solutions for rectangular bidirectional compositesand sandwich plates, Journal of Composite Materials 4(1970) 20–34.
  • [37] A. Ferreira, E. Carrera, M. Cinefra, C. Roque, Radial basis functionscollocation for the bending and free vibration analysis oflaminated plates using the Reissner-Mixed variational theorem,European Journal of Mechanics - A/Solids 39 (2012) 104–112.[WoS]
  • [38] J. Reddy, W. Chao, A comparison of closed-form and finiteelementsolutions of thick laminated anisotropic rectangularplates, Nuclear Engineering and Design 64 (1981) 153–167.[Crossref]
  • [39] E. Carrera, Evaluation of layer-wise mixed theories for laminatedplates analysis, AIAA J 26 (1998) 830–839.[Crossref]
  • [40] K. Liew, Y. Huang, J. Reddy, Vibration analysis of symmetricallylaminated plates based on FSDT using the moving least squaresdifferential quadrature, Computer Methods in Applied Mechanicsand Engineering 192 (2003) 2203–2222.[Crossref]
  • [41] A. Khdeir, L. Librescu, Analysis of symmetric cross-ply elasticplates using a higher-order theory: Part II: buckling and free vibration,Composite Structures 9 (1988) 259–277.[Crossref]
  • [42] A. Ferreira, C. Roque, E. Carrera, M. Cinefra, Analysis of thickisotropic and cross-ply laminated plates by radial basis functionsand a unified formulation, Journal of Sound and Vibration330 (2011) 771–787.[WoS]
  • [43] J. Whitney, N. Pagano, Shear deformation in heterogeneousanisotropic plates, ASME J Appl Mech 37 (4) (1970) 1031–1036.[Crossref]
  • [44] N. Senthilnathan, K. Lim, K. Lee, S. Chow, Buckling of shear deformableplates, AIAA J 25 (9) (1987) 1268–1271.[Crossref]
  • [45] C. H. Thai, A. Ferreira, S. Bordas, T. Rabczuk, H. Nguyen-Xuan,Isogeometric analysis of laminated composite and sandwichplates using a new inverse trigonometric shear deformation theory,European Journal of Mechanics - A/Solids 43 (2014) 89–108.[WoS][Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_cls-2014-0001
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