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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 plate bending analysis based on the scaled boundary finite element method, International Journal for Numerical Methods in Engineering 95 (2013) 331–360.
  • [2] T. Xiang, S. Natarajan, H. Man, C. Song, W. Gao, Free vibration and mechanical buckling of plates with in-plane material inhomogeneity - a three dimensional consistent approach, Composite Structures.
  • [3] R. Khandan, S. Noroozi, P. Sewell, J. Vinney, The development of laminated composite plate theories: a review, J. Mater. Sci. 47 (2012) 5901–5910. [Crossref]
  • [4] Mallikarjuna, T. Kant, A critical review and some results of recently developed refined theories of fibre reinforced laminated composites and sandwiches, Composite Structures 23 (1993) 293–312. [Crossref]
  • [5] J. Reddy, A simple higher order theory for laminated composite plates, ASME J Appl Mech 51 (1984) 745–752. [Crossref]
  • [6] Y. Guo, A. P. Nagy, Z. Gürdal, A layerwise theory for laminated composites in the framework of isogeometric analysis, Composite Structures 107 (2014) 447–457. [Crossref][WoS]
  • [7] L. Demasi, 16 Mixed plate theories based on the Generalized Unified Formulation Part I: Governing equations, Composite Structures 87 (2009) 1–11. [WoS]
  • [8] R. Rolfes, K. Rohwer, Improved transverse shear stresses in composite finite elements based on first order shear formation theory, International Journal for Numerical Methods in Engineering 40 (1997) 51–60.
  • [9] T. Kant, K. Swaminathan, Analytical solutions for free vibration of laminated composite and sandwich plates based on a higherorder refined theory, Composite Structures 53 (1) (2001) 73–85. [Crossref]
  • [10] E. Carrera, Developments, ideas and evaluations based upon the Reissner’s mixed variational theorem in the modelling of multilayered plates and shells, Appl. Mech. Rev. 54 (2001) 301– 329. [Crossref]
  • [11] E. Carrera, L. Demasi, Classical and advancedmultilayered plate elements based upon PVD and RMVT. Part 1: derivation of finite element matrices, International Journal for Numerical Methods in Engineering 55 (2002) 191–231.
  • [12] A. Ferreira, E. Viola, F. Tornabene, N. Fantuzzi, A. Zenkour, Analysis of sandwich plates by generalized differential quadrature method, 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 laminated plates by generalized differential quadrature method and a unified formulation, Composite Part B: Engineering 58 (2014) 544–552. [WoS]
  • [14] C. Shu,W.Wu, H. Ding, C.Wang, Free vibration analysis of plates using least-square finite difference method, Computer Methods in Applied Mechanics and Engineering 196 (2007) 1330–1343. [Crossref]
  • [15] O. Civalek, B. Ozturk, Vibration analysis of plates with curvilinear quadrilateral domains by discrete singular convolution method, 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 and dynamic) analysis of laminates, International Journal for Numerical Methods in Engineering 39 (1996) 3453–3474.
  • [17] H. Kapoor, R. Kapania, Geometrically nonlinear NURBS isogeometric finite 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 method for vibration analysis of laminated composite plates, Computational Mechanics 48 (2011) 175–193. [WoS][Crossref]
  • [19] K. Liew, X. Zhao, A. J. Ferreira, A review of meshless methods for laminated and functionally graded plates and shells, Composite Structures 93 (2011) 2031–2041. [WoS][Crossref]
  • [20] Y. Xing, B. Liu, High-accuracy differential quadrature finite element method and its application to free vibration of thin plate with curvilinear domain, International Journal for Numerical Methods in Engineering 80 (2009) 1718–1742. [WoS]
  • [21] X. Wang, Y. Wang, Z. Yuan, Accurate vibration analysis of skew plates 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 variable kinematic multilayered plate elements, Composite Structures 92 (2010) 1888–1895. [WoS][Crossref]
  • [23] S. Natarajan, A. Ferreira, S. Bordas, E. Carrera, M. Cinefra, Analysis of composite plates by a unified formulation-cell based smoothed finite element method and field consistent elements, Composite Structures 105 (2013) 75–81. [Crossref]
  • [24] T. Hughes, M. Cohen, M. Haroun, Reduced and selective integration techniques in finite element method of plates, Nuclear Engineering Design 46 (1978) 203–222. [Crossref]
  • [25] H. Nguyen-Xuan, T. Rabczuk, S. Bordas, J. Debongnie, A smoothed finite element method for plate analysis, Computer Methods in Applied Mechanics and Engineering 197 (2008) 1184–1203. [Crossref]
  • [26] B. R. Somashekar, G. Prathap, C. R. Babu, A field-consistent four-noded laminated anisotropic plate/shell element, Computers and Structures 25 (1987) 345–353.
  • [27] K. Bathe, E. Dvorkin, A four-node plate bending element based on 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 quadrilaterals and assessment of convergence, Computer Methods in Applied Mechanics 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 buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach, International Journal for Numerical 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 bending problem, Computer Methods in Applied Mechanics and Engineering 45–53 (2012) 209–212. [WoS]
  • [31] E. Carrera, L. Demasi, Classical and advancedmultilayered plate elements based upon PVD and RMVT. Part 2: Numerical implementations, International Journal for Numerical Methods in Engineering 55 (2002) 253–291.
  • [32] J. Cottrell, T. Hughes, Y. Bazilevs, Isogeometric analysis: toward integration 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 analysis of 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 plate bending element of the Reissner-Mindlin type, Compuational Mechanics 23 (1999) 240–249.
  • [35] M. Touratier, An eficient standard plate theory, International Journal of Engineering Science 29 (1991) 901–916. [Crossref]
  • [36] N. Pagano, Exact solutions for rectangular bidirectional composites and sandwich plates, Journal of Composite Materials 4 (1970) 20–34.
  • [37] A. Ferreira, E. Carrera, M. Cinefra, C. Roque, Radial basis functions collocation for the bending and free vibration analysis of laminated 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 finiteelement solutions of thick laminated anisotropic rectangular plates, Nuclear Engineering and Design 64 (1981) 153–167. [Crossref]
  • [39] E. Carrera, Evaluation of layer-wise mixed theories for laminated plates analysis, AIAA J 26 (1998) 830–839. [Crossref]
  • [40] K. Liew, Y. Huang, J. Reddy, Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature, Computer Methods in Applied Mechanics and Engineering 192 (2003) 2203–2222. [Crossref]
  • [41] A. Khdeir, L. Librescu, Analysis of symmetric cross-ply elastic plates 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 thick isotropic and cross-ply laminated plates by radial basis functions and a unified formulation, Journal of Sound and Vibration 330 (2011) 771–787. [WoS]
  • [43] J. Whitney, N. Pagano, Shear deformation in heterogeneous anisotropic plates, ASME J Appl Mech 37 (4) (1970) 1031–1036. [Crossref]
  • [44] N. Senthilnathan, K. Lim, K. Lee, S. Chow, Buckling of shear deformable plates, 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 sandwich plates 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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