An enhanced discrete Mindlin finite element model using a zigzag function

References

• Ambartsumian, S.A. (1969). Theory of anisotropic plates: Strength, Stability and Vibrations. Translated from Russian by T. Cheron and edited by J. E. Ashton, Technomic.
   Google Scholar
• Ayad, R. (2002). Contribution à la Modélisation numérique pour l’analyse des solides et des structures, et pour la mise en forme des fluides non newtoniens. Application à des matériaux d’emballage (HDR Thesis, University of Reims Champagne Ardenne).
   Google Scholar
• Ayad , R. , Dhatt , G. and Batoz , J.L. 1998 . A new hybrid-mixed variational approach for Reissner–Mindlin plates. The MiSP model . International Journal for Numerical Methods in Engineering , 42 ( 7 ) : 1149 – 1179 .
   Web of Science ®Google Scholar
• Ayad , R. and Rigolot , A. 2002 . An improved four-node hybrid-mixed element based upon Mindlin’s plate theory . International Journal for Numerical Methods in Engineering , 55 ( 6 ) : 705 – 731 .
   Web of Science ®Google Scholar
• Ayad , R. , Talbi , N. and Ghomari , T. 2009 . Modified discrete Mindlin hypothesises for laminated composite structures . Composites Science and Technology , 69 ( 1 ) : 125 – 128 . doi: 10.1016/j.compscitech.2007.10.038
   Web of Science ®Google Scholar
• Batoz , J.-L. and Tahar , M.B. 1982 . Evaluation of a new quadrilateral thin plate bending element . International Journal for Numerical Methods in Engineering , 18 ( 11 ) : 1655 – 1677 . doi: 10.1002/nme.1620181106
   Web of Science ®Google Scholar
• Carrera , E. 1996 . C0 Reissner–Mindlin multilayred plate elements including zig-zag and interlaminar stress continuity . International Journal for Numerical Methods in Engineering , 39 ( 11 ) : 1797 – 1820 .
   Web of Science ®Google Scholar
• Carrera , E. 2002 . Theories and finite elements for multilayered, anisotropic, composite plates and shells . Archives of Computational Methods in Engineering , 9 ( 2 ) : 87 – 140 . doi: 10.1007/bf02736649
   Web of Science ®Google Scholar
• Carrera , E. and Demasi , L. 2002 . Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices . International Journal for Numerical Methods in Engineering , 55 ( 2 ) : 191 – 231 . doi: 10.1002/nme.492
   Web of Science ®Google Scholar
• Di-Sciuva , M. 1992 . Multilayered anisotropic plate models with continuous interlaminar stresses . Composite Structures , 22 ( 3 ) : 149 – 167 . doi: 10.1016/0263-8223(92)90003-u
   Web of Science ®Google Scholar
• Engblom , J.J. and Ochoa , O.O. 1985 . Through-the-thickness stress predictions for laminated plates of advanced composite materials . International Journal for Numerical Methods in Engineering , 21 ( 10 ) : 1759 – 1776 . doi: 10.1002/nme.1620211003
   Web of Science ®Google Scholar
• Fares , M.E. and Elmarghany , M.K. 2008 . A refined zigzag nonlinear first-order shear deformation theory of composite laminated plates . Composite Structures , 82 ( 1 ) : 71 – 83 . doi: 10.1016/j.compstruct.2006.12.007
   Web of Science ®Google Scholar
• Katili , I. 1993 . A new discrete Kirchhoff–Mindlin element based on Mindlin–Reissner plate theory and assumed shear strain fields – part II: An extended DKQ element for thick-plate bending analysis . International Journal for Numerical Methods in Engineering , 36 ( 11 ) : 1885 – 1908 . doi: 10.1002/nme.1620361107
   Web of Science ®Google Scholar
• Lardeur, P. (1990). Développement et évaluation de deux nouveaux éléments finis de plaques et coques composites avec influence du cisaillement transversal (PhD Thesis, University of Technology of Compiègne, France).
   Google Scholar
• Lekhnitskii, S.G. (1935). Strength calculation of composite beams, Vestnik inzhen i tekhnikov.
   Google Scholar
• Mindlin , R. 1951 . Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates . Journal of Applied Mechanics , 18 ( 1 ) : 31 – 38 .
   Web of Science ®Google Scholar
• Murakami , H. 1986 . Laminated composite plate theory with improved in-plane responses . Journal of Applied Mechanics , 53 : 661 – 666 .
   Web of Science ®Google Scholar
• Pagano , N.J. 1970 . Exact solutions for rectangular bidirectional composites and sandwich plates . Journal of Composite Materials , 1 ( 4 ) : 257 doi: 10.1016/0010-4361(70)90076-5
   Google Scholar
• Rath , B.K. and Das , Y.C. 1973 . Vibration of layered shells . Journal of Sound and Vibration , 28 ( 4 ) : 737 – 757 . doi: 10.1016/s0022-460x(73)80146-4
   Web of Science ®Google Scholar
• Reddy , J.N. 1984 . Simple higher-order theory for laminated composite plates . Journal of Applied Mechanics Transactions ASME , 51 ( 4 ) : 745 – 752 .
   Web of Science ®Google Scholar
• Reissner , E. 1943 . The effect of transverse shear deformation on the bending of elasticplates . Journal of applied Mechanics , 12 : A69 – A77 .
   Web of Science ®Google Scholar
• Sakami S. (2008). Modélisation numérique des structures composites multicouches à l’aide d’une approche discrète au sens de Mindlin. Le modèle DDM (Displacement Discrete Mindlin) (Doctorat Thesis, University of Reims Champagne Ardenne).
   Google Scholar
• Tafla , A. , Ayad , R. and Sedira , L. 2010 . A Mindlin multilayered hybrid-mixed approach for laminated and sandwich structures without shear correction factors . Européenne de Mécanique Numérique [European Journal of Computational Mechanics/Revue] , 19 ( 8 ) : 725 – 742 . doi: 10.3166/ejcm.19.725-742
   Google Scholar
• Topdar , P. , Sheikh , A.H. and Dhang , N. 2003 . Finite element analysis of composite and sandwich plates using a continuous inter-laminar shear stress model . Journal of Sandwich Structures and Materials , 5 ( 3 ) : 207 – 231 . doi: 10.1177/10996362030 05003001
   Web of Science ®Google Scholar
• Whitney , J.M. 1969 . The effect of transverse shear deformation on the bending of laminated plates . Journal of Composite Materials , 3 ( 3 ) : 534 – 547 . doi: 10.1177/002199836900300316
   Web of Science ®Google Scholar