DOI QR코드

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Assumed strain quadrilateral C0 laminated plate element based on third-order shear deformation theory

  • Shi, G. (Institute of High Performance Computing, National University of Singapore) ;
  • Lam, K.Y. (Institute of High Performance Computing, National University of Singapore) ;
  • Tay, T.E. (Institute of High Performance Computing, National University of Singapore) ;
  • Reddy, J.N. (Department of Mechanical Engineering, Texas A & M University)
  • 발행 : 1999.12.25

초록

This paper presents a four-noded quadrilateral $C^0$ strain plate element for the analysis of thick laminated composite plates. The element formulation is based on: 1) the third-order shear deformation theory; 2) assumed strain element formulation; and 3) interrelated edge displacements and rotations along element boundaries. Unlike the existing displacement-type composite plate elements based on the third-order theory, which rely on the $C^1$-continuity formulation, the present plate element is of $C^0$-continuity, and its element stiffness matrix is evaluated explicitly. Because of the third-order expansion of the in-plane displacements through the thickness, the resulting theory and hence elements do not need shear correction factors. The explicit element stiffness matrix makes the present element more computationally efficient than the composite plate elements using numerical integration for the analysis of thick layered composite plates.

키워드

참고문헌

  1. Argyris, J. and Tenek, L. (1993), "A natural triangular layered element for bending analysis of isotropic, sandwich, laminated composite and hybrid plates", Computer Meth. Appl. Mech. Eng., 109, 197-218. https://doi.org/10.1016/0045-7825(93)90078-C
  2. Carrera. E. (1996), "$C^0$ Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stress continuity", Int. J. Num. Meth. Eng., 39, 1797-1820. https://doi.org/10.1002/(SICI)1097-0207(19960615)39:11<1797::AID-NME928>3.0.CO;2-W
  3. Carrera. E. and Kroplin, B. (1997), "Zig-zag and interlaminar equilibria effects in large-deflection and postbuckling analysis of multilayered plates" , Mech. Comp. Mater. Struct., 4, 69-94. https://doi.org/10.1080/10759419708945875
  4. Cho, M. and Pannerter, R.R. (1992), "An efficient higher order plate theory for laminated plates", Composite Structures, 20, 113-123. https://doi.org/10.1016/0263-8223(92)90067-M
  5. Cho, M. and Pamerter, R. (1994), "Finite element for composite plate bending based on efficient higher order theory" , AIAA J., 32, 2241-2248. https://doi.org/10.2514/3.12283
  6. Hu, H.-C. (1981), Variational Principles in Elasticity and Applications (in Chinese), Science Press, Beijing.
  7. Kant, T., Owen, D.R.J. and Zienkiewicz, O.C. (1982), "A refined higher-order $C^0$ plate bending element", Comput. & Structures, 15, 177-183. https://doi.org/10.1016/0045-7949(82)90065-7
  8. Kant, T. and Kommineni (1994), "Large amplitude free vibration analysis of cross-ply composite and sandwich laminates with a refined theory and $C^0$ finite elements" , Comput. & Structures, 50, 123- 134. https://doi.org/10.1016/0045-7949(94)90443-X
  9. Kapania, R.K. and Raciti, S. (1989), "Recent advances in analysis of laminated beams and plates, Part I: Shear effect and buckling" , AIAA J., 27, 923-934. https://doi.org/10.2514/3.10202
  10. Levinson, M. (1980), "An accurate, simple theory of the statics and dynamics of elastic plates" , Mech. Res. Commun., 7, 343-350. https://doi.org/10.1016/0093-6413(80)90049-X
  11. Murakami. H. (1986), "Laminated composite plate theory with improved in-plane responses", J. Applied. Mech., 53, 661-666. https://doi.org/10.1115/1.3171828
  12. Pagano, N.J. (1970), "Exact solutions for rectangular bidirectional composite anisotropic plates", J. Compo Materials, 4, 20-34. https://doi.org/10.1177/002199837000400102
  13. Pagano, N.J. and Hatfield, S.J. (1972), "Elastic behavior of multilayered bidirectional composites", AlAA J., 10, 931-933. https://doi.org/10.2514/3.50249
  14. Pandya, B.N. and Kant, T. (1988), "Flexural analysis of laminated compostie using refined higher-order $C^0$ plate bending elements" , Computer Meth. Appl. Mech. Eng., 66, 173-198. https://doi.org/10.1016/0045-7825(88)90075-8
  15. Phan, N.D. and Reddy, J.N. (1985), "Analysis of laminated composite plates using a higher-order shear deformation theory", Int. J. Num. Meth. Eng., 21, 2201-2219. https://doi.org/10.1002/nme.1620211207
  16. Putcha, N.S. and Reddy, J.N., (1986), "Stability and natural vibration analysis of laminated plates by using a mixed element on a refined plate thoery" , J. Sound Vib., 104, 285-300. https://doi.org/10.1016/0022-460X(86)90269-5
  17. Reddy, J.N. (1984), "A simple higher-order theory for laminated composites", J. Applied. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719
  18. Reddy, J.N. (1989), "On refined computational models of composite laminates", Int. J. Num. Meth. Eng., 27, 361-382. https://doi.org/10.1002/nme.1620270210
  19. Reddy, J.N. (1997), Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, Boca Raton, Florida.
  20. Ren, J.G. and Hinton, E. (1986), "The finite element analysis of homogeneous and laminated composite plates using a simple higher-order theory" , Commun. Applied Num. Meth., 2, 217-228. https://doi.org/10.1002/cnm.1630020214
  21. Rohwer, K. (1991), "Application of higher order theories to the bending analysis of layered composite plates", Int. J. Solids & Structures, 29, 105-119.
  22. Shi, G. and Voyiadjis, G.Z. (1991), "Efficient and accurate four-noded quadrilateral $C^0$ plate element based on assumed strain fields" , Int. J. Num. Meth. Eng., 32, 1041-1055. https://doi.org/10.1002/nme.1620320508
  23. Shi, G. and Lam K.Y. (1999), "Finite element vibration analysis of composite beams based on higher-order theory" , J. Sound and Vibration, 219, 707-721. https://doi.org/10.1006/jsvi.1998.1903
  24. Tang, L., Chen, W. and Liu, Y. (1980), "The quasi-conforming element method and the generalized variational principle", J. Dalian Inst. Tech. (in Chinese), 19, 1-15.
  25. Taylor, L. and Auricchio, F. (1993), "Linked interpolation for Reissner-Mindlin plate elements, Part II: A simple triangle", Int. J. Num. Meth. Eng., 36, 3057-3066. https://doi.org/10.1002/nme.1620361803
  26. Zienkiewicz, O.C., Xu, Z., Zeng, L.F., Samuelsson, A. and Wiberg, N.E. (1993), "Linked interpolation for Reissner-Mindlin plate elements, Part I: A simple quadrilateral" , Int. J. Num. Meth. Eng., 36, 3043-3056. https://doi.org/10.1002/nme.1620361802

피인용 문헌

  1. A new simple third-order shear deformation theory of plates vol.44, pp.13, 2007, https://doi.org/10.1016/j.ijsolstr.2006.11.031
  2. Finite element linear and nonlinear, static and dynamic analysis of structural elements, an addendum vol.19, pp.5, 2002, https://doi.org/10.1108/02644400210435843