Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A refined discrete triangular Mindlin element for laminated composite plates

  • Ge, Zengjie (Key Laboratories of the State for Structural Analysis of Industrial Equipment, Dalian University of Technology) ;
  • Chen, Wanji (Key Laboratories of the State for Structural Analysis of Industrial Equipment, Dalian University of Technology)
  • Received : 2002.01.28
  • Accepted : 2002.09.24
  • Published : 2002.11.25
⟨ Previous Next ⟩

Abstract

Based on the Mindlin plate theory, a refined discrete 15-DOF triangular laminated composite plate finite element RDTMLC with the re-constitution of the shear strain is proposed. For constituting the element displacement function, the exact displacement function of the Timoshenko's laminated composite beam as the displacement on the element boundary is used to derive the element displacements. The proposed element can be used for the analysis of both moderately thick and thin laminated composite plate, and the convergence for the very thin situation can be ensured theoretically. Numerical examples presented show that the present model indeed possesses the properties of higher accuracy for anisotropic laminated composite plates and is free of locking even for extremely thin laminated plates.

Keywords

References

  1. Auricchio, F. and Sacco, E. (1999), "A mixed-enhanced finite-element for the analysis of laminated composite plates", Int. J. Num. Meth. Eng., 44, 1481-1504. https://doi.org/10.1002/(SICI)1097-0207(19990410)44:10<1481::AID-NME554>3.0.CO;2-Q
  2. Auricchio, F. and Sacco, E. (1999), "Partial-mixed formulation and refined models for the analysis of composite laminates within an FSDT", Composite Structures, 46, 103-113. https://doi.org/10.1016/S0263-8223(99)00035-5
  3. Batoz, J.L. and Lardeur, P. (1989), "A discrete shear triangular nine d.o.f. element for the analysis of thick to very thin plates", Int. J. Num. Meth. Eng., 29, 533-560.
  4. Batoz, J.L. and Katili, I. (1992), "On a simple triangular Reissner/Mindlin plate element based on incompatible modes and discrete constraints", Int. J. Num. Meth. Eng., 35, 1603-1632. https://doi.org/10.1002/nme.1620350805
  5. Chen, Wanji and Cheung, Y.K. (2000), "Refined quadrilateral element based on Midlin/Reissner plate theory", Int. J. Num. Meth. Eng., 47, 605-627. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<605::AID-NME785>3.0.CO;2-E
  6. Chen, Wanji and Cheung, Y.K. (2001), "Refined 9-DOF triangular Mindlin plate element, Int. J. Num. Meth. Eng., 51, 1259-1281. https://doi.org/10.1002/nme.196
  7. Hughes, T.J.R., Cohen, M. and Haroun, M. (1978), "Reduced and selective integration techniques in finite element analysis of plates", Nucl. Eng. Design, 46, 203-222. https://doi.org/10.1016/0029-5493(78)90184-X
  8. Katili, I. (1993), "A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields-Part I: An extended DKT element for thick-plate bending analysis", Int. J. Num. Meth. Eng., 36, 1859-1883. https://doi.org/10.1002/nme.1620361106
  9. Kirchhoff, G. (1850), "Uber das gleichgewicht und bewegung einer elastischen scheibe", Journal für die reine und angewandte Math., 40, 51-88.
  10. Lakshminarayana, H.V. and Murthy, S.S. (1984), "A shear-flexible triangular finite element model for laminated composite plates", Int. J. Num. Meth. Eng., 20, 591-623. https://doi.org/10.1002/nme.1620200403
  11. Lardeur, P. and Batoz, J.L. (1989), "Composite plane analysis using a new discrete shear triangular finite element", Int. J. Num. Meth. Eng., 27, 343-359. https://doi.org/10.1002/nme.1620270209
  12. Lo, K.H., Christensen, R.M. and Wu, E.M. (1977), "A higher-order theory of plate deformation. Part 2: laminated plates", J. Appl. Mech., 44, 669-676. https://doi.org/10.1115/1.3424155
  13. Malkus, D.S. and Hughes, T.J.R. (1978), "Mixed finite element methods-reduced and selective integration techniques: a unification of concepts", Comput. Meth. Appl. Mech. Eng., 15, 63-81. https://doi.org/10.1016/0045-7825(78)90005-1
  14. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic elastic plates", J. Appl. Mech., 18, 31-38.
  15. Noor, A.K. and Mathers, M.D. (1975), "Shear-flexible finite element method of laminated composite plates", NASA TN D-8044.
  16. Pagano, N.J. and Hatfield, S.J. (1972), "Elastic behavior of multilayered bi-directional composites", AIAA J., 10, 931-933. https://doi.org/10.2514/3.50249
  17. Pryor, C.W. and Barker, R.M. (1971), "A finite element analysis including transverse shear effects for application to laminated plates", AIAA J., 9, 912-917. https://doi.org/10.2514/3.6295
  18. Pugh, E.D., Hinton, E. and Zienkiewicz, O.C. (1978), "A study of triangular plate bending element with reduced integration", Int. J. Num. Meth. Eng., 12, 1059-1078. https://doi.org/10.1002/nme.1620120702
  19. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719
  20. Rolfes, R. and Rohwer, K. (1997), "Improved transverse shear stresses in composite finite elements based on first order shear deformation theory", Int. J. Num. Meth. Eng., 40, 51-60. https://doi.org/10.1002/(SICI)1097-0207(19970115)40:1<51::AID-NME49>3.0.CO;2-3
  21. Rolfes, R., Rohwer, K. and Ballerstaedt, M. (1998), "Efficient linear transverse normal stress analysis of layered composite plates", Comput. Struct., 68, 643-652. https://doi.org/10.1016/S0045-7949(98)00097-2
  22. Sadek, E.A.(1998), "Some serendipity finite element for the analysis of laminate plates", Comput. Struct., 69, 37- 51. https://doi.org/10.1016/S0045-7949(98)00077-7
  23. Satish Kumar, Y.V. and Madhujit Mukhopadhyay (2000), "A new triangular stiffened plate element for laminate analysis", Composites Science and Technology, 60, 935-943. https://doi.org/10.1016/S0266-3538(99)00190-6
  24. Sheikh, A.H., Haldar, S. and Sengupta, D. (2002), "A high precision shear deformable element for the analysis of laminated composite plates of different shapes", Comput. Struct., 55, 329-336. https://doi.org/10.1016/S0263-8223(01)00149-0
  25. Singh, G., Raju, K.K. and Rao, G.V. (1998), "A new lock-free, material finite element for flexure of moderately thick rectangular composite plates", Comput. Struct., 69, 609-623.
  26. Somashekar, B.R., Prathap, G. and Ramesh, B.C. (1987), "A field consistent four-node laminated anisotropic plate/shell element", Comput. Struct., 25(3), 345-353. https://doi.org/10.1016/0045-7949(87)90127-1
  27. Spilker, R.L., Jakobs, D.M. and Engelmann, B.E. (1985), "Efficient hybrid stress isoparametric elements for moderately thick and thin multiplayer plates", In: Spilker, R.L. and Reed, K.W., editors. Hybrid and Mixed Finite Element Methods, ASME, AMD-vol-73, New York.
  28. Sze, K.Y., He, L.W. and Cheung, Y.K. (2000), "Predictor-corrector procedures for analysis of laminated plates using standard Mindlin finite element models", Composite Structures, 50, 171-182. https://doi.org/10.1016/S0263-8223(00)00095-7
  29. Whitney, J.M. (1973), "Shear correction factors for orthotropic laminates under static load", J. Appl. Mech., 40, 302-304. https://doi.org/10.1115/1.3422950
  30. Wilt, T.E., Saleeb, A.F. and Chang, T.Y. (1990), "A mixed element for laminated plates and shells", Comput. Struct., 37(4), 597-611 https://doi.org/10.1016/0045-7949(90)90048-7
  31. Vlachoutsis, S. (1992), "Shear correction factors for plates and shells", Int. J. Num. Meth. Eng., 33, 1537-1552. https://doi.org/10.1002/nme.1620330712
  32. Zienkiewicz, O.C., Taylor, R.L. and Too, J.M. (1971), "Reduced integration technique in general analysis of plates and shells", Int. J. Num. Meth. Eng., 3, 275-290. https://doi.org/10.1002/nme.1620030211

Cited by

  1. Interlaminar stress analysis of multilayered composites based on the Hu-Washizu variational theorem 2017, https://doi.org/10.1177/0021998317733532
  2. Geometrically nonlinear analysis of laminated composite plates by two new displacement-based quadrilateral plate elements vol.72, pp.3, 2006, https://doi.org/10.1016/j.compstruct.2005.01.001
  3. Two simple and efficient displacement-based quadrilateral elements for the analysis of composite laminated plates vol.61, pp.11, 2004, https://doi.org/10.1002/nme.1123
  4. A novel one-dimensional two-node shear-flexible layered composite beam element vol.47, pp.7, 2011, https://doi.org/10.1016/j.finel.2011.01.010
  5. A review on the design of laminated composite structures: constant and variable stiffness design and topology optimization vol.1, pp.3, 2018, https://doi.org/10.1007/s42114-018-0032-7
  6. An Improved Four-Node Element for Analysis of Composite Plate/Shell Structures Based on Twice Interpolation Strategy vol.17, pp.6, 2002, https://doi.org/10.1142/s0219876219500208