Structural Engineering and Mechanics

  • 제18권6호
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  • Pages.807-829
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  • 2004
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

An element-based 9-node resultant shell element for large deformation analysis of laminated composite plates and shells

  • Han, S.C. (Department of Civil Engineering, Daewon Science College) ;
  • Kim, K.D. (School of Civil Engineering, Asian Institute of Technology) ;
  • Kanok-Nukulchai, W. (School of Civil Engineering, Asian Institute of Technology)
  • 투고 : 2003.11.15
  • 심사 : 2004.10.03
  • 발행 : 2004.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

The Element-Based Lagrangian Formulation of a 9-node resultant-stress shell element is presented for the isotropic and anisotropic composite material. The effect of the coupling term between the bending strain and displacement has been investigated in the warping problem. The strains, stresses and constitutive equations based on the natural co-ordinate have been used throughout the Element-Based Lagrangian Formulation of the present shell element which offers an advantage of easy implementation compared with the traditional Lagrangian Formulation. The element is free of both membrane and shear locking behavior by using the assumed natural strain method such that the element performs very well in thin shell problems. In composite plates and shells, the transverse shear stiffness is defined by an equilibrium approach instead of using the shear correction factor. The arc-length control method is used to trace complex equilibrium paths in thin shell applications. Several numerical analyses are presented and discussed in order to investigate the capabilities of the present shell element. The results showed very good agreement compared with well-established formulations in the literature.

키워드

참고문헌

  1. Ahmad, S., Irons, B.M. and Zienkiewicz, O.C. (1970), "Analysis of thick and thin shell structures by curved finite elements", Int. J. Num. Meth. Eng., 2, 419-451. https://doi.org/10.1002/nme.1620020310
  2. Belytschko, T., Wong, B.L. and Stolarski, H. (1989), "Assumed strain stabilization procedure for the 9-node Lagrange shell element", Int. J. Num. Meth. Eng., 28, 385-414. https://doi.org/10.1002/nme.1620280210
  3. Chaisomphob, T., Kanok-Nuculchai, W. and Nishino, F. (1988), "An automatic arc length algorithm for tracing equilibrium paths of nonlinear structures", Proc. of JSCE, Struct. Eng./Earthq. Eng., 5, 205-208.
  4. Crisfield, M.A. (1981), "A fast incremental/iterative solution procedure that handles snap-through", Comput. Struct., 13, 55-62. https://doi.org/10.1016/0045-7949(81)90108-5
  5. Fontes Valente, R.A., Natal Jorge, R.M., Cardoso, R.P.R., Cesar de Sa, J.M.A. and Gra´cio, J.J.A. (2003), "On the use of an enhanced transverse shear strain shell element for problems involving large rotations", Comput. Mech., 30, 286-296. https://doi.org/10.1007/s00466-002-0388-x
  6. Huang, H.C. and Hinton, E. (1986), "A new nine node degenerated shell element with enhanced membrane and shear interpolation", Int. J. Num. Meth. Eng., 22, 73-92. https://doi.org/10.1002/nme.1620220107
  7. Hughes, T.J.R. and Liu, W.K. (1981), "Nonlinear finite element analysis of shells: Part I. Three-dimensional shells", Comput. Meth. Appl. Mech. Eng., 26, 331-362. https://doi.org/10.1016/0045-7825(81)90121-3
  8. Jang, J. and Pinsky, P.M. (1987), "An assumed covariant strain based 9-node shell element", Int. J. Num. Meth. Eng., 24, 2389-2411. https://doi.org/10.1002/nme.1620241211
  9. Kanok-Nukulchai, W. and Wong, W.K. (1988), "Element-based Lagrangian formulation for large-deformation analysis", Comput. Struct., 30, 967-974. https://doi.org/10.1016/0045-7949(88)90136-8
  10. Kim, K.D., Lomboy, G.R. and Han, S.C. (2003), "A co-rotational 8-node assumed strain shell element for postbuckling analysis of laminated composite plates and shells", Comput. Mech., 30(4), 330-342. https://doi.org/10.1007/s00466-003-0415-6
  11. Kim, K.D. and Park, T.H. (2002), "An 8-node assumed strain element with explicit integration for isotropic and laminated composite shells", Struct. Eng. Mech., 13(4), 387-410. https://doi.org/10.12989/sem.2002.13.4.387
  12. Kim, K.D., Park, T. and Voyiadjis, G.Z. (1998), "Postbuckling analysis of composite panels with imperfection damage", Comput. Mech., 22, 375-387. https://doi.org/10.1007/s004660050369
  13. Kim, K.D. and Voyiadjis, G.Z. (1999), "Non-linear finite element analysis of composite panels", Composites Part B: Engineering, 30(4), 365-381. https://doi.org/10.1016/S1359-8368(99)00007-4
  14. Lee, S.J. and Kanok-Nukulchai, W. (1998), "A nine-node assumed strain finite element for large deformation analysis of laminated shells", Int. J. Num. Meth. Eng., 42, 777-798. https://doi.org/10.1002/(SICI)1097-0207(19980715)42:5<777::AID-NME365>3.0.CO;2-P
  15. Lee, S.W. and Pian, T.H.H. (1978), "Improvement of plate and shell finite elements by mixed formulation", AIAA J., 16, 29-34. https://doi.org/10.2514/3.60853
  16. Liu, W.K., Lam, D., Law, S.E. and Belytschko, T. (1986), "Resultant stress degenerated shell element", Comput. Meth. Appl. Mech. Eng., 55, 259-300. https://doi.org/10.1016/0045-7825(86)90056-3
  17. Ma, H. and Kanok-Nukulchai, W. (1989), "On the application of assumed strained methods", Structural Engineering and Construction, Achievements, Trends and Challenges, Kanok-Nukulchai et al. (eds.), AIT, Bankok.
  18. MacNeal, R.H. (1982), "Derivation of element stiffness matrices by assumed strain distributions", Nicl. Enggr. Design, 33, 1049-1058.
  19. Noor, A.K. and Mathers, M.D. (1976), "Anisotropy and shear deformation in laminated composite plates", AIAA, 14, 282-285. https://doi.org/10.2514/3.7096
  20. Ramm, E. (1977), "A plate/shell element for large deflections and rotations", Nonlinear Finite Element Analysis in Structural Mechanics, Wunderlich, W., Stein, E., Bathe, K.J. (eds.), M.I.T. Press, NY.
  21. Reddy, J.N. (1997), Mechanics of Laminated Composite Plates, CRC Press, Florida.
  22. Rolfes, R. and Rohwer, K. (1997), "Improved transverse shear stress in composite finite element 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
  23. Saigal, S., Kapania, R.K. and Yang, Y.T. (1986), "Geometrically nonlinear finite element analysis of imperfect laminated shells", J. Compos. Mater., 20, 197-214. https://doi.org/10.1177/002199838602000206
  24. Simo, J.C. and Hughes, T.J.R. (1986), "On the variational formulations of assumed strain methods", J. Appl. Mech., ASME, 53, 51-54. https://doi.org/10.1115/1.3171737
  25. Simo, J.C. (1993), "On a stress resultant geometrically exact shell model. Part VII: Shell intersections with 5/6- DOF finite element formulations", Comput. Meth. Appl. Mech. Eng., 108, 319-339. https://doi.org/10.1016/0045-7825(93)90008-L
  26. White, D.W. and Abel, J.F. (1989), "Testing of shell finite element accuracy and robustness", Finite Element Method in Analysis and Design, 6, 129-151. https://doi.org/10.1016/0168-874X(89)90040-1
  27. Wong, Wai-Kong (1984), "Pseudo Lagrangian formulation for large deformation analysis of continua and structures", Master Thesis, School of Civil Engineering, A.I.T.
  28. XFINAS (2003), Nonlinear Structural Dynamic Analysis System, School of Civil Engineering, A.I.T., Thailand.
  29. Yoo, S.W. and Choi, C.K. (2000), "Geometrically nonlinear analysis of laminated composites by an improved degenerated shell element", Struct. Eng. Mech., 9(1), 123-456.

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  8. Geometrically Nonlinear Analysis of Hinged Cylindrical Laminated Composite Shells vol.3, pp.2, 2012, https://doi.org/10.11004/kosacs.2012.3.2.001
  9. Buckling Analysis of Laminated Composite Plates under the In-plane Compression and Shear Loadings vol.11, pp.12, 2010, https://doi.org/10.5762/KAIS.2010.11.12.5199
  10. An 8-Node Shell Element for Nonlinear Analysis of Shells Using the Refined Combination of Membrane and Shear Interpolation Functions vol.2013, 2013, https://doi.org/10.1155/2013/276304
  11. The development of laminated composite plate theories: a review vol.47, pp.16, 2012, https://doi.org/10.1007/s10853-012-6329-y
  12. A literature review on computational models for laminated composite and sandwich panels vol.1, pp.1, 2011, https://doi.org/10.2478/s13531-011-0005-x
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  14. A solid-shell corotational element based on ANDES, ANS and EAS for geometrically nonlinear structural analysis vol.95, pp.2, 2013, https://doi.org/10.1002/nme.4504
  15. Transient analysis of FGM and laminated composite structures using a refined 8-node ANS shell element vol.56, 2014, https://doi.org/10.1016/j.compositesb.2013.08.044
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  18. Non-linear analysis of laminated composite and sigmoid functionally graded anisotropic structures using a higher-order shear deformable natural Lagrangian shell element vol.89, pp.1, 2009, https://doi.org/10.1016/j.compstruct.2008.08.006
  19. Free and forced vibration analysis of laminated composite plates and shells using a 9-node assumed strain shell element vol.39, pp.1, 2006, https://doi.org/10.1007/s00466-005-0007-8
  20. Postbuckling analysis of laminated composite shells under shear loads vol.21, pp.2, 2016, https://doi.org/10.12989/scs.2016.21.2.373
  21. Nine-Node Resultant-Stress Shell Element for Free Vibration and Large Deflection of Composite Laminates vol.19, pp.2, 2006, https://doi.org/10.1061/(asce)0893-1321(2006)19:2(103)
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  24. An improved treatment of mixed interpolation functions in eight-node assumed natural strain shell element for vibration analysis vol.5, pp.1, 2004, https://doi.org/10.1080/19373260.2012.638062