Structural Engineering and Mechanics

  • 제15권1호
  • /
  • Pages.83-114
  • /
  • 2003
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Development of triangular flat-shell element using a new thin-thick plate bending element based on semiLoof constrains

  • Chen, Yong-Liang (Department of Engineering Mechanics, Tsinghua University) ;
  • Cen, Song (Department of Engineering Mechanics, Tsinghua University) ;
  • Yao, Zhen-Han (Department of Engineering Mechanics, Tsinghua University) ;
  • Long, Yu-Qiu (Department of Civil Engineering, Tsinghua University) ;
  • Long, Zhi-Fei (Department of Science & Art, China University of Mining & Technology)
  • 투고 : 2002.04.19
  • 심사 : 2002.11.12
  • 발행 : 2003.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

A new simple 3-node triangular flat-shell element with standard nodal DOF (6 DOF per node) is proposed for the linear and geometrically nonlinear analysis of very thin to thick plate and shell structures. The formulation of element GT9 (Long and Xu 1994), a generalized conforming membrane element with rigid rotational freedoms, is employed as the membrane component of the new shell element. Both one-point reduced integration scheme and a corresponding stabilization matrix are adopted for avoiding membrane locking and hourglass phenomenon. The bending component of the new element comes from a new generalized conforming Kirchhoff-Mindlin plate element TSL-T9, which is derived in this paper based on semiLoof constrains and rational shear interpolation. Thus the convergence can be guaranteed and no shear locking will happen. Furthermore, a simple hybrid procedure is suggested to improve the stress solutions, and the Updated Lagrangian formulae are also established for the geometrically nonlinear problems. Numerical results with solutions, which are solved by some other recent element models and the models in the commercial finite element software ABAQUS, are presented. They show that the proposed element, denoted as GMST18, exhibits excellent and better performance for the analysis of thin-think plates and shells in both linear and geometrically nonlinear problems.

키워드

참고문헌

  1. ABAQUS/Standard User's Manual, Version 5.8 (1998), Hibbitt, Karlsson & Sorensen, Inc.: Rawtucket, RhodeIsland.
  2. Allman, D.J. (1984), "A compatible triangular element including vertex rotations for plane elasticity analysis",Comput. Struct., 19(1-2), 1-8. https://doi.org/10.1016/0045-7949(84)90197-4
  3. Allman, D.J. (1988), "Evaluation of the constant triangle with drilling rotations", Int. J. Numer. Meth. Eng., 50,25-69.
  4. Ayad, R., Dhatt, G. and Batoz, J.L. (1998), "A new hybrid-mixed variational approach for Reissner-Mindlinplates: The MiSP model", Int. J. Numer. Meth. Eng., 42, 1149-1179. https://doi.org/10.1002/(SICI)1097-0207(19980815)42:7<1149::AID-NME391>3.0.CO;2-2
  5. Ayad, R., Rigolot, A. and Talbi, N. (2001), "An improved three-node hybrid-mixed element for Mindlin/Reissnerplates", Int. J. Numer. Meth. Eng., 51, 919-942 https://doi.org/10.1002/nme.188
  6. Babuška, I. and Scapolla, T. (1989), "Benchmark computation and performance evaluation for a rhombic platebending problem", Int. J. Numer. Meth. Eng., 28, 155-179. https://doi.org/10.1002/nme.1620280112
  7. Badiansky, B. (1974), "Theory of buckling and post-buckling behavior of elastic structure", In: Advances inApplied Mechanics, New York: Academic Press.
  8. Bathe, K.J. and Bolourchi, S. (1980), "A geometric and material nonlinear plate and shell element", Comput.Struct., 21, 367-383.
  9. Bathe, K.J. and Dvorkin, E. (1985), "Short communication - a four node plate bending element based onMindlin/Reissner plate theory and mixed interpolation", Int. J. Numer. Meth. Eng., 21, 367-383. https://doi.org/10.1002/nme.1620210213
  10. Batoz, J.L., Bathe, K.J. and Ho, W.J. (1980), "A Study of three-node triangular plate bending elements", Int. J.Numer. Meth. Eng., 15, 1771-1812. https://doi.org/10.1002/nme.1620151205
  11. Batoz, J.L. and Lardeur, P. (1989), "A discrete shear triangular nine d.o.f. element for the analysis of thick tovery thin plates", Int. J. Numer. Meth. Eng., 29, 533-560.
  12. Batoz, J.L. and Katili, I. (1992), "On a simple triangular Reissner/Mindlin plate element based on incompatiblemodes and discrete constrains", Int. J. Numer. Meth. Eng., 35, 1603-1632. https://doi.org/10.1002/nme.1620350805
  13. Bazeley, G.P., Cheung, Y.K., Irons, B.M. and Zienkiewicz, O.C. (1965), "Triangular elements in bendingconforming and non-conforming solutions", Proc. Conf. Matrix Methods in Struct. Mech., Air Force Instituteof Technology, Wright-Patterson A.F.Base, OH, 547-576.
  14. Carpenter, N., Stolarski, H. and Belytschko, T. (1986), "Improvements in 3-node triangular shell elements", Int.J. Numer. Meth. Eng., 23, 1643-1667. https://doi.org/10.1002/nme.1620230906
  15. Cheung, Y.K. and Wanji, C. (1995), "Refined nine-parameter triangular thin plate bending element by usingrefined direct stiffness method", Int. J. Numer. Meth. Eng., 38, 283-298. https://doi.org/10.1002/nme.1620380208
  16. Darendeliler, H., Oral, S. and Turgut, A. (1999), "A pseudo-layered, elastic-plastic, flat-shell finite element", Comput. Meth. Appl. Mech. Eng., 174, 211-218.
  17. Felippa, C.A. and Alexander, S. (1992), "Membrane triangles with corner drilling freedom - III Implementationand performance evolution", Finite Elements in Analysis and Design, 12, 203-239. https://doi.org/10.1016/0168-874X(92)90035-B
  18. Fish, J. and Belytshko, T. (1992), "Stabilized rapidly convergent 18-degree-of-freedom flat shell triangularelement", Int. J. Numer. Meth. Eng., 33, 149-162. https://doi.org/10.1002/nme.1620330111
  19. Guan, Y. and Tang, L. (1992), "A quasi-conforming nine-node degenerated shell finite element", Finite Elementsin Analysis and Design, 11, 165-176. https://doi.org/10.1016/0168-874X(92)90048-H
  20. Hughes, T.J.R. and Liu, W.K. (1981), "Nonlinear finite element analysis of shells, Part I: Three dimensionalshells", Comput. Method Appl. Mech. Eng., 26, 331-362. https://doi.org/10.1016/0045-7825(81)90121-3
  21. Katili, I. (1993), "A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory andassumed shear strain fields - Part I: An extended DKT element for thick-plate bending analysis", Int. J.Numer. Meth. Eng., 36, 1859-1883. https://doi.org/10.1002/nme.1620361106
  22. Katili, I. (1993), "A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory andassumed shear strain fields Part II: An extended DKQ element for thick-plate bending analysis", Int. J. Numer.Meth. Eng., 36, 1885-1908. https://doi.org/10.1002/nme.1620361107
  23. Long, Y.Q., Bu, X., Long, Z. and Xu, Y. (1995), "Generalized conforming plate bending elements using pointand line compatibility conditions", Comput. Struct., 54(4), 717-723. https://doi.org/10.1016/0045-7949(94)00362-7
  24. Long, Y.Q. and Xin, K. (1989), "Generalized conforming element for bending and buckling analysis of plates",Finite Elements in Analysis and Design, 5, 15-30. https://doi.org/10.1016/0168-874X(89)90003-6
  25. Long, Y.Q. and Xu, Y. (1994), "Generalized conforming triangular membrane element with rigid rotationalfreedoms", Finite Elements in Analysis and Design, 17, 259-271. https://doi.org/10.1016/0168-874X(94)90002-7
  26. Long, Y.Q. and Zhao, J. (1988), "A new generalized conforming triangular element for thin plates",Communications in Applied Numerical Methods, 4, 781-792. https://doi.org/10.1002/cnm.1630040612
  27. Long, Z.F. (1992), "Triangular and rectangular plate elements based on generalized compatibility conditions",Comput. Mech., 10, 281-288. https://doi.org/10.1007/BF00370094
  28. Long, Z.F. (1993), "Two generalized conforming plate elements based on semiLoof constrains", Comput. Struct.,47(2), 299-304. https://doi.org/10.1016/0045-7949(93)90380-V
  29. Morley, L.S.D. (1963), Skew Plates and Structures, International Series of Monographs in Aeronautics andAstronautics, Macmillan, New York.
  30. Olson, M.D. and Bearden, T.W. (1979), "The simple flat triangular shell element revisited", Int. J. Numer. Meth.Eng., 14, 51-68. https://doi.org/10.1002/nme.1620140105
  31. Parisch, H. (1979), "A critical survey of the 9-node degenerated shell element with special emphasis on thinshell", Comput. Method Appl. Mech. Eng., 20, 323-350. https://doi.org/10.1016/0045-7825(79)90007-0
  32. Providas, E. and Kattis, M.A. (2000), "An assessment of two fundamental flat triangular shell elements withdrilling rotations", Comput. Struct., 77(2), 129-139. https://doi.org/10.1016/S0045-7949(99)00215-1
  33. Razzaque, A. (1973), "Program for triangular bending elements with derivative smoothing", Int. J. Numer. Meth.Eng., 6, 333-345. https://doi.org/10.1002/nme.1620060305
  34. Saleeb, A.F., Chang, T.Y., Graf, W. and Yingyeunyong, S. (1990), "A hybrid/mixed model for non-linear shellanalysis and its applications to large rotation problems", Int. J. Numer. Meth. Eng., 29, 407-446. https://doi.org/10.1002/nme.1620290213
  35. Soh, A.K., Cen, S., Long, Y.Q. and Long, Z.F. (2001), "A new twelve DOF quadrilateral element for analysis ofthick and thin plate", European Journal of Mechanics A/Solids, 20(2), 299-326. https://doi.org/10.1016/S0997-7538(00)01129-3
  36. Soh, A.K., Long, Z.F. and Cen, S. (1999), "A new nine DOF triangular element for analysis of thick and thinplates", Comput. Mech., 24, 408-417. https://doi.org/10.1007/s004660050461
  37. Taylor, R.L. and Auricchio, F. (1993), "Linked interpolation for Reissner-Mindlin plate element: part II-a simpletriangle", Int. J. Numer. Meth. Eng., 36, 3057-3066. https://doi.org/10.1002/nme.1620361803
  38. To, C.W.S. and Liu, M.L. (1994), "Hybrid strain based three-node flat triangular shell elements", Finite Elementsin Analysis and Design, 17, 169-203. https://doi.org/10.1016/0168-874X(94)90080-9
  39. To, C.W.S. and Liu, M.L. (1995), "Hybrid strain based three-node flat triangular shell elements-II. Numericalinvestigation of nonlinear problems", Comput. Struct., 54(6), 1057-1076. https://doi.org/10.1016/0045-7949(94)00396-K
  40. Wanji, C. and Cheung, Y.K. (1998), "Refined triangular discrete Kirchhoff thin plate bending element", Int. J.Numer. Meth. Eng., 41, 1507-1525. https://doi.org/10.1002/(SICI)1097-0207(19980430)41:8<1507::AID-NME351>3.0.CO;2-T
  41. Wanji, C. and Cheung, Y.K. (1999), "Refined non-conforming triangular elements for analysis of shell structures", Int. J. Numer. Meth. Eng., 46, 433-455. https://doi.org/10.1002/(SICI)1097-0207(19990930)46:3<433::AID-NME683>3.0.CO;2-Z
  42. Wanji, C. and Cheung, Y.K. (2001), "Refined 9-Dof triangular Mindlin plate elements", Int. J. Numer. Meth.Eng., 51, 1259-1281. https://doi.org/10.1002/nme.196
  43. Zhang, Q., Lu, M. and Kuang, W. (1998), "Geometric non-linear analysis of space shell structures usinggeneralized conforming flat shell elements for space shell structures", Communications in Numerical Methodsin Engineering, 14, 941-957. https://doi.org/10.1002/(SICI)1099-0887(1998100)14:10<941::AID-CNM200>3.0.CO;2-S
  44. Zhang, Y., Cheung, Y.K. and Chen, W.J. (2000), "Two refined nonconforming flat shell elements", Int. J. Numer.Meth. Eng., 49, 355-382. https://doi.org/10.1002/1097-0207(20000930)49:3<355::AID-NME966>3.0.CO;2-A
  45. Zienkiewicz, O.C. and Taylor, R.L. (2000), The Finite Element Method (fifths edition), Volume 2: SolidMechanics, Butterworth-Heinemann, Oxford.
  46. Zienkiewicz, O.C., Xu, Z., Ling, F.Z., Samuelsson, A. and Wiberg, N.E. (1993), "Linked interpolation forReissner-Mindlin plate element: part I-a simple quadrilateral", Int. J. Numer. Meth. Eng., 36, 3043-3056. https://doi.org/10.1002/nme.1620361802

피인용 문헌

  1. Developments of Mindlin-Reissner Plate Elements vol.2015, 2015, https://doi.org/10.1155/2015/456740
  2. Application of the quadrilateral area coordinate method: a new element for laminated composite plate bending problems vol.23, pp.5, 2007, https://doi.org/10.1007/s10409-007-0088-z
  3. Application of the quadrilateral area co-ordinate method: a new element for Mindlin–Reissner plate vol.66, pp.1, 2006, https://doi.org/10.1002/nme.1533
  4. A hybrid-stress element based on Hamilton principle vol.26, pp.4, 2010, https://doi.org/10.1007/s10409-010-0352-5
  5. Hybrid displacement function element method: a simple hybrid-Trefftz stress element method for analysis of Mindlin-Reissner plate vol.98, pp.3, 2014, https://doi.org/10.1002/nme.4632
  6. A concave-admissible quadrilateral quasi-conforming plane element using B-net method vol.57, 2016, https://doi.org/10.1016/j.euromechsol.2015.12.001
  7. Two generalized conforming quadrilateral Mindlin–Reissner plate elements based on the displacement function vol.99, 2015, https://doi.org/10.1016/j.finel.2015.01.012
  8. Linear and Geometrically nonlinear analysis of plates and shells by a new refined non-conforming triangular plate/shell element vol.36, pp.5, 2005, https://doi.org/10.1007/s00466-004-0625-6