Structural Engineering and Mechanics

  • 제17권1호
  • /
  • Pages.113-140
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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

A mixed 8-node hexahedral element based on the Hu-Washizu principle and the field extrapolation technique

  • Chen, Yung-I (Bureau of High Speed Rail, Ministry of Transportation and Communications) ;
  • Wu, Guan-Yuan (Department of Fire Science, Central Police University)
  • 투고 : 2002.10.24
  • 심사 : 2003.09.16
  • 발행 : 2004.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

A mixed eight-node hexahedral element formulated via the Hu-Washizu principle as well as the field extrapolation technique is presented. The mixed element with only three translational degrees of freedom at each node can provide extremely accurate and reliable performance for popular benchmark problems such as spacial beams, plates, shells as well as general three-dimensional elasticity problems. Numerical calculations also show that when extremely skewed and coarse meshes and nearly incompressible materials are used, the proposed mixed element can still possess excellent behaviour. The mixed formulation starts with introduction of a parallelepiped domain associated with the given general eight-node hexahedral element. Then, the assumed strain field at the nodal level is constructed via the Hu-Washizu variational principle for that associated parallelepiped domain. Finally, the assumed strain field at the nodal level of the given hexahedral element is established by using the field extrapolation technique, and then by using the trilinear shape functions the assumed strain field of the whole element domain is obtained. All matrices involved in establishing the element stiffness matrix can be evaluated analytically and expressed explicitly; however, a 24 by 24 matrix has to be inverted to construct the displacement extrapolation matrix. The proposed hexahedral element satisfies the patch test as long as the element with a shape of parallelepiped.

키워드

참고문헌

  1. Belytschko, T. and Bindeman, L.P. (1993), "Assumed strain stabilization of the eight node hexahedral element", Comp. Meth. Appl. Mech. Eng., 105, 225-260. https://doi.org/10.1016/0045-7825(93)90124-G
  2. Cao, Y.P., Hu, N., Lu, J., Fukunaga, H. and Yao, Z.H. (2002), "A 3D brick element based on Hu-Washizu variational principle for mesh distortion", Int. J. Num. Meth. Eng., 53, 2529-2548. https://doi.org/10.1002/nme.409
  3. Chandra, S. and Prathap, G. (1989), "A field-consistent formulation for the eight-noded solid finite element", Comp. Struct., 33, 345-355. https://doi.org/10.1016/0045-7949(89)90005-9
  4. Chen, W.-J. and Cheung, Y.K. (1992), "Three-dimensional 8-node and 20-node refined hybrid isoparametric elements", Int. J. Num. Meth. Eng., 35, 1871-1889. https://doi.org/10.1002/nme.1620350909
  5. Chen, Y.-I and Stolarski, H.K. (1998), "Extrapolated fields in the formulation of the assumed strain elements. Part 1: Three-dimensional problems", Comp. Meth. Appl. Mech. Eng., 154, 1-29. https://doi.org/10.1016/S0045-7825(97)00084-4
  6. Chen, Y.-I (2002), "Mixed formulation based on Hu-Washizu principle and concept of field extrapolation for the four-node quadrilateral element", Int. J. Num. Meth. Eng. (submitted).
  7. Cheung, Y.K. and Chen, W.-J. (1988), "Isoparametric hybrid hexahedral elements for three dimensional stress analysis", Int. J. Num. Meth. Eng., 26, 677-693. https://doi.org/10.1002/nme.1620260311
  8. Flanagan, D.P. and Belytschko, T. (1981), "A uniform strain hexahedron and quadrilateral with orthogonal hourglass control", Int. J. Num. Meth. Eng., 17, 679-706. https://doi.org/10.1002/nme.1620170504
  9. Ibrahimbegovic, A. and Wilson, E.L. (1991), "Thick shell and solid finite elements with independent rotation fields", Int. J. Num. Meth. Eng., 31, 1393-1414. https://doi.org/10.1002/nme.1620310711
  10. MacNeal, R.H. and Harder, R.L. (1985), "A proposed standard set of problems to test finite element accuracy", Finite Elements Anal. Des., 1, 3-20. https://doi.org/10.1016/0168-874X(85)90003-4
  11. MacNeal, R.H. (1987), "A theorem regarding the locking of tapered four-noded membrane elements", Int. J. Num. Meth. Eng., 24, 1793-1799. https://doi.org/10.1002/nme.1620240913
  12. Pian, T.H.H. (1964), "Derivation of element stiffness matrices by assumed stress distributions", AIAA J., 2, 1333-1336. https://doi.org/10.2514/3.2546
  13. Pian, T.H.H. and Chen, D.P. (1983), "On the suppression of zero energy deformation modes", Int. J. Num. Meth. Eng., 19, 1741-1752. https://doi.org/10.1002/nme.1620191202
  14. Pian, T.H.H. and Sumihara, K. (1984), "Rational approach for assumed stress finite elements", Int. J. Num. Meth. Eng., 20, 1685-1695. https://doi.org/10.1002/nme.1620200911
  15. Pian, T.H.H. and Tong, P. (1986), "Relations between incompatible displacement model and hybrid stress model", Int. J. Num. Meth. Eng., 22, 173-181. https://doi.org/10.1002/nme.1620220112
  16. Simo, J.C., Fox, D.D. and Rifai, M.S. (1989), "On a stress resultant geometrically exact shell model. Part II: The linear theory; computational aspects", Comp. Meth. Appl. Mech. Eng., 73, 53-92. https://doi.org/10.1016/0045-7825(89)90098-4
  17. Sze, K.Y. and Ghali, A. (1993), "Hybrid hexahedral element for solids, plates, shells and beams by selective scaling", Int. J. Num. Meth. Eng., 36, 1519-1540. https://doi.org/10.1002/nme.1620360907
  18. Sze, K.Y., Soh, A.K. and Sim, Y.S. (1996), "Solid elements with rotational DOFs by explicit hybrid stabilization", Int. J. Num. Meth. Eng., 39, 2987-3005. https://doi.org/10.1002/(SICI)1097-0207(19960915)39:17<2987::AID-NME986>3.0.CO;2-H
  19. Sze, K.Y. and Yao, L.Q. (2000), "A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part I-solid-shell element formulation", Int. J. Num. Meth. Eng., 48, 545-564. https://doi.org/10.1002/(SICI)1097-0207(20000610)48:4<545::AID-NME889>3.0.CO;2-6
  20. Taylor, R.L., Beresford, P.J. and Wilson, E.L. (1976), "A nonconforming element for stress analysis", Int. J. Num. Meth. Eng., 10, 1211-1219. https://doi.org/10.1002/nme.1620100602
  21. Wang, X.-J. and Belytschko, T. (1987), "An efficient flexurally superconvergent hexahedral element", Eng. Comp., 4, 281-288. https://doi.org/10.1108/eb023706
  22. Weissman, S.L. (1996), "High-accuracy low-order three-dimensional brick elements", Int. J. Num. Meth. Eng., 39, 2337-2361. https://doi.org/10.1002/(SICI)1097-0207(19960730)39:14<2337::AID-NME957>3.0.CO;2-7
  23. Wilson, E.L., Taylor, R.L., Doherty, W.P. and Ghaboussi, J. (1973), "Incompatible displacement models", in: S.J. Fenves et al., eds., Numerical and Computer Methods in Structural Mechanics, Academic Press, New York, pp.43-57.
  24. Yeo, S.T. and Lee, B.C. (1997), "New stress assumption for hybrid stress elements and refined four-node plane and eight node brick elements", Int. J. Num. Meth. Eng., 40, 2933-2952. https://doi.org/10.1002/(SICI)1097-0207(19970830)40:16<2933::AID-NME198>3.0.CO;2-3
  25. Yunus, S.M., Pawlak, T.P. and Cook, R.D. (1991), "Solid elements with rotational degrees of freedom: Part 1 - hexahedral elements", Int. J. Num. Meth. Eng., 31, 573-592. https://doi.org/10.1002/nme.1620310310

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