DOI QR코드

DOI QR Code

A hybrid 8-node hexahedral element for static and free vibration analysis

  • Darilmaz, Kutlu (Department of Civil Engineering, Istanbul Technical University)
  • Received : 2005.04.27
  • Accepted : 2005.09.05
  • Published : 2005.11.30

Abstract

An 8 node assumed stress hexahedral element with rotational degrees of freedom is proposed for static and free vibration analyses. The element formulation is based directly on an 8-node element. This direct formulation requires fewer computations than a similar element that is derived from an internal 20-node element in which the midside degrees of freedom are eliminated by expressing them in terms of displacements and rotations at corner nodes. The formulation is based on Hellinger-Reissner variational principle. Numerical examples are presented to show the validity and efficiency of the present element for static and free vibration analysis.

References

  1. ANSYS, Swanson Analysis Systems, Swanson J., ANSYS 5.4. USA
  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 8-noded solid finite element', Comp. Struct., 33, 345-355 https://doi.org/10.1016/0045-7949(89)90005-9
  4. Chen, Y.I. and Wu, GY. (2004), 'A mixed 8-node hexahedral element based on the Hu-Washizu principle and the field extrapolation technique', Struct. Eng. Mech., 17(1), 113-140 https://doi.org/10.12989/sem.2004.17.1.113
  5. 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
  6. Choi, C.K. and Chung, K.Y. (1996), 'Three dimensional non-conforming 8-node solid elements with rotational degrees of freedom', Struct. Eng. Meek, 4(5), 569-586 https://doi.org/10.12989/sem.1996.4.5.569
  7. Choi, C.K., Chung, K.Y. and Lee, E.J. (2001), 'Mixed formulated 13-node hexahedral elements with rotational degrees of freedom: MR-H13 elements', Struct. Eng. Mech., 11(1), 105-122 https://doi.org/10.12989/sem.2001.11.1.105
  8. Choi, C.K. and Lee, N.H. (1993), 'Three dimensional transition solid elements for adaptive mesh gradation', Struct. Eng. Mech., 1(1), 61-74 https://doi.org/10.12989/sem.1993.1.1.061
  9. Darilmaz, K. (2005), 'An assumed-stress finite element for static and free vibration analysis of Reissner-Mindlin plates', Struct. Eng. Meek, 19(2), 199-215
  10. Feng, W., Hoa, S.V. and Huang, Q. (1997), 'Classification of stress modes in assumed stress fields of hybrid finite elements', Int. J. Num. Meth. Eng., 40, 4313-4339 https://doi.org/10.1002/(SICI)1097-0207(19971215)40:23<4313::AID-NME259>3.0.CO;2-N
  11. 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
  12. MacNeal, R.H. and Harder, R.L. (1985), 'A proposed standard set of problems to test finite element accuracy', Finite Elem. Anal. Des., 1, 3-20 https://doi.org/10.1016/0168-874X(85)90003-4
  13. MacNeal, R.H. and Harder, R.L. (1988), 'A refined four-noded membrane element with rotational degrees of freedom', Comp. Struct., 28, 75-84 https://doi.org/10.1016/0045-7949(88)90094-6
  14. Leissa, A.W. (1969), Vibration of Plates, Scientific and Technical Information Division, NASA, Washington, DC
  15. Leissa, A.W. and Narita, Y (1980), 'Natural frequencies of simply supported circular plates', J. Sound Vib., 70(2), 221-229 https://doi.org/10.1016/0022-460X(80)90598-2
  16. Ooi, E.T., Rajendran, S. and Yeo, J.H. (2004), 'A 20-node hexahedron element with enhanced distortion tolerance', Int. J. Numer. Meth. Engng, 60(15), 2501-2530 https://doi.org/10.1002/nme.1056
  17. 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
  18. 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
  19. Pian, T.H.H. and Sumihara, K. (1984), 'Rational approach for assumed stress finite elements', Int. J. Numer. Meth. Engng., 20, 1685-1695 https://doi.org/10.1002/nme.1620200911
  20. Pian, T.H.H. and Tong, P. (1986), 'Relations between incompatible model and hybrid stress model', Int. J. Num. Meth. Eng., 22, 173-181 https://doi.org/10.1002/nme.1620220112
  21. Punch, E.F. and Atluri, S.N. (1984), 'Development and testing of stable, isoparametric curvilinear 2 and 3-D hybrid stress elements', Comput. Meth. Appl. Mech. Eng., 47, 331-356 https://doi.org/10.1016/0045-7825(84)90083-5
  22. Rajendran, S. and Prathap, G (1999), 'Eight-node field-consistent hexahedron element in dynamic problems', Struct. Eng. Meek, 8(1), 19-26 https://doi.org/10.12989/sem.1999.8.1.019
  23. 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
  24. Sze, K.Y. and Lo, S.H. (1999), 'A 12-node hybrid stress brick element for beam/column analysis', Eng. Comp., 16(6-7), 752-766 https://doi.org/10.1108/02644409910298101
  25. Sze, K.Y. and Pan, Y.S. (2000), 'Hybrid stress tetrahedral elements with Allman's rotational D.O.F.s', Int. J. Num. Meth. Eng, 48, 1055-1070 https://doi.org/10.1002/(SICI)1097-0207(20000710)48:7<1055::AID-NME916>3.0.CO;2-P
  26. Sze, K.Y, Soh, A.K. and Sim, YS. (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
  27. 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. Numer. Meth. Engng., 48, 545-564 https://doi.org/10.1002/(SICI)1097-0207(20000610)48:4<545::AID-NME889>3.0.CO;2-6
  28. Timoshenko, S. and Goodier, J.N. (1951), Theory of Elasticity, Mc-Graw Hill, New York
  29. Timoshenko, S., Young, D.H. and Weaver Jr. W (1974), Vibration Problems in Engineering, 4th. ed., John Wiley & Sons, New York
  30. 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
  31. Yunus, S.M., Saigal, S. and Cook, R.D. (1989), 'On improved hybrid finite elements with rotational degrees of freedom', Int. J. Num. Meth. Eng., 28, 785-800 https://doi.org/10.1002/nme.1620280405
  32. 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

Cited by

  1. Stiffened orthotropic corner supported hypar shells: Effect of stiffener location, rise/span ratio and fiber orientaton on vibration behavior vol.12, pp.4, 2012, https://doi.org/10.12989/scs.2012.12.4.275
  2. An assumed-stress hybrid element for static and free vibration analysis of folded plates vol.25, pp.4, 2007, https://doi.org/10.12989/sem.2007.25.4.405
  3. Analysis of sandwich plates: A three-dimensional assumed stress hybrid finite element vol.14, pp.4, 2012, https://doi.org/10.1177/1099636212443916