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An assumed-stress hybrid element for static and free vibration analysis of folded plates

  • Darilmaz, Kutlu (Department of Civil Engineering, Istanbul Technical University)
  • Received : 2004.12.30
  • Accepted : 2006.09.05
  • Published : 2007.03.10

Abstract

A four-node hybrid stress element for analysing orthotropic folded plate structures is presented. The formulation is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. The proposed element has six degree of freedom per node and permits an easy connection to other type of elements. An equilibrated stress field in each element and inter element compatible boundary displacement field are assumed independently. Static and free vibration analyses of folded plates are carried out on numerical examples to show that the validity and efficiency of the present element.

References

  1. Allman, D.J. (1984), 'A compatible triangular element including vertex rotations for plane elasticity problems', Comput. Struct., 19, 1-8 https://doi.org/10.1016/0045-7949(84)90197-4
  2. ANSYS. (1997), Swanson Analysis Systems, Swanson J. ANSYS 5.4. USA
  3. Ayad, R., and Rigolot, A. (2002), 'An improved four-node hybrid-mixed element based upon Mindlin's plate theory', Int. J. Numer. Meth. Eng, 55(6), 705-731 https://doi.org/10.1002/nme.528
  4. Bergan, P.G and Felippa, C.A. (1985), 'A triangular membrane element with rotational degrees of freedom', Comput. Meth. Appl. Mech. Eng, 50, 25-69 https://doi.org/10.1016/0045-7825(85)90113-6
  5. Choi, C.K. and Lee, W.H. (1996), 'Versatile variable-node flat-shell element', J. Eng Mech., 122(5), 432-441 https://doi.org/10.1061/(ASCE)0733-9399(1996)122:5(432)
  6. Cook, R.D. (1986), 'On the Allman triangle and a related quadrilateral element', Comput. Struct., 22, 1065-1067 https://doi.org/10.1016/0045-7949(86)90167-7
  7. Ibrahimbegovic, A., Taylor, R.L. and Wison, E.L. (1990), 'A robust quadrilateral membrane finite element with drilling degrees of freedom', Int. J. Numer. Meth. Eng, 30, 445-457 https://doi.org/10.1002/nme.1620300305
  8. Danlmaz, K. (2005), 'An assumed-stress finite element for static and free vibration analysis of Reissner-Mindlin plates', Struct. Eng Mech., 19(2), 199-215 https://doi.org/10.12989/sem.2005.19.2.199
  9. Danlmaz, K. (2005), 'A hybrid 8-node hexahedral element for static and free vibration analysis', Struct. Eng Mech., 21(5), 571-590 https://doi.org/10.12989/sem.2005.21.5.571
  10. Duan, M. and Miyamoto, Y. (2002), 'Effective hybrid/mixed finite elements for folded-plate structures', J. Eng Mech., ASCE, 128(2), 202-208 https://doi.org/10.1061/(ASCE)0733-9399(2002)128:2(202)
  11. Eratli, N. and Akoz, A.Y. (2002), 'Mixed finite element formulation for folded plates', Struct. Eng Mech., 13(2), 155-170 https://doi.org/10.12989/sem.2002.13.2.155
  12. Feng, W, Hoa, S.V. and Huang, Q. (1997), 'Classification of stress modes in assumed stress fields of hybrid finite elements', Int. J. Numer. Meth. Eng., 40, 4313-4339 https://doi.org/10.1002/(SICI)1097-0207(19971215)40:23<4313::AID-NME259>3.0.CO;2-N
  13. Lee, S.Y. and Wooh, S.C. (2004) 'Finite element vibration analysis of composite box structures using the high order plate theory', J. Sound Vib .. 277(4-5), 801-814 https://doi.org/10.1016/j.jsv.2003.09.024
  14. Liu, W.H. and Huang, C.C. (1992), 'Vibration Analysis of folded plates', J. Sound Vib., 157, 123-137 https://doi.org/10.1016/0022-460X(92)90570-N
  15. MacNeal, R.H. and Harder, R.L. (1988), 'A refined four-noded membrane element with rotational degrees of freedom', Comput. Struct., 28, 75-84 https://doi.org/10.1016/0045-7949(88)90094-6
  16. Niyogi, A.G, Laha, M.K. and Sinha, P.K. (1999), 'Finite element vibration analysis of laminated composite folded plate structures', Shock and Vibration, 6, 273-283 https://doi.org/10.1155/1999/354234
  17. Perry, B., Bar- Yoseph, P. and Rosenhouse, G. (1992), 'Rectangular hybrid shell element for analysing folded plate structures', Comput. Struct., 44, 177-183 https://doi.org/10.1016/0045-7949(92)90236-S
  18. Pian, T.H.H. (1964), 'Derivation of element stiffness matrices by assumed stress distributions', AIAA J., 12, 1333-1336
  19. Pian, T.H.H. and Chen, D.P. (1983), 'On the suppression of zero energy deformation modes', Int. .J Numer. Meth. Eng., 19, 1741-1752 https://doi.org/10.1002/nme.1620191202
  20. 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
  21. Yunus, S.M., Saigal, S. and Cook, R.D. (1989), 'On improved hybrid finite elements with rotational degrees of freedom', Int. J. Numer. Meth. Eng, 28, 785-800 https://doi.org/10.1002/nme.1620280405