DOI QR코드

DOI QR Code

Influence of aspect ratio and fibre orientation on the stability of simply supported orthotropic skew plates

  • Kutlu, Darilmaz (Department of Civil Engineering, Istanbul Technical University)
  • Received : 2011.03.13
  • Accepted : 2011.06.10
  • Published : 2011.09.25

Abstract

In this paper, the influence of fibre orientation and aspect ratio on stability analysis of simply supported skew plates subjected to in plane loading is studied by using a four noded hybrid plate finite element. The formulation of the element is based on Hellinger-Reissner variational principle. The element is developed by combining a hybrid plane stress element and a hybrid plate element. Some numerical problems are solved and the effects of skew angle, aspect ratio, fibre orientation and loading type on the critical buckling loads are highlighted.

Keywords

stability;buckling;orthotropic plate;fibre orientation;boundary condition;hybrid finite element

References

  1. Allman, D. J., (1984), "A compatible triangular element including vertex rotations for plane elasticity problems", Comp. Struct., 19(1-2), 1-8. https://doi.org/10.1016/0045-7949(84)90197-4
  2. Bergan, P. G. And Felippa, C. A. (1985), "A triangular membrane element with rotational degrees of freedom", Comp. Methods Appl. Mech. Eng., 50(1), 25-69. https://doi.org/10.1016/0045-7825(85)90113-6
  3. Chelladurai T., Shastry B. P., Rao, G. V., (1984), "Effect of Fibre Orientation on the Stability of Orthotropic Rectangular Plates", Fibre Science and Technology, 20(2), 121-134. https://doi.org/10.1016/0015-0568(84)90004-6
  4. 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)
  5. Civalek O, Korkmaz A., Demir C., (2010), "Discrete singular convolution approach for buckling analysis of rectangularKirchhoff plates subjected to compressive loads on two-opposite edges", Adv. Eng. Softw., 41(4), 557-560. https://doi.org/10.1016/j.advengsoft.2009.11.002
  6. Civalek, O. (2004), "Application of Differential Quadrature (DQ) and Harmonic Differential Quadrature (HDQ) For Buckling Analysis of Thin Isotropic Plates and Elastic Columns", Eng. Struct., 26(2), 171-186. https://doi.org/10.1016/j.engstruct.2003.09.005
  7. Gurses, M., Civalek, O., Korkmaz, A. and Ersoy, H. (2009), "Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first-order shear deformation theory", Int. J. Numer. Meth. Eng., 79(3), 290-313. https://doi.org/10.1002/nme.2553
  8. Cook, R. D., (1986), "On the Allman triangle and a related quadrilateral element", Comp. Struct., 22(6), 1065-1067. https://doi.org/10.1016/0045-7949(86)90167-7
  9. Darilmaz, 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
  10. Darilmaz, K. (2007), "An assumed-stress hybrid element for static and free vibration analysis of folded plates", Struct. Eng. Mech., 25(4), 405-421. https://doi.org/10.12989/sem.2007.25.4.405
  11. Darilmaz, K. (2009), "An assumed-stress hybrid element for modeling of plates with shear deformations on elastic foundation", Struct. Eng. Mech., 33(5), 573-588. https://doi.org/10.12989/sem.2009.33.5.573
  12. Dhananjaya, H.R., Pandey, P.C. and Nagabhushanam, J. (2009), "New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method". Struct. Eng. Mech.33(4)485-502. https://doi.org/10.12989/sem.2009.33.4.485
  13. Durvasula, S. (1971) "Buckling of simply supported skew plates" J. Engrg. Mech. Div., ASCE, 97(3), 967-979.
  14. Edwardes, R. J., and Kabaila, A. P, (1978) "Buckling of simply supported skew plates", Int. J. Numer. Methods Engrg., 12(5), 779-785. https://doi.org/10.1002/nme.1620120504
  15. Ibrahimbegovic, A., Taylor, R. L. and Wison, E. L., (1990), "A robust quadrilateral membrane finite element with drilling degrees of freedom", Int. J. Numer. Methods Eng., 30(3), 445-457. https://doi.org/10.1002/nme.1620300305
  16. Lee, S.Y. and Park, T. (2009), "Free vibration of laminated composite skew plates with central cutouts". Struct. Eng. Mech. 31(5)587-603. https://doi.org/10.12989/sem.2009.31.5.587
  17. MacNeal, R. H. And Harder, R. L., (1988), "A refined four-noded membrane element with rotational degrees of freedom", Comp. Struct., 28(1), 75-84. https://doi.org/10.1016/0045-7949(88)90094-6
  18. Pian T. H. H., (1964), "Derivation of element stiffness matrices by assumed stress distributions", AIAA J., 12, 1333-1336.
  19. Shi G., (1990),"Flexural Vibration and buckling analysis of orthotropic plates by the boundary element method", Int. J. Solids Structures, 26(12), 1351-1370. https://doi.org/10.1016/0020-7683(90)90083-8
  20. Thangam Babu P.V., Reddy D. V., (1978) "Stability analysis of skew orthotropic plates by the finite strip method", Computers & Structures, 8(5), 599-607. https://doi.org/10.1016/0045-7949(78)90097-4
  21. Wang, C. M. ; Liew, K.M.; Alwis, W.A.M. (1992), "Buckling of skew plates and corner condition for simply supported edges", Journal Of Engineering Mechanics-ASCE, 118(4), 651-662. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:4(651)
  22. Wang, X., Gan, L., Zhang, Y.(2008), "Differential quadrature analysis of the buckling of thin rectangular plates with cosine-distributed compressive loads on two opposite sides", Adv. Eng. Softw., 39(6), 497-504. https://doi.org/10.1016/j.advengsoft.2007.03.011
  23. Wang, X.W., Wang, X.F. and Shi, X.D., (2007), "Accurate buckling loads of thin rectangular plates under parabolic edge compressions by the differential quadrature method", Int. J. Mech. Sci. 49(4), 447-453 https://doi.org/10.1016/j.ijmecsci.2006.09.004
  24. Yunus S. M., Saigal S., Cook R. D., (1989), "On improved hybrid finite elements with rotational degrees of freedom", Int. J. Numer. Meth. Eng., 28(4), 785-800. https://doi.org/10.1002/nme.1620280405
  25. Zhong H., Gu, C., (2006), "Buckling of Simply Supported Rectangular Reissner-Mindlin Plates Subjected to Linearly Varying In-Plane Loading", J. Engrg. Mech., 132(5), 578-581. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:5(578)

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