Structural Engineering and Mechanics

  • 제26권1호
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  • Pages.69-86
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  • 2007
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Alternative plate finite elements for the analysis of thick plates on elastic foundations

  • Ozgan, K. (Yuksel Proje Uluslararasi) ;
  • Daloglu, Ayse T. (Dept. of Civil Engineering, Karadeniz Technical University)
  • 투고 : 2006.04.25
  • 심사 : 2006.10.31
  • 발행 : 2007.05.10
⟨ 이전 논문 다음 논문 ⟩

초록

A four-noded plate bending quadrilateral (PBQ4) and an eight-noded plate bending quadrilateral (PBQ8) element based on Mindlin plate theory have been adopted for modeling the thick plates on elastic foundations using Winkler model. Transverse shear deformations have been included, and the stiffness matrices of the plate elements and the Winkler foundation stiffness matrices are developed using Finite Element Method based on thick plate theory. A computer program is coded for this purpose. Various loading and boundary conditions are considered, and examples from the literature are solved for comparison. Shear locking problem in the PBQ4 element is observed for small value of subgrade reaction and plate thickness. It is noted that prevention of shear locking problem in the analysis of the thin plate is generally possible by using element PBQ8. It can be concluded that, the element PBQ8 is more effective and reliable than element PBQ4 for solving problems of thin and thick plates on elastic foundations.

키워드

참고문헌

  1. AbdaIla, J.A. and Ibrahim, A.M. (2006), 'Development of a discrete reissner-mindlin element on winkler foundation', Finite Elem. Anal. Des., 42, 740-748 https://doi.org/10.1016/j.finel.2005.11.004
  2. AI-Khaiat, H. and West, H.H. (1990), 'Analysis of plates on an elastic foundation by the initial value method', Mech. Struct. Mach., 18(1), 1-15 https://doi.org/10.1080/08905459008915656
  3. Bathe, K.J. (1996), Finite Element Procedures, Upper Saddle River, NJ: Prentice-HaIl
  4. Buczkowski, R. and Torbacki, W. (2001), 'Finite element modeling of thick plates on two-parameter elastic foundation', Int. J Numer. Anal. Met. Geom., 25, 1409-1427 https://doi.org/10.1002/nag.187
  5. Chucheepsakul, S. and Chinnaboon, B. (2002), 'An alternative domain/boundary element technique for analyzing plates on two-parameter elastic foundations', Eng. Anal. Bound. Elem., 26, 547-555 https://doi.org/10.1016/S0955-7997(02)00007-3
  6. Daloglu, A.T. and VaIlabhan, C.V.G. (2000), 'Values of $\kappa$ for slab on winkler foundation', J. Geotech. Geoenviron., 126(5), 463-471 https://doi.org/10.1061/(ASCE)1090-0241(2000)126:5(463)
  7. Eratli, N. and Akoz, A.Y. (1997), 'The mixed finite element formulation for the thick plates on elastic foundations', Compul. Struct., 65(4), 515-529 https://doi.org/10.1016/S0045-7949(96)00403-8
  8. Hetenyi, M. (1950), 'A general solution for the bending of beams on an elastic foundation of arbitrary continuity', J. Appl. Phys., 21, 55-58 https://doi.org/10.1063/1.1699420
  9. Liu, F.-L. (2000), 'Rectangular thick plates on winkler foundation: Differential quadrature element solution', Int. J. Solids Struct., 37, 1743-1763 https://doi.org/10.1016/S0020-7683(98)00306-0
  10. Mishra, R.C. and Chakrabarti, S.K. (1997), 'Shear and attachment effects on the behaviour of rectangular plates resting on tensionless elastic foundation', Eng. Struct., 19(7), 551-567 https://doi.org/10.1016/S0141-0296(97)00122-3
  11. Rashed, Y.F., Aliabadi, M.H. and Brebbia, C.A.(1998), 'The boundary element method for thick plates on a winkler foundation', Int. J. Numer. Meth. Eng., 41, 1435-1462 https://doi.org/10.1002/(SICI)1097-0207(19980430)41:8<1435::AID-NME345>3.0.CO;2-O
  12. Sadecka, L. (2000), 'A finite/infinite element analysis of thick plate on a layered foundation', Comput. Struct., 76, 603-610 https://doi.org/10.1016/S0045-7949(99)00180-7
  13. Selvaduari, A.P.S. (1979), Elastic Analysis of Soil-Foundation Interaction, Elsevier Scientific Publishing Company, Amsterdam
  14. Teo, T.M. and Liew, K.M. (2002), 'Differential cubature method for analysis of shear deformable rectangular plates on pasternak foundations', Int. J. Mech. Sci., 44, 1179-1194 https://doi.org/10.1016/S0020-7403(02)00034-6
  15. Timoshenko, S.P. and Krieger, W. (1970), Theory ofPlates and Shells, McGraw-Hill
  16. Turhan, A. (1992), A Consistent Vlasov Model for Analysis of Plates on Elastic Foundations Using the Finite Element Method, Ph. D. Thesis, The Graduate School of Texas Tech. University. Lubbock, Texas
  17. Voyiadjis, G.Z. and Kattan, P.I. (1986), 'Thick rectangular plates on an elastic foundation', J. Eng. Mech., 112(11), 1218-1240 https://doi.org/10.1061/(ASCE)0733-9399(1986)112:11(1218)
  18. Wang, Y.H., Tham, L.G., Tsui, Y. and Yue, Z.Q. (2003), 'Plate on layered foundation analyzed by a semianalytical and semi-numerical method', Comput. Struct., 30, 409-418
  19. Weaver, W. and Johnston, P.R. (1984), Finite Elements for Structural Analysis, Englewood Cliffs, NJ: PrenticeHall, Inc
  20. Yettram, A.L. and Whiteman, J.R. (1984), 'Effect of Thickness on The Behaviour of Plates on Foundation', Comput. Struct., 19(4), 501-509 https://doi.org/10.1016/0045-7949(84)90096-8
  21. Celik, M. and Omurtag, M.H. (2005), 'Determination of the vlasov foundation parameters-quadratic variation of elasticity modulus-using FE analysis', Struct. Eng. Mech., 19(6), 619-637 https://doi.org/10.12989/sem.2005.19.6.619
  22. Celik, M. and Saygun, A. (1999), 'A method for the analysis of plates on a two-parameter foundation', Int. J. Solids Struct., 36, 2891-2915 https://doi.org/10.1016/S0020-7683(98)00135-8

피인용 문헌

  1. Finite Element Analysis of Plate on Layered Tensionless Foundation vol.56, pp.3, 2010, https://doi.org/10.2478/v.10169-010-0014-9
  2. Development of a higher order finite element on a Winkler foundation vol.48, pp.1, 2012, https://doi.org/10.1016/j.finel.2011.08.010
  3. A refined four-unknown plate theory for advanced plates resting on elastic foundations in hygrothermal environment vol.111, 2014, https://doi.org/10.1016/j.compstruct.2013.12.033
  4. A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation vol.73, 2013, https://doi.org/10.1016/j.ijmecsci.2013.03.017
  5. An Integrated Kirchhoff Element by Galerkin Method for Free Vibration Analysis of Plates on Elastic Foundation vol.24, 2016, https://doi.org/10.1016/j.protcy.2016.05.021
  6. Analysis of flexible raft resting on soft soil improved by granular piles considering soil shear interaction vol.94, 2018, https://doi.org/10.1016/j.compgeo.2017.09.007
  7. A simplified first-order shear deformation theory for bending, buckling and free vibration analyses of isotropic plates on elastic foundations 2017, https://doi.org/10.1007/s12205-017-1517-6
  8. Problems with a popular thick plate element and the development of an improved thick plate element vol.29, pp.3, 2007, https://doi.org/10.12989/sem.2008.29.3.327
  9. New eight node serendipity quadrilateral plate bending element for thin and moderately thick plates using Integrated Force Method vol.33, pp.4, 2007, https://doi.org/10.12989/sem.2009.33.4.485
  10. New twelve node serendipity quadrilateral plate bending element based on Mindlin-Reissner theory using Integrated Force Method vol.36, pp.5, 2007, https://doi.org/10.12989/sem.2010.36.5.625
  11. New nine-node Lagrangian quadrilateral plate element based on Mindlin-Reissner theory using IFM vol.41, pp.2, 2007, https://doi.org/10.12989/sem.2012.41.2.205
  12. Bending response of FG plates resting on elastic foundations in hygrothermal environment with porosities vol.213, pp.None, 2007, https://doi.org/10.1016/j.compstruct.2019.01.065
  13. Free Vibration and Static Bending Analysis of Piezoelectric Functionally Graded Material Plates Resting on One Area of Two-Parameter Elastic Foundation vol.2020, pp.None, 2007, https://doi.org/10.1155/2020/9236538