DOI QR코드

DOI QR Code

A sectorial element based on Reissner plate theory

  • Akoz, A. Yalcin (Department of Civil Engineering, Istanbul Technical University) ;
  • Eratli, Nihal (Department of Civil Engineering, Istanbul Technical University)
  • 발행 : 2000.06.25

초록

In this study, a new functional based on the Reissner theory, for thick plates on a Winkler foundation is obtained. This functional has geometric and dynamic boundary conditions. In deriving the new functional, the $G{\hat{a}}teaux$ differential is used. This functional which is in polar coordinates is also transformable into the classical potential energy equation. Bending and torsional moments, transverse shear forces, rotations and displacements are the basic unknowns of the functional. Two different sectorial elements are developed with $3{\times}8$ degrees of freedom (SEC24) and $4{\times}8$ degrees of freedom (SEC32). The accuracy of the SEC24 and SEC32 elements together are verified by applying the method to some problems taken from literature.

키워드

참고문헌

  1. Akoz, A.Y. (1985), "A new functional for bars and its applications", IV National Applied Mechanics Meeting (in Turkish).
  2. Akoz, A.Y., Omurtag, M.H. and Dogruoglu, A.N. (1991), "The mixed finite element formulation for three dimensional bars", Int. J. Solids Structures, 28, 225-234. https://doi.org/10.1016/0020-7683(91)90207-V
  3. Akoz, A.Y. and Uzcan (Eratli), N. (1992), "The new functional for Reissner plates and its application", Computers & Structures, 44,1139-1144. https://doi.org/10.1016/0045-7949(92)90334-V
  4. Akoz, A.Y. and Kadioglu, F. (1996), "The mixed finite element solution of circular beam on elastic foundation", Computers & Structures, 60, 643-651. https://doi.org/10.1016/0045-7949(95)00418-1
  5. Akoz, A.Y. and Ozutok, A. (2000), "A functional for shells of arbitrary geometry and a mixed finite element method for parabolic and circular cylindrical shells" (Accepted for publication in Int. J. Numer. Methods Eng.).
  6. Al-Hosani, K., Fadhil, S. and El-Zafrany, A. (1999), "Fundamental solution and boundary element analysis of thick plates on Winkler foundation", Computers & Structures, 70, 325-336. https://doi.org/10.1016/S0045-7949(98)00171-0
  7. Bathe, K.J. (1982), Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, NJ.
  8. Batoz, J.L and Lardeur, A (1989), "Discrete shear triangular nine d.o.f. element for the analysis of thick to very thin plates", Int. J. Numer. Methods Eng., 28, 533-560. https://doi.org/10.1002/nme.1620280305
  9. Batoz, J.L and Katili, I. (1992), "On a simple triangular Reissner-Mindlin plate element based on incompatible modes and discrete constraints", Int. J. Numer. Methods Eng., 35,1603-1632. https://doi.org/10.1002/nme.1620350805
  10. Belytschko, T., Tsay, C.S. and Liu, W.K. (1981), "A Stabilization matrix for the bilinear Mindlin plate element", Computer Methods in Applied Mechanics and Engineering, 29, 313-327. https://doi.org/10.1016/0045-7825(81)90048-7
  11. Cheung, M.S. and Chan, M.Y.T. (1981), "Static and dynamic analysis of thin and thick sectorial plates by the finite strip method", Computers & Structures, 14, 79-88. https://doi.org/10.1016/0045-7949(81)90086-9
  12. Dym, C.L and Shames, I.H. (1973), Solid Mechanics A Variational Approach, McGraw-Hill
  13. EI-Zafrany, A., Fadhil, S. and AI-Hosani, K. (1995), "A new fundamental solution for boundary element analysis of thin plates on Winkler foundation", Int. J. Numer. Methods Eng., 38, 887-903. https://doi.org/10.1002/nme.1620380602
  14. Eratli, N. and Akoz, A.Y. (1997), "The mixed finite element formulation for the thick plates on elastic foundations", Computers & Structures, 65, 515-529. https://doi.org/10.1016/S0045-7949(96)00403-8
  15. Eratli, N. and Akoz, A.Y., "Mixed finite element formulation for folded plates" (Submitted for publication in Computers & Structures),
  16. Gallagher, R.H. (1975), Finite Element Analysis: Fundamentals, Prentice-Hall.
  17. Goldenveizer, A.L. (1961), Theory of Elastic Thin Shells, Pergomon Press, New York.
  18. Huebner, K.H. (1975), The Finite Element Method for Engineers, John Wiley & Sons.
  19. Hughes, T.J.R, Taylor, R.L. and Kanok-Nukulchai, W. (1977), "A simple and efficient finite element for plate bending", Int. J. Numer. Methods Eng., 11, 1529-1543. https://doi.org/10.1002/nme.1620111005
  20. Katili, I. (1993a), "A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields-Part I: An extended DKT element for thick-plate bending analysis", Int. J. Numer. Methods Eng., 36,1859-1883. https://doi.org/10.1002/nme.1620361106
  21. Katili, I. (1993b), "A new discrete Kirchhoff-Mindlin element based on Mindlin-Reissner plate theory and assumed shear strain fields-Part II: An extended DKQ element for thick-plate bending analysis", Int. J. Numer. Methods Eng., 36, 1885-1908. https://doi.org/10.1002/nme.1620361107
  22. Kavanagh, K.T. and Kay, S.W. (1972), "A note on selective and reduced integration techniques in the finite element method", Int. J. Numer. Methods Eng., 4, 148-150. https://doi.org/10.1002/nme.1620040118
  23. Mindlin, R.D. (1951), "The Influence of rotatory inertia and shear on the flexural motions of elastic plates", J. Appl. Mech., ASME, 18,31-38.
  24. Morris, A.J. (1973), "Deficiency in current finite elements for thin shell applications", Int. J. Solids Structures, 9, 331-346. https://doi.org/10.1016/0020-7683(73)90084-X
  25. Oden, J.D. and Reddy, J.N. (1976), Variational Method in Theoretical Mechanics, Springer.
  26. Omurtag, M.H. and Akoz, A.Y. (1994), "Hyperbolic paraboloid shell analysis via mixed finite element formulation", Int. J. Numer. Methods. Eng., 37, 3037-3056. https://doi.org/10.1002/nme.1620371803
  27. Pane, V. (1975), Theories of Elastic Plates, Noordhoff International Publishing.
  28. Papadopoulos, P. and Taylor, R.L. (1990), "A triangular element based on Reissner-Mindlin Plate theory", Int. J. Numer. Methods Eng., 30, 1029-1049. https://doi.org/10.1002/nme.1620300506
  29. Pugh, E.D.L., Hinton, E. and Zienkiewicz, A (1978), "Study of quadrilateral plate bending elements with reduced integration", Int. J. Numer. Methods Eng., 12, 1059-1079. https://doi.org/10.1002/nme.1620120702
  30. 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. Methods Eng., 41, 1435-1462. https://doi.org/10.1002/(SICI)1097-0207(19980430)41:8<1435::AID-NME345>3.0.CO;2-O
  31. Reissner, E. (1946), "The effects of transverse shear deformation bending of elastic plates", J. Appl. Mech., ASME, 12, 69-77.
  32. Reissner, E. (1975), "On thansverse bending of plates, including the effect of transverse shear deformation", Int. J. Solids Structures, 11, 569-573. https://doi.org/10.1016/0020-7683(75)90030-X
  33. Reddy, J.N. (1984), Energy and Variational Methods in Applied Mechanics, John Wiley & Sons.
  34. Reddy, J.N. (1993), Finite Element Method, McGraw-Hill
  35. Reddy, J.N. and Wang, C.M. (1997), "Relationnships between classical and shear deformation theoris of axisymmentric circular plates", AIAA Journal, 35(12), 1862-1868. https://doi.org/10.2514/2.62
  36. Timoshenko, S. and Woinowisky-Krieger, S. (1959), Theory of Plates and Shells, McGraw-Hill.
  37. Wang, C.M. and Lee, K.H. (1996), "Deflection and stree-resultants of axisymmetric Mindlim plates in terms of corresponding Kirchhoff soultion", Int. J. Mech. Sci., 38(11),1179-1185. https://doi.org/10.1016/0020-7403(96)00019-7
  38. Washizu, K. (1975), Variational Methods in Elasticity and Plasticity, Pergamon Press.
  39. Zienkiewicz, O.C., Taylor, R.L. and Too, J. (1971), "Reduced integration technique in general analysis of plates and shells", Int. J. Numer. Methods Eng., 3, 275-290. https://doi.org/10.1002/nme.1620030211
  40. Zienkiewicz, O.C. (1977), The Finite Element Method, McGraw-Hill, London.
  41. Zienkiewicz, O.C., Bauer, J., Morgan, K. and Onate, E. (1977), "A simple and efficient element for axisymmetric shells", Int. J. Numer. Methods Eng. 11, 1545-1558. https://doi.org/10.1002/nme.1620111006

피인용 문헌

  1. Mixed finite element formulation for folded plates vol.13, pp.2, 2002, https://doi.org/10.12989/sem.2002.13.2.155
  2. Exact Bending Solutions of Axisymmetric Reissner Plates in Terms of Classical Thin Plate Solutions vol.7, pp.2, 2004, https://doi.org/10.1260/1369433041211075
  3. Finite element linear and nonlinear, static and dynamic analysis of structural elements, an addendum vol.19, pp.5, 2002, https://doi.org/10.1108/02644400210435843
  4. Free vibration analysis of Reissner plates by mixed finite element vol.13, pp.3, 2002, https://doi.org/10.12989/sem.2002.13.3.277
  5. Static analysis of laminated composite beams based on higher-order shear deformation theory by using mixed-type finite element method vol.130, 2017, https://doi.org/10.1016/j.ijmecsci.2017.06.013
  6. A BEM formulation based on Reissner’s theory to perform simple bending analysis of plates reinforced by rectangular beams vol.42, pp.5, 2008, https://doi.org/10.1007/s00466-008-0266-2
  7. Variational approximate for high order bending analysis of laminated composite plates vol.73, pp.1, 2000, https://doi.org/10.12989/sem.2020.73.1.097