Structural Engineering and Mechanics

  • 제65권3호
  • /
  • Pages.213-222
  • /
  • 2018
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Using fourth order element for free vibration parametric analysis of thick plates resting on elastic foundation

  • Ozdemir, Y.I. (Department of Civil Engineering, Karadeniz Technical University)
  • 투고 : 2017.05.08
  • 심사 : 2017.11.13
  • 발행 : 2018.02.10
⟨ 이전 논문 다음 논문 ⟩

초록

The purpose of this paper is to study free vibration analysis of thick plates resting on Winkler foundation using Mindlin's theory with shear locking free fourth order finite element, to determine the effects of the thickness/span ratio, the aspect ratio, subgrade reaction modulus and the boundary conditions on the frequency paramerets of thick plates subjected to free vibration. In the analysis, finite element method is used for spatial integration. Finite element formulation of the equations of the thick plate theory is derived by using higher order displacement shape functions. A computer program using finite element method is coded in C++ to analyze the plates free, clamped or simply supported along all four edges. In the analysis, 17-noded finite element is used. Graphs are presented that should help engineers in the design of thick plates subjected to earthquake excitations. It is concluded that 17-noded finite element can be effectively used in the free vibration analysis of thick plates. It is also concluded that, in general, the changes in the thickness/span ratio are more effective on the maximum responses considered in this study than the changes in the aspect ratio.

키워드

참고문헌

  1. Ayvaz, Y. and Durmus, A. (1995), "Earhquake analysis of simply supported reinforced concrete slabs", J. Sound Vibr., 187(3), 531-539. https://doi.org/10.1006/jsvi.1995.0539
  2. Bathe, K.J. (1996), Finite Element Procedures, Prentice Hall, Upper Saddle River, New Jersey, U.S.A.
  3. Belounar, L. and Guenfound, M. (2005), "A new rectangular finite element based on the strain approach for plate bending", Thin-Wall. Struct., 43, 47-63. https://doi.org/10.1016/j.tws.2004.08.003
  4. Bergan, P.G. and Wang, X. (1984), "Quadrilateral plate bending elements with shear deformations", Comput. Struct., 19(1-2) 25-34. https://doi.org/10.1016/0045-7949(84)90199-8
  5. Brezzi, F. and Marini, L.D. (2003), "A nonconforming element for the Reissner-Mindlin plate", Comput. Struct., 81, 515-522. https://doi.org/10.1016/S0045-7949(02)00418-2
  6. Caldersmith, G.W. (1984), "Vibrations of orthotropic rectangular plates", ACUSTICA, 56, 144-152.
  7. Cen, S., Long, Y.Q., Yao, Z.H. and Chiew, S.P. (2006), "Application of the quadrilateral area co-ordinate method: Anew element for Mindlin-Reissner plate", J. Numer. Meth. Eng., 66, 1-45. https://doi.org/10.1002/nme.1533
  8. Cook, R.D., Malkus, D.S. and Michael, E.P. (1989), Concepts and Applications of Finite Element Analysis, John Wiley & Sons, Inc., Canada.
  9. Fallah, A., Aghdam, M.M. and Kargarnovin, M.H. (2013), "Free vibration analysis of moderately thick functionally graded plates on elastic foundation using the extended Kantorovich method", Arch. Appl. Mech., 83(2), 177-191. https://doi.org/10.1007/s00419-012-0645-1
  10. Grice, R.M. and Pinnington, R.J. (2002), "Analysis of the flexural vibration of a thin-plate box using a combination of finite element analysis and analytical impedances", J. Sound Vibr., 249(3), 499-527. https://doi.org/10.1006/jsvi.2001.3847
  11. Gunagpeng, Z., Tianxia, Z. and Yaohui, S. (2012), "Free vibration analysis of plates on Winkler elastic foundation by boundary element method", Opt. Electr. Mater. Appl. II, 529, 246-251.
  12. Hinton, E. and Huang, H.C. (1986), "A family of quadrilateral Mindlin plate element with substitute shear strain fields", Comput. Struct., 23(3), 409-431. https://doi.org/10.1016/0045-7949(86)90232-4
  13. Hughes, T.J.R., Taylor, R.L. and Kalcjai, W. (1977), "Simple and efficient element for plate bending", J. Numer. Meth. Eng., 11, 1529-1543. https://doi.org/10.1002/nme.1620111005
  14. Jahromim, H.N., Aghdam, M.M. and Fallah, A. (2013), "Free vibration analysis of Mindlin plates partially resting on Pasternak foundation", J. Mech. Sci., 75, 1-7. https://doi.org/10.1016/j.ijmecsci.2013.06.001
  15. Leissa, A.W. (1973), "The free vibration of rectangular plates", J. Sound Vibr., 31(3), 257-294. https://doi.org/10.1016/S0022-460X(73)80371-2
  16. Leissa, A.W. (1981), "Plate vibration research, 1976-1980: complicating effects", Shock Vibr. Dig., 13(10) 19-36.
  17. Leissa, A.W (1987), "Plate vibration research, 1981-1985-part II: Complicating effects", Shock Vibr. Dig., 19(3), 10-24. https://doi.org/10.1177/058310248701900304
  18. Leissa, A.W. (1977), "Recent research in plate vibrations, 1973-1976: Complicating effects", Shock Vibr. Dig., 9(11), 21-35. https://doi.org/10.1177/058310247700901106
  19. Leissa, A.W. (1977), "Recent research in plate vibrations", 1973-1976: classical theory, Shock Vibr. Dig., 9(10), 13-24. https://doi.org/10.1177/058310247700901005
  20. Leissa, A.W. (1981), "Plate vibration research, 1976-1980: Classical theory", Shock Vibr. Dig., 13(9), 11-22. https://doi.org/10.1177/058310248101300905
  21. Leissa, A.W. (1987), "Plate vibration research, 1981-1985-part I: Classical theory", Shock Vibr. Dig., 19(2), 11-18. https://doi.org/10.1177/058310248701900204
  22. Lok, T.S. and Cheng, Q.H. (2001), "Free and forced vibration of simply supported, orthotropic sandwich panel", Comput. Struct., 79(3), 301-312. https://doi.org/10.1016/S0045-7949(00)00136-X
  23. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18(1), 31-38.
  24. Ozdemir, Y.I. (2012), "Development of a higher order finite element on a Winkler foundation", Fin. Elem. Anal. Des., 48, 1400-1408. https://doi.org/10.1016/j.finel.2011.08.010
  25. Ozdemir, Y.I. and Ayvaz, Y. (2009), "Shear locking-free earthquake analysis of thick and thin plates using Mindlin's theory", Struct. Eng. Mech., 33(3), 373-385. https://doi.org/10.12989/sem.2009.33.3.373
  26. Ozdemir, Y.I., Bekiroglu, S. and Ayvaz, Y. (2007), "Shear locking-free analysis of thick plates using Mindlin's theory", Struct. Eng. Mech., 27(3), 311-331. https://doi.org/10.12989/sem.2007.27.3.311
  27. Ozgan, K. and Daloglu, A.T. (2012), "Free vibration analysis of thick plates on elastic foundations using modified Vlasov model with higher order finite elements", J. Eng. Mater. Sci., 19, 279-291.
  28. Ozgan, K. and Daloglu, A.T. (2015), "Free vibration analysis of thick plates resting on Winkler elastic foundation", Chall. J. Struct. Mech., 1(2), 78-83.
  29. Ozkul, T.A. and Ture, U. (2004), "The transition from thin plates to moderately thick plates by using finite element analysis and the shear locking problem", Thin-Wall. Struct., 42, 1405-1430. https://doi.org/10.1016/j.tws.2004.05.003
  30. Providakis, C.P. and Beskos, D.E. (1989), "Free and forced vibrations of plates by boundary and interior elements", J. Numer. Meth. Eng., 28, 1977-1994. https://doi.org/10.1002/nme.1620280902
  31. Providakis, C.P. and Beskos, D.E. (1989), "Free and forced vibrations of plates by boundary elements", Comput. Meth. Appl. Mech. Eng., 74, 231-250. https://doi.org/10.1016/0045-7825(89)90050-9
  32. Qian, R.C., Batra, L.M. and Chen. (2003), "Free and forced vibration of thick rectangular plates using higher-order shear and normal deformable plate theory and meshless Petrov-Galerkin (MLPG) method", Comput. Model. Eng. Sci., 4(5), 519-534.
  33. Raju, K.K. and Hinton, E. (1980), "Natural frequencies and modes of rhombic Mindlin plates", Earhq. Eng. Struct. Dyn., 8, 55-62. https://doi.org/10.1002/eqe.4290080106
  34. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12, A69-A77.
  35. Reissner, E. (1947), "On bending of elastic plates", Quarter. Appl. Math., 5(1), 55-68. https://doi.org/10.1090/qam/20440
  36. Reissner, E. (1950), "On a variational theorem in elasticity", J. Math. Phys., 29, 90-95. https://doi.org/10.1002/sapm195029190
  37. Sakata, T. and Hosokawa, K. (1988), "Vibrations of clamped orthotropic rectangular plates", J. Sound Vibr., 125(3), 429-439. https://doi.org/10.1016/0022-460X(88)90252-0
  38. Shen, H.S., Yang, J. and Zhang, L. (2001), "Free and forced vibration of Reissner-Mindlin plates with free edges resting on elastic foundation", J. Sound Vibr., 244(2), 299-320. https://doi.org/10.1006/jsvi.2000.3501
  39. Si, W.J., Lam, K.Y. and Gang, S.W. (2005), "Vibration analysis of rectangular plates with one or more guided edges via bicubic B-spline method", Shock Vibr., 12(5).
  40. Soh, A.K., Cen, S., Long, Y. and Long, Z. (2001), "A new twelve DOF quadrilateral element for analysis of thick and thin plates", Eur. J. Mech. A/Sol., 20, 299-326. https://doi.org/10.1016/S0997-7538(00)01129-3
  41. Tedesco, J.W., McDougal, W.G. and Ross, C.A. (1999), Structural Dynamics, Addison Wesley Longman Inc., California, U.S.A.
  42. Ugural, A.C. (1981), Stresses in Plates and Shells, McGraw-Hill, New York, U.S.A.
  43. Wanji, C. and Cheung, Y.K. (2000), "Refined quadrilateral element based on Mindlin/Reissner plate theory", J. Numer. Meth. Eng., 47, 605-627. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<605::AID-NME785>3.0.CO;2-E
  44. Warburton, G.B. (1954), "The vibration of rectangular plates", Proceedings of the Institude of Mechanical Engineers, 168, 371-384. https://doi.org/10.1243/PIME_PROC_1954_168_040_02
  45. Weaver, W. and Johnston, P.R. (1984), Finite Elements for Structural Analysis, Prentice Hall, Inc., Englewood Cliffs, New Jersey, U.S.A.
  46. Woo, K.S., Hong, C.H., Basu, P.K. and Seo, C.G. (2003), "Free vibration of skew Mindlin plates by p-version of F.E.M.", J. Sound Vibr., 268, 637-656. https://doi.org/10.1016/S0022-460X(02)01536-5
  47. Zienkiewich, O.C., Taylor, R.L. and Too, J.M. (1971), "Reduced integration technique in general analysis of plates and shells", J. Numer. Meth. Eng., 3, 275-290. https://doi.org/10.1002/nme.1620030211