Structural Engineering and Mechanics

  • 제46권2호
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  • Pages.269-294
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  • 2013
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Buckling and vibration of rectangular plates of variable thickness with different end conditions by finite difference technique

  • 투고 : 2012.06.19
  • 심사 : 2013.04.09
  • 발행 : 2013.04.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper is concerned with the determination of exact buckling loads and vibration frequencies of variable thickness isotropic plates using well known finite difference technique. The plates are subjected to uni, biaxial compression and shear loadings and various combinations of boundary conditions are considered. The buckling load is found out as the in plane load that makes the determinant of the stiffness matrix equal to zero and the natural frequencies are found out by carrying out eigenvalue analysis of stiffness and mass matrices. New and exact results are given for many cases and the results are in close agreement with the published results. In this paper, like finite element method, finite difference method is applied in a very simple manner and the application of boundary conditions is also automatic.

키워드

참고문헌

  1. Allen, H.B. and Bulson, P.S. (1980), Background to buckling, McGraw-Hill, London.
  2. Annonymous (1971), Handbook of Structural Stability (Editors Column Research committee of Japan), S.S. Corona Pub co, Tokyo.
  3. Azhari, M. (1993), "Local and post-local buckling of plates and plate assemblies using finite strip method", Ph.D Thesis, The University of New South Wales, Kensington.
  4. Bradford, M.A. and Azhari, M. (1995), "Buckling of plates with different end conditions using the finite strip method", Comput. Struct, 56(1), 75-83. https://doi.org/10.1016/0045-7949(94)00528-B
  5. Bradford, M.A. and Azhari, M. (1997), "The use of bubble functions for the stability of plates with different end conditions", Eng. Struct, 19(2), 151-161. https://doi.org/10.1016/S0141-0296(96)00038-7
  6. Chehil, D.S. and Dua, S.S. (1973), "Buckling of rectangular plates with general variation in thickness", J. App. Mech. Trans, ASME, 40, 745-751. https://doi.org/10.1115/1.3423084
  7. Chen, W.F. and Lui, E.M. (1987), Structural stability theory and implementation, New York, Elsevier.
  8. Chung, M.S. and Cheung, Y.K. (1971), "Natural vibration of thin flat walled structures with different boundary conditions", J.Sound Vib., 18(3), 325-337. https://doi.org/10.1016/0022-460X(71)90705-X
  9. Eisenberger, M. and Alexandrov, A. (2003), "Buckling loads of variable thickness thin isotropic plates", Thin Wall. Struct., 41, 871-889. https://doi.org/10.1016/S0263-8231(03)00027-2
  10. Felix, D.H., Bambill, D.V. and Rossit, C.A. (2011), "A note on buckling and vibration of clamped orthotropic plate under in plane load", Struct. Eng. Mech., 39(1), 115-123. https://doi.org/10.12989/sem.2011.39.1.115
  11. Gambir, M.L. (2004), Stability Analysis and Design of Structures, Springer -Verlag, Berlin.
  12. Gupta, U.S., Lal, R. and Seema, S. (2006), "Vibration analysis of non homogenous circular plate of nonlinear thickness variation by differential quadrature method", J. Sound Vib., 298, 892-906. https://doi.org/10.1016/j.jsv.2006.05.030
  13. Hancock, G.J. (1978), "Local distortional and lateral buckling of I beams", J. Struct. Division, ASCE, 104, (ST11), 1787-1798.
  14. Harik, E., Liu, X. and Ekambaram, R. (1991), "Elastic stability of plats with varying rigidities", Comput. Struct., 38, 161-168. https://doi.org/10.1016/0045-7949(91)90094-3
  15. Hashami, S.H., Fadace, M. and Atashipour, S.R. (2011), "Study on the free vibration of thick functionally graded rectangular plate according to a new exact closed-form procedure", Compos. Struct, 93, 722-735. https://doi.org/10.1016/j.compstruct.2010.08.007
  16. Hwang, S.S. (1973), "Stability of plats with piecewise varying thickness", ASME, J. Appl. Mech., 1127- 1128.
  17. Leissa, A.W. (1973), "The free vibration of rectangular plates", J. Sound Vib., 31(3), 237-293.
  18. Matsunga, H. (2008), "Free vibration and stability of functionality graded plates according to a 2D higherorder deformation theory", Compos. Struct, 82, 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030
  19. Navaneethakrishnan, P.V. (1968), "Buckling of non uniform plates: spline method", J. Eng. Mech., ASCE, 114(5), 893-898.
  20. Nerantzaki, M.S. and Katsikadalils, J.T. (1996), "Buckling of plates with variable thickness and analog equation solution", Eng. Anal. Bound. Elem., 18, 149-154. https://doi.org/10.1016/S0955-7997(96)00045-8
  21. Nie, G.J. and Zhong, Z. (2008), "Vibration analysis of functionality graded annular sectorial plates with simply supported radial edges", Compos. Struct., 84,167-176. https://doi.org/10.1016/j.compstruct.2007.07.003
  22. Przemieniecki, J.S. (1973), "Finite element analysis of local instability", AIAA. J., 11, 33-39. https://doi.org/10.2514/3.50433
  23. Sakiyama, T. and Huang, M. (1998), "Free vibration analysis of rectangular plates with variable thickness", Report of the Faculty of Eng., Nagasaki University, 28(51),163-171.
  24. Singh, J.P. and Dey, S.S. (1990), "Variational finite difference approach to buckling of plates of variable thickness", Comput. Struct., 36, 39-45. https://doi.org/10.1016/0045-7949(90)90172-X
  25. Subramanian, K., Elangovan, A. and Rajkumar, R. (1993), "Elastic stability of varying thickness plates using the finite element method", Comput. Struct., 48(4), 733-738. https://doi.org/10.1016/0045-7949(93)90267-H
  26. Szilard, R. (2004), Theory and applications of Plate analysis- classical and Numerical and Engineering methods,John-Wiley and sons, USA.
  27. Timoshenko, S.P. and Gere, J.M. (1961), Theory of Elastic stability, McGraw-Hill, New York.
  28. Wilson, J.A. and Rajasekaran, S. (2012), "Elastic stability of all edges simply supported, stepped and stiffened rectangular plate under uniaxial loading", Appl. Math. Model., 36, 5758-5772. https://doi.org/10.1016/j.apm.2012.01.020
  29. Wittrick, W.H. and Ellen, C.H. (1962), "Buckling of tapered rectangular plates in compression", Aeronaut Quart, 13, 308-326. https://doi.org/10.1017/S0001925900002547
  30. Xiang, Y. and Wang, C.M. (2002), "Exact buckling and vibration solutions for stepped rectangular plates", J. Sound Vib., 250(3), 503-517. https://doi.org/10.1006/jsvi.2001.3922
  31. Xiang, Y. and Wei, G.W. (2004), "Exact solutions for buckling and vibration of stepped rectangular Mindliln plates", Int. J. Solids Struct., 41, 279-294. https://doi.org/10.1016/j.ijsolstr.2003.09.007
  32. Xiang, Y. and Zhang, L. (2005), "Free vibration analysis of stepped circular Mindlin plates", J. Sound Vib., 280, 633-655. https://doi.org/10.1016/j.jsv.2003.12.017
  33. Xiang, Y. (2007), "Vibrations of plates with abrupt changes in properties", Analysis and Design of Plated Structures, 2, Dynamics, Ed. N.E. Shanmugam and C.M. Wang, 254-274.
  34. Yalcin, H.S., Arikoglu, A. and Ozkol, I. (2009), "Free vibration analysis of circular plates by differential transformation method", Appl.Math. Comput., 212, 377-386. https://doi.org/10.1016/j.amc.2009.02.032
  35. Yuan, J. and Dickinson, S.M. (1992), "The flexural vibration of rectangular plate systems approached by using artificial spring in the Rayleigh - Ritz method", J. Sound Vib., 159,39-55. https://doi.org/10.1016/0022-460X(92)90450-C
  36. Yuan, S. and Yin, Y. (1998), "Computation of elastic buckling loads of rectangular thin plates using the extended Kantorovich method", Comput. Struct., 66(6), 861-867. https://doi.org/10.1016/S0045-7949(97)00111-9

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