Structural Engineering and Mechanics

  • 제20권4호
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  • Pages.405-420
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  • 2005
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Efficient geometric nonlinear analyses of circular plate bending problems

  • Duan, Mei (School of Civil and Environmental Engineering, The University of New South Wales)
  • 투고 : 2003.10.10
  • 심사 : 2005.04.11
  • 발행 : 2005.07.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, a hybrid/mixed nonlinear shell element is developed in polar coordinate system based on Hellinger/Reissner variational principle and the large-deflection theory of plate. A numerical solution scheme is formulated using the hybrid/mixed finite element method (HMFEM), in which the nodal values of bending moments and the deflection are the unknown discrete parameters. Stability of the present element is studied. The large-deflection analyses are performed for simple supported and clamped circular plates under uniformly distributed and concentrated loads using HMFEM and the traditional displacement finite element method. A parametric study is also conducted in the research. The accuracy of the shell element is investigated using numerical computations. Comparisons of numerical solutions are made with theoretical results, finite element analysis and the available numerical results. Excellent agreements are shown.

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참고문헌

  1. Babusa, I. (1973), 'The finite element method with Largrange multipliers', Numer. Math., 20, 179-192 https://doi.org/10.1007/BF01436561
  2. Bathe, K.J. (2001), 'The inf-sup condition and its evaluation for mixed finite element methods', J Comput. Struct., 79, 243-252 https://doi.org/10.1016/S0045-7949(00)00123-1
  3. Chia, C.Y. (1980), Nonlinear Analysis of Plates, McGraw-Hill
  4. Duan, M., Miyamoto, Y., Iwasaki, S. and Deto, H. (1998), 'Hybrid/mixed finite element analysis of circular plate bending based on Reissner-Mindlin theory', J of Structural and Construction Engineering (JSCE), 44A, 323-330
  5. Dumir, P.C. (1987), 'Circular plates on pasternak elastic foundations', Int. J. Numer. Anal. Methods Geomech., 11(1), 51-60 https://doi.org/10.1002/nag.1610110105
  6. Dumir, P.C. and Shingal, L. (1986), 'Nonlinear analysis of thick circular plates', J. Eng. Mech., 112(3),260-272 https://doi.org/10.1061/(ASCE)0733-9399(1986)112:3(260)
  7. Hitoshi, W. (1980), 'Nonlinear analysis of plates and shells by the incremental procedure using a mixed model of the finite element method', Bulletin of the JSME. 23(186), 1945-1951 https://doi.org/10.1299/jsme1958.23.1945
  8. Hong, T (1999), 'Axisymmetric shells and plates on tensionless elastic foundations', Int. J. Solids Struct., 36(34), 5277-5300 https://doi.org/10.1016/S0020-7683(98)00228-5
  9. Khathlan, A.A. (1994), 'Large-deformation analysis of plates on unilateral elastic foundation', J. Eng. Mech., 120(8), 1820-1827 https://doi.org/10.1061/(ASCE)0733-9399(1994)120:8(1820)
  10. Kohnke, P. (1998), Theory Manual. Houston, PA. USA: ANSYS, Inc
  11. Kondo, K. and Pian, T.H.H. (1981) 'Large deformations of rigid-plastic circular plates', Int. J. Solids Struct., 17(11) 1043-1055 https://doi.org/10.1016/0020-7683(81)90012-3
  12. Kraytennan, B.L. and Fu, C.C. (1985), 'Nonlinear analysis of clamped circulars', J. Struct. Eng., 111(11), 2402-2415 https://doi.org/10.1061/(ASCE)0733-9445(1985)111:11(2402)
  13. Michiya, K. (1993) 'Strain analysis of 3-dimensional elastic large deformation for a thick circular plate by convected coordinates (comparison with the classical plate theory), Nippon Kikai Gakkai Ronbunshu', A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A, 59(561), 1232-1237 https://doi.org/10.1299/kikaia.59.1232
  14. Pian, T.H.H. (1964), 'Derivation of element stiffness matrices by assumed stress distributions', AIAA 7, 1333-1335
  15. Pian, T.H.H. (1976), 'Variational principle for incremental finite element methods', Journal of The Franklin Institute, 302(5 & 6), 473-488 https://doi.org/10.1016/0016-0032(76)90037-5
  16. Pian, TH.H. (1996), 'Survey of hybrid/mixed finite element methods for plate and shell analysis', Third Asian Pacific Conf. on Computational Mechanics, 227-232
  17. Sansour, C. and Kollmann, F.G. (2000), 'Families of 4-node and 9-node finite elements for a finite deformation shell theory', Comput. Mech., 24, 435-447 https://doi.org/10.1007/s004660050003
  18. Stippes, M. and Hausrath, A.H. (1952), 'Large deflections of circular plates', Trans. ASME, J. Appl. Mech., 19, 187-292
  19. Szilard, R. (1974), Theory and Analysis ofPlates, Prentice-Hall, INC. Englewood Cliffs, New Jersey
  20. Takezono, S. (1980), 'Elasto/viscoplastic analysis of thin circular plates under large strains and large deformations', J. Appl. Mech., Transactions ASME, 47(4), 741-747 https://doi.org/10.1115/1.3153784
  21. Timoshenko, S. and Woinowsky-Kreiger, S. (1959), Theory of Plates and Shells, McGraw-Hill New York
  22. Turvey, G.J. and Salehi, M. (1997), 'Circular plates with one diametral stiffener - an elastic large deflection analysis', Comput. Struct., 63(4), 775-783 https://doi.org/10.1016/S0045-7949(96)00077-6
  23. Vallabhan, C.V (1994), 'Parametric study of axisymmetric circular-glass plates', J. Struct. Eng., 120(5), 16631671. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:1(120)
  24. Well,NA and Newmark, N.M. (1956), 'Large deflection of elliptical plates', Trans. ASME, J. Appl. Mech., 23, 21-26