DOI QR코드

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Axisymmetric large deflection analysis of fully and partially loaded shallow spherical shells

  • Altekin, Murat (Department of Civil Engineering, Yildiz Technical University) ;
  • Yukseler, Receb F. (Department of Civil Engineering, Yildiz Technical University)
  • 투고 : 2013.03.31
  • 심사 : 2013.08.16
  • 발행 : 2013.08.25

초록

Geometrically non-linear axisymmetric bending of a shallow spherical shell with a clamped or a simply supported edge under axisymmetric load was investigated numerically. The partial load was introduced by the Heaviside step function, and the solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for three geometrical parameters. The accuracy of the algorithm was checked by comparing the central deflection, the radial membrane stress at the edge, or the transverse shear force with the solutions of plates and shells in the literature and good agreement was obtained. The main findings of the study can be outlined as follows: (i) If the shell is fully loaded the central deflection of a clamped shell is larger than that of a simply supported shell provided that the shell is not very shallow, (ii) if the shell is partially loaded the central deflection of the shell is sensitive to the parameters of thickness, depth, and partial loading but the influence of the boundary conditions is negligible.

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참고문헌

  1. Akkas, N. and Toroslu, R. (1999), "Snap-through buckling analyses of composite shallow spherical shells", Mechanics of Composite Materials and Structures, 6(4), 319-330. https://doi.org/10.1080/107594199305485
  2. Altekin, M. and Yükseler, R.F. (2012), "Axisymmetric large deflection analysis of an annular circular plate subject to rotational symmetric loading", Proceedings of the Eleventh Int. Conference on Computational Structures Technology, Dubrovnik, September.
  3. Arciniega, R.A. and Reddy, J.N. (2007), "Large deformation analysis of functionally graded shells", Int. J. of Solids and Structures, 44(6), 2036-2052. https://doi.org/10.1016/j.ijsolstr.2006.08.035
  4. Dube, G.P., Joshi, S. and Dumir, P.C. (2001), "Nonlinear analysis of thick shallow spherical and conical orthotropic caps using Galerkin's method", Applied Mathematical Modelling, 25(9), 755-773. https://doi.org/10.1016/S0307-904X(01)00012-9
  5. Filho, L.A.D. and Awruch, A.M. (2004), "Geometrically nonlinear static and dynamic analysis of shells and plates using the eight-node hexahedral element with one-point quadrature", Finite Elements in Analysis and Design, 40(11), 1297-1315. https://doi.org/10.1016/j.finel.2003.08.012
  6. Federhofer, K. and Egger, H. (1946), "Berechnung der dunnen kreisplatte mit grosser ausbiegung", Akad. Wiss. Wien. Math.-Naturwiss, 155(2a), 15-43.
  7. Hamdouni, A. and Millet, O. (2003), "Classification of thin shell models deduced from the nonlinear threedimensional elasticity. part I: the shallow shells", Archives of Mechanics, 55(2), 135-175.
  8. Hamed, E., Bradford, M.A. and Gilbert, R.I. (2010), "Nonlinear long-term behavior of spherical shallow thin-walled concrete shells of revolution", Int. J. of Solids and Structures, 47(2), 204-215. https://doi.org/10.1016/j.ijsolstr.2009.09.027
  9. Huang, N.C. (1964), "Unsymmetrical buckling of thin shallow spherical shells", J. of Applied Mechanics, 31(3), 447-457. https://doi.org/10.1115/1.3629662
  10. Krayterman, B. and Sabnis, G.M. (1985), "Large deflected plates and shells with loading history", J. of Engineering Mechanics, 111(5), 653-663. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:5(653)
  11. Kim, T.H., Park, J.G., Choi, J.H. and Shin, H.M. (2010), "Nonlinear dynamic analysis of reinforced concrete shell structures", Structural Engineering and Mechanics, 34(6), 685-702. https://doi.org/10.12989/sem.2010.34.6.685
  12. Maksimyuk, V.A., Storozhuk, E.A. and Chernyshenko, I.S. (2009), "Using mesh-based methods to solve nonlinear problems of statics for thin shells", Int. Applied Mechanics, 45(1), 32-56. https://doi.org/10.1007/s10778-009-0166-y
  13. Nath, Y. and Alwar, R.S. (1978), "Non-linear static and dynamic response of spherical shells", Int. J. of Non-Linear Mechanics, 13 (3), 157-170. https://doi.org/10.1016/0020-7462(78)90004-5
  14. Nath, Y., Dumir, P.C. and Bhatia, R.S. (1985), "Non-linear static and dynamic analysis of circular plates and shallow spherical shells using the collocation method", Int. J. for Numerical Methods in Engineering, 21(3), 565-578. https://doi.org/10.1002/nme.1620210314
  15. Nath, Y. and Jain, R.K. (1986), "Non-linear studies of orthotropic shallow spherical shells on elastic foundation", Int. J. of Non-Linear Mechanics, 21(6), 447-458. https://doi.org/10.1016/0020-7462(86)90041-7
  16. Nie, G.H. and Yao, J.C. (2010), "An asymptotic solution for non-linear behavior of ımperfect shallow spherical shells", J. of Mechanics, 26(2), 113-122. https://doi.org/10.1017/S1727719100002975
  17. Perrone, N. and Kao, R. (1970), "Large deflection response and buckling of partially and fully loaded spherical caps", AIAA J., 8(12), 2130-2136. https://doi.org/10.2514/3.6075
  18. Pica, A., Wood, R.D. and Hinton, E. (1980), "Finite element analysis of geometrically nonlinear plate behaviour using a Mindlin formulation", Computers and Structures, 11(3), 203-215. https://doi.org/10.1016/0045-7949(80)90160-1
  19. Ramachandra, L.S. and Roy, D. (2001), "A novel technique in the solution of axisymmetric large deflection analysis of a circular plate", J. of Applied Mechanics, 68(5), 814-816. https://doi.org/10.1115/1.1379039
  20. Sofiyev, A.H., Omurtag, M.H. and Schnack, E. (2009), "The vibration and stability of orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure", J. of Sound and Vibration, 319 (3-5), 963-983. https://doi.org/10.1016/j.jsv.2008.06.033
  21. Sofiyev, A. and Özyigit, P. (2012), "Thermal buckling analysis of non-homogeneous shallow spherical shells", J. of the Faculty of Engineering and Architecture of Gazi University, 27(2), 397-405. (in Turkish)
  22. Sze, K.Y., Liu, X.H. and Lo, S.H. (2004), "Popular benchmark problems for geometric nonlinear analysis of shells", Finite Elements in Analysis and Design, 40(11), 1551-1569. https://doi.org/10.1016/j.finel.2003.11.001
  23. Szilard, R. (1974), Theory and Analysis of Plates, Prentice-Hall, Englewood Cliffs, New Jersey, USA.
  24. Teng, J.G. and Rotter, J.M. (1989), "Elastic-plastic large deflection analysis of axisymmetric shells", Computers and Structures, 31(2), 211-233. https://doi.org/10.1016/0045-7949(89)90227-7
  25. Timoshenko, S.P. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, McGraw-Hill Int. Editions, Singapore.
  26. Ventsel, E. and Krauthammer, T. (2001), Thin Plates and Shells: Theory, Analysis, and Applications, Marcel Dekker Inc., USA.
  27. Ye, J. (1991), "Large deflection analysis of axisymmetric circular plates with variable thickness by the boundary element method", Applied Mathematical Modelling, 15(6), 325-328. https://doi.org/10.1016/0307-904X(91)90048-T
  28. Zhang, Y.X. and Kim, K.S. (2006), "Geometrically nonlinear analysis of laminated composite plates by two new displacement-based quadrilateral plate elements", Composite Structures, 72(3), 301-310. https://doi.org/10.1016/j.compstruct.2005.01.001

피인용 문헌

  1. Temperature-dependent nonlinear analysis of shallow shells: A theoretical approach vol.141, 2016, https://doi.org/10.1016/j.compstruct.2016.01.060