Structural Engineering and Mechanics

  • 제54권4호
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  • Pages.649-664
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  • 2015
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Analytical solution for axisymmetric buckling of joined conical shells under axial compression

  • Kouchakzadeh, M.A. (Department of Aerospace Engineering and Center of Excellence in Aerospace Systems, Sharif University of Technology) ;
  • Shakouri, M. (Department of Aerospace Engineering, Sharif University of Technology)
  • 투고 : 2014.04.03
  • 심사 : 2014.11.22
  • 발행 : 2015.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, the authors present an analytical approach to find the axisymmetric buckling load of two joined isotropic conical shells under axial compression. The problem of two joined conical shells may be considered as the generalized form of joined cylindrical and conical shells with constant or stepped thicknesses. Thickness of each cone is constant; however it may be different from the thickness of the other cone. The boundary conditions are assumed to be simply supported with rigid rings. The governing equations for the conical shells are obtained and solved with an analytical approach. A simple closed-form expression is obtained for the buckling load of two joined truncated conical shells. Results are compared and validated with the numerical results of finite element method. The variation of buckling load with changes in the thickness and semi-vertex angles of the two cones is studied. Finally, application of the results in practical design and range of engineering validity are investigated.

키워드

참고문헌

  1. Anwen, W. (1998), "Stresses and stability for the cone-cylinder shells with toroidal transition", Int. J. Press. Vess. Pip., 75(1), 49-56. https://doi.org/10.1016/S0308-0161(98)00013-1
  2. Bushnell, D. and Galletly, G.D. (1974), "Comparisons of test and theory for nonsymmetric elastic-plastic buckling of shells of revolution", Int. J. Solid. Struct., 10(11), 1271-1286. https://doi.org/10.1016/0020-7683(74)90072-9
  3. Civalek, O. (2013), "Vibration analysis of laminated composite conical shells by the method of discrete singular convolution based on the shear deformation theory", Compos. Part B, 45(1), 1001-1009. https://doi.org/10.1016/j.compositesb.2012.05.018
  4. Civalek, O. and Gurses, M. (2009), "Free vibration analysis of rotating cylindrical shells using discrete singular convolution technique", Int. J. Press. Vess. Pip., 86(10), 677-683. https://doi.org/10.1016/j.ijpvp.2009.03.011
  5. Cullum, J.K. and Willoughby, R.A. (2002), Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Vol. 1: Theory, SIAM
  6. Flores, F.G. and Godoy, L.A. (1991), "Post-buckling of elastic cone-cylinder and sphere-cylinder complex shells", Int. J. Press. Vess. Pip., 45(2), 237-258. https://doi.org/10.1016/0308-0161(91)90095-J
  7. Grimes, R.G., Lewis, J.G. and Simon, H.D. (1994), "A shifted block Lanczos algorithm for solving sparse symmetric generalized eigenproblems", SIAM J. Matrix Anal. Appl., 15(1), 228-272. https://doi.org/10.1137/S0895479888151111
  8. Gupta, N., Sheriff, N.M. and Velmurugan, R. (2006), "A study on buckling of thin conical frusta under axial loads", Thin Wall. Struct., 44(9), 986-996. https://doi.org/10.1016/j.tws.2006.08.010
  9. Hafeez, G., El Ansary, A. and El Damatty, A. (2010), "Stability of combined imperfect conical tanks under hydrostatic loading", J. Constr. Steel Res., 66(11), 1387-1397. https://doi.org/10.1016/j.jcsr.2010.05.007
  10. Hui, D. (1988), "Effects of shear loads on vibration and buckling of antisymmetric cross-ply cylindrical panels", Int. J. Nonlin. Mech., 23(3), 177-187. https://doi.org/10.1016/0020-7462(88)90010-8
  11. Kamat, S., Ganapathi, M. and Patel, B.P. (2001), "Analysis of parametrically excited laminated composite joined conical-cylindrical shells", Comput. Struct., 79(1), 65-76. https://doi.org/10.1016/S0045-7949(00)00111-5
  12. Kouchakzadeh, M.A. and Shakouri, M. (2014), "Free vibration analysis of joined cross-ply laminated conical shells", Int. J. Mech. Sci., 78, 118-125. https://doi.org/10.1016/j.ijmecsci.2013.11.008
  13. Lackman, L. and Penzien, J. (1960), "Buckling of circular cones under axial compression", J. Appl. Mech., 27, 458. https://doi.org/10.1115/1.3644024
  14. Lawrence, K.L. (2012), ANSYS Tutorial: Release 14, SDC Publications
  15. Patel, B.P., Nath, Y. and Shukla, K.K. (2006), "Nonlinear thermo-elastic buckling characteristics of cross-ply laminated joined conical-cylindrical shells", Int. J. Solid. Struct., 43(16), 4810-4829. https://doi.org/10.1016/j.ijsolstr.2005.07.025
  16. Patel, B.P., Shukla, K.K. and Nath, Y. (2005), "Thermal postbuckling analysis of laminated cross-ply truncated circular conical shells", Compos. Struct., 71(1), 101-114. https://doi.org/10.1016/j.compstruct.2004.09.030
  17. Patel, B.P., Singh, S. and Nath, Y. (2008), "Postbuckling characteristics of angle-ply laminated truncated circular conical shells", Commun. Nonlin. Sci. Numer. Simul., 13(7), 1411-1430. https://doi.org/10.1016/j.cnsns.2007.01.001
  18. Ross, C.T.F., Little, A.P.F. and Adeniyi, K.A. (2005), "Plastic buckling of ring-stiffened conical shells under external hydrostatic pressure", Ocean Eng., 32(1), 21-36. https://doi.org/10.1016/j.oceaneng.2004.05.007
  19. Ross, C.T.F., Sawkins, D. and Johns, T. (1999), "Inelastic buckling of thick-walled circular conical shells under external hydrostatic pressure", Ocean Eng., 26(12), 1297-1310. https://doi.org/10.1016/S0029-8018(98)00066-3
  20. Rotter, J.M. and Schmidt, H. (2008), ECCS TWG 8.4. Buckling of steel shells, 5th Edition, European Convention for Constructional Steelwork, Brussels.
  21. Seide, P. (1956), "Axisymmetrical buckling of circular cones under axial compression", J. appl. Mech, 23(4), 625-628.
  22. Seide, P. (1956), "Axisymmetrical buckling of circular cones under axial compression", J Appl. Mech., 23(4), 625-628.
  23. Shadmehri, F., Hoa, S.V. and Hojjati, M. (2012), "Buckling of conical composite shells", Compos. Struct., 94(2), 787-792. https://doi.org/10.1016/j.compstruct.2011.09.016
  24. Simitses, G.J. (1996), "Buckling of moderately thick laminated cylindrical shells: a review", Compos. Part B, 27(6), 581-587. https://doi.org/10.1016/1359-8368(95)00013-5
  25. Sofiyev, A.H. (2003), "The buckling of an orthotropic composite truncated conical shell with continuously varying thickness subject to a time dependent external pressure", Compos. Part B, 34(3), 227-233. https://doi.org/10.1016/S1359-8368(02)00105-1
  26. Sofiyev, A.H. (2007), "The buckling of functionally graded truncated conical shells under dynamic axial loading", J. Sound Vib., 305(4-5), 808-826. https://doi.org/10.1016/j.jsv.2007.05.002
  27. Sofiyev, A.H. (2010), "The buckling of FGM truncated conical shells subjected to combined axial tension and hydrostatic pressure", Compos. Struct., 92(2), 488-498. https://doi.org/10.1016/j.compstruct.2009.08.033
  28. Sofiyev, A.H. (2011), "Influence of the initial imperfection on the non-linear buckling response of FGM truncated conical shells", Int. J. Mech. Sci., 53(9), 753-761. https://doi.org/10.1016/j.ijmecsci.2011.06.007
  29. Sofiyev, A.H. (2011), "Non-linear buckling behavior of FGM truncated conical shells subjected to axial load", Int. J. Nonlin. Mech., 46(5), 711-719. https://doi.org/10.1016/j.ijnonlinmec.2011.02.003
  30. Tani, J. and Yamaki, N. (1970), "Buckling of truncated conical shells under axial compression", AIAA J., 8, 568-571.
  31. Teng, J.G. (1996), "Elastic buckling of cone-cylinder intersection under localized circumferential compression", Eng. Struct., 18(1), 41-48. https://doi.org/10.1016/0141-0296(95)00114-3
  32. Teng, J.G. and Barbagallo, M. (1997), "Shell restraint to ring buckling at cone-cylinder intersections", Eng. Struct., 19(6), 425-431. https://doi.org/10.1016/S0141-0296(96)00087-9
  33. Teng, J.G. and Ma, H.-W. (1999), "Elastic buckling of ring-stiffened cone-cylinder intersections under internal pressure", Int. J. Mech. Sci., 41(11), 1357-1383. https://doi.org/10.1016/S0020-7403(98)00097-6
  34. Ventsel, E. and Krauthammer, T. (2001), Thin plates and shells: theory, analysis, and applications, Marcel Dekker.
  35. Zhao, Y. and Teng, J.G. (2003), "A stability design proposal for cone-cylinder intersections under internal pressure", Int. J. Press. Vess. Pip., 80(5), 297-309. https://doi.org/10.1016/S0308-0161(03)00048-6
  36. Zingoni, A. (2002), "Discontinuity effects at cone-cone axisymmetric shell junctions", Thin Wall. Struct., 40(10), 877-891. https://doi.org/10.1016/S0263-8231(02)00022-8
  37. Zingoni, A. (2004), "On analytical solutions for liquid-filled non-shallow conical shell assemblies", J. South African Inst. Civil Eng., 46(3), 10.

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