Buckling analysis of eccentrically stiffened functionally graded circular cylindrical thin shells under mechanical load
Main Article Content
Abstract
Abstract: An analytical approach is presented to investigate the linear buckling of eccentrically stiffened functionally graded thin circular cylindrical shells subjected to axial compression, external pressure and tosional load. Based on the classical thin shell theory and the smeared stiffeners technique, the governing equations of buckling of eccentrically stiffened functionally graded circular cylindrical shells are derived. The functionally graded cylindrical shells with simply supported edges are reinforced by ring and stringer stiffeners system on internal and (or) external surface. The resulting equations in the case of compressive and pressive loads are solve directly, while in the case of torsional load is solved by the Galerkin procedure to obtain the explicit expression of static critical buckling load. The obtained results show the effects of stiffeners and input factors on the buckling behavior of these structures.
Keywords: Functionally graded material; Cylindrical shells; Stiffeners; Buckling loads; Axial compression; External pressure; Tosional load.
References
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[2] Shen HS. Postbuckling of axially-loaded FGM hybrid cylindrical shells in thermal environments. Compos Sci Technol 2005;65(11-12):1675–90.
[3] Bahtui A, Eslami MR. Coupled thermoelasticity of functionally graded cylindrical shells. Mech Res Commun 2007 ;34(1):1–18.
[4] Huang H, Han Q. Buckling of imperfect functionally graded cylindrical shells under axial compression. Eur J Mech – A/Solids 2008;27(6):1026–36.
[5] Huang H, Han Q, Nonlinear elastic buckling and postbuckling of axially compressed functionally graded cylindrical shells, Int J Mech Sci 2009;51(7):500-7.
[6] Huang H, Han Q. Nonlinear buckling and postbuckling of heated functionally graded cylindrical shells under combined axial compression and radial pressure. Int J Non-Linear Mech 2009;44(2):209–18.
[7] Huang H, Han Q. Research on nonlinear postbuckling of FGM cylindrical shells under radial loads. Compos Struct 2010;92(6):1352-7.
[8] Shen HS. Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium. Int J Mech Sci 51(5) 2009: 372-83
[9] Sofiyev AH. Buckling analysis of FGM circular shells under combined loads and resting on the Pasternak type elastic foundation. Mech Res Commun 2010;37( 6):539–44.
[10] Zozulya VV, Zhang Ch. A high order theory for functionally graded axisymmetric cylindrical shells. Int J Mech Sci 2012;60(1):12-22.
[11] Ng TY, Lam KY, Liew KM, Reddy JN. Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading. Int J Solids Struct 2001;38(8):1295-309.
[12] Darabi M, Darvizeh M, Darvizeh A. Non-linear analysis of dynamic stability for functionally graded cylindrical shells under periodic axial loading. Compos Struct 2008;83(2):201–11.
[13] Chen WQ, Bian ZG, Ding HJ. Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells. Int J Mech Sci 2004;46(1):159-71.
[14] Sofiyev AH, Schnack E. The stability of functionally graded cylindrical shells under linearly increasing dynamic torsional loading. Eng Struct 2004;26(10):1321–31.
[15] Sofiyev AH. The stability of compositionally graded ceramic–metal cylindrical shells under aperiodic axial impulsive loading. Compos Struct 2005;69(2):247–57.
[16] Shariyat M. Dynamic thermal buckling of suddenly heated temperature-dependent FGM cylindrical shells, under combined axial compression and external pressure. Int J Solids Struct 2008;45(9):2598–612.
[17] Shariyat M. Dynamic buckling of suddenly loaded imperfect hybrid FGM cylindrical shells with temperature-dependent material properties under thermo-electro-mechanical loads. Int J Mech Sci 2008;50(12):1561–71.
[18] Li SR, Fu XH, Batra RC. Free vibration of three-layer circular cylindrical shells with functionally graded middle layer. Mech Res Commun 2010;37(6): 577–80.
[19] Huang H, Han Q. Nonlinear dynamic buckling of functionally graded cylindrical shells subjected to a time-dependent axial load. Compos. Struct. 2010;92(2):593–8.
[20] Budiansky B, Roth RS. Axisymmetric dynamic buckling of clamped shallow spherical shells. NASA technical note 1962;D_510:597–609.
[21] Shariyat M. Nonlinear transient stress and wave propagation analyses of the FGM thick cylinders, employing a unified generalized thermoelasticity theory. Int J Mech Sci 2012;65(1):24-37.
[22] Najafizadeh MM, Hasani A, Khazaeinejad P. Mechanical stability of functionally graded stiffened cylindrical shells. Appl Math Model 2009;54(2):1151–7.
[23] Bich DH, Nam VH, Phuong NT. Nonlinear postbuckling of eccentrically stiffened functionally graded plates and shallow shells. Vietnam J Mech 2011;33(3):132–47.
[24] Bich DH, Dung DV, Nam VH. Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels. Compos Struct 2012;94(8):2465-73.
[25] Brush DO, Almroth BO. Buckling of bars, plates and shells. Mc Graw-Hill, 1975.
[26] Volmir AS. Non-linear dynamics of plates and shells. Science Edition M, 1972. (in Russian).
[27] Baruch M, Singer J. Effect of eccentricity of stiffeners on the general instability of stiffened cylindrical shells under hydro-static pressure. J. Mech. Eng. Sci. 1963;5:23–7.
[28] Shen HS. Post-buckling analysis of imperfect stiffened laminated cylindrical shells under combined external pressure and thermal loading. Int. J. Mech. 1998;40: 339-355.
[29] Shen HS. Torsional buckling and postbuckling of FGM cylindrical shells in thermal environments. Int. J. Non-Linear Mech. 2009;44:644-57.
[30] Ekstrom RE. Buckling of cylindrical shells under combined torsion and hydrostatic pressure. Exp. Mech. 1963;3:192–7.