Buckling Analysis of Functionally Graded Annular Spherical Shells and Segments Subjected to Mechanic Loads
Main Article Content
Abstract
Abstract: An analytical approach is presented to investigate the buckling of functionally graded annular spherical segments subjected to compressive load and radial pressure. Based on the classical thin shell theory, the governing equations of functionally graded annular spherical segments are derived. Approximate solutions are assumed to satisfy the simply supported boundary condition of segments and Galerkin method is applied to obtain closed-form relations of bifurcation type of buckling loads. Numerical results are given to evaluate effects of inhomogeneous and dimensional parameters to the buckling of structure.
Keywords: Functionally graded material; annular spherical segment; critical buckling load.
References
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[26] Aghdam MM, Shahmansouri N, Bigdeli K. Bending analysis of moderately thick functionally graded conical panels. Compos Struct 2011; 93:1376–1384.
[27] Bich DH, Phuong NT, Tung HV. Buckling of functionally graded conical panels under mechanical loads. Composite Structures 2012;94:1379–1384.
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[2] Huang NC. Unsymmetrical buckling of thin shallow spherical shells. J Appl Mech Trans ASME 1964; 31: 447–457.
[3] Tillman SC, On the buckling behavior of shallow spherical caps under a uniform pressure load. Int J Solids Struct1970; 6:37–52.
[4] Ball R, Burt JA. Dynamic buckling of shallow spherical shells. ASME J Appl Mech 1973; 41: 411–416.
[5] Kao R, Perrone N. Dynamic buckling of axisymmetric spherical caps with initial imperfection. Comput Struct 1978; 9:463–473.
[6] Ganapathi M, Varadan TK, Dynamic buckling of orthotropic shallow spherical shells, Comput Struct 1982; 15:517–520.
[7] Dumir PC, Nonlinear axisymmetric response of orthotropic thin spherical caps on elastic foundations, Int J Mech Sci 1985; 27: 751–760.
[8] Chao CC, Lin IS. Static and dynamic snap-through of orthotropic spherical caps. Compos Struct 1990; 14: 281–301.
[9] Xu CS. Buckling and post-buckling of symmetrically laminated moderately thick spherical caps. Int J Solids Struct 1991; 28:1171–1184.
[10] Muc A, Buckling and postbuckling behavior of laminated shallow spherical shells subjected to external pressure. Int J Nonlinear Mech 1992; 27(3):465–476.
[11] Ganapathi M, Varadan TK. Dynamic buckling of laminated anisotropic spherical caps. J Appl Mech 1995; 62:13–19.
[12] Dube GP, Joshi S, Dumir PC. Nonlinear analysis of thick shallow spherical and conical orthotropic caps using Galerkin’s method. Appl Math Modelling 2001;25:755–773.
[13] Nie GH, Asymptotic buckling analysis of imperfect shallow spherical shells on non-linear elastic foundation. Int J Mech Sci 2001;43:543–555.
[14] Eslami MR, Ghorbani HR, Shakeri M. Thermoelastic buckling of thin spherical shells. J Therm Stresses 2001:24:1177–1198.
[15] Shahsiah R, Eslami MR. Thermal and mechanical instability of an imperfect shallow spherical cap. J Therm Stresses 2003;26(7):723–737.
[16] Wunderlich W, Albertin U. Buckling behavior of imperfect spherical shells. Int J Nonlinear Mech 2002; 37:589–604.
[17] Li QS, Liu J, Tang J. Buckling of shallow spherical shells including the effects of transverse shear deformation. Int J Mech Sci 2003; 45:1519–1529.
[18] Shahsiah R, Eslami MR, Naj R. Thermal instability of functionally graded shallow spherical shell. J Therm Stresses 2006; 29(8):771–790.
[19] Prakash T, Sundararajan N, Ganapathi M. On the nonlinear axisymmetric dynamic buckling behavior of clamped functionally graded spherical caps. J. Sound Vibrat 2007; 299:36–43.
[20] Ganapathi M. Dynamic stability characteristics of functionally graded materials shallow spherical shells. Compos Struct 2007;79:338–343.
[21] Bich DH. Nonlinear buckling analysis of FGM shallow spherical shells. Vietnam J Mech 2009; 31:17–30.
[22] Bich DH, Hoa LK. Nonlinear vibration of functionally graded shallow spherical shells. Vietnam J Mech 2010; 32:199–210.
[23] Bich DH, Tung HV. Nonlinear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects. Int J Nonlinear Mech 2011;46:1195–1204.
[24] Shahsiah R, Eslami MR, Sabzikar Boroujerdy M. Thermal instability of functionally graded deep spherical shell. Arch Appl Mech2011; 81:1455–1471.
[25] Bich DH, Dung DV, Hoa LK. Nonlinear static and dynamic buckling analysis of functionally graded shallow spherical shells including temperature effects. Compos Struct 2012;94:2952-2960.
[26] Aghdam MM, Shahmansouri N, Bigdeli K. Bending analysis of moderately thick functionally graded conical panels. Compos Struct 2011; 93:1376–1384.
[27] Bich DH, Phuong NT, Tung HV. Buckling of functionally graded conical panels under mechanical loads. Composite Structures 2012;94:1379–1384.
[28] Brush DO, Almroth BO. Buckling of Bars, Plates and Shells. McGraw-Hill, New York, 1975.
[29] Timoshenko SP, Gere JM. Theory of elastic stability. McGraw-Hill, New York, 1961.
[30] Paczos P, Zielnica J. Stability of orthotropic elastic–plastic open conical shells. Thin-Walled Structures 2008; 46:530-540.