Nonlinear thermo-mechanical stability of shear deformable FGM sandwich shallow spherical shells with tangential edge constraints
Keywords:functionally graded material, shallow spherical shell, sandwich shell, nonlinear stability, tangential edge constraint
AbstractThis paper presents an analytical approach to investigate the nonlinear axisymmetric response of moderately thick FGM sandwich shallow spherical shells resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. Material properties are assumed to be temperature independent, and effective properties of FGM layer are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations and various degree of tangential constraint of boundary edge into consideration. Approximate solutions are assumed to satisfy clamped boundary condition and Galerkin method is applied to derive closed-form expressions of critical buckling loads and nonlinear load-deflection relation. Effects of geometrical parameters, thickness of face sheets, foundation stiffness, imperfection, thermal environments and degree of tangential edge constraints on the nonlinear stability of FGM sandwich shallow spherical shells are analyzed and discussed.
M. Sathyamoorthy. Vibrations of moderately thick shallow spherical shells at large amplitudes. Journal of Sound and Vibration, 172, (1), (1994), pp. 63–70. doi:10.1006/jsvi.1994.1158.
M. R. Eslami, H. R. Ghorbani, and M. Shakeri. Thermoelastic buckling of thin spherical shells. Journal of Thermal Stresses, 24, (12), (2001), pp. 1177–1198. doi:10.1080/014957301753251746.
R. Shahsiah and M. R. Eslami. Thermal and mechanical instability of an imperfect shallow spherical cap. Journal of Thermal Stresses, 26, (7), (2003), pp. 723–737. doi:10.1080/713855992.
Q. S. Li, J. Liu, and J. Tang. Buckling of shallow spherical shells including the effects of transverse shear deformation. International Journal of Mechanical Sciences, 45, (9), (2003), pp. 1519–1529. doi:10.1016/j.ijmecsci.2003.09.020.
G. H. Nie. Asymptotic buckling analysis of imperfect shallow spherical shells on non-linear elastic foundation. International Journal of Mechanical Sciences, 43, (2), (2001), pp. 543–555. doi:10.1016/s0020-7403(99)00118-6.
O. Civalek. Geometrically nonlinear dynamic and static analysis of shallow spherical shell resting on two-parameters elastic foundations. International Journal of Pressure Vessels and Piping, 113, (2014), pp. 1–9. doi:10.1016/j.ijpvp.2013.10.014.
X. Chang-Shi. Buckling and post-buckling of symmetrically laminated moderately-thick spherical caps. International Journal of Solids and Structures, 28, (9), (1991), pp. 1171–1184. doi:10.1016/0020-7683(91)90110-2.
Y. Nath and K. Sandeep. Postbuckling of symmetrically laminated, moderately thick, axisymmetric shallow spherical shells. International Journal of Mechanical Sciences, 35, (11), (1993), pp. 965–975. doi:10.1016/0020-7403(93)90033-q.
A. Muc. Buckling and post-buckling behaviour of laminated shallow spherical shells subjected to external pressure. International Journal of Non-Linear Mechanics, 27, (3), (1992), pp. 465–476. doi:10.1016/0020-7462(92)90013-w.
R. Shahsiah, M. R. Eslami, and R. Naj. Thermal instability of functionally graded shallow spherical shell. Journal of Thermal Stresses, 29, (8), (2006), pp. 771–790. doi:10.1080/01495730600705406.
R. Shahsiah, M. R. Eslami, and M. S. Boroujerdy. Thermal instability of functionally graded deep spherical shell. Archive of Applied Mechanics, 81, (10), (2011), pp. 1455–1471. doi:10.1007/s00419-010-0495-7.
D. H. Bich and H. V. Tung. Non-linear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects. International Journal of Non-Linear Mechanics, 46, (9), (2011), pp. 1195–1204. doi:10.1016/j.ijnonlinmec.2011.05.015.
M. S. Boroujerdy and M. R. Eslami. Axisymmetric snap-through behavior of Piezo-FGM shallow clamped spherical shells under thermo-electro-mechanical loading. International Journal of Pressure Vessels and Piping, 120, (2014), pp. 19–26. doi:10.1016/j.ijpvp.2014.03.008.
N. D. Duc, V. T. T. Anh, and P. H. Cong. Nonlinear axisymmetric response of FGM shallow spherical shells on elastic foundations under uniform external pressure and temperature. European Journal of Mechanics-A/Solids, 45, (2014), pp. 80–89. doi:10.1016/j.euromechsol.2013.11.008.
D. H. Bich, D. Van Dung, and L. K. Hoa. Nonlinear static and dynamic buckling analysis of functionally graded shallow spherical shells including temperature effects. Composite Structures, 94, (9), (2012), pp. 2952–2960. doi:10.1016/j.compstruct.2012.04.012.
H. V. Tung. Nonlinear thermomechanical stability of shear deformable FGM shallow spherical shells resting on elastic foundations with temperature dependent properties. Composite Structures, 114, (2014), pp. 107–116. doi:10.1016/j.compstruct.2014.04.004.
L. Librescu, W. Lin, M. P. Nemeth, and J. H. Starnes Jr. Thermomechanical postbuckling of geometrically imperfect flat and curved panels taking into account tangential edge constraints. Journal of Thermal Stresses, 18, (4), (1995), pp. 465–482. doi:10.1080/01495739508946314.
H. V. Tung. Postbuckling behavior of functionally graded cylindrical panels with tangential edge constraints and resting on elastic foundations. Composite Structures, 100, (2013), pp. 532–541. doi:10.1016/j.compstruct.2012.12.051.
H. V. Tung. Thermal and thermomechanical postbuckling of FGM sandwich plates resting on elastic foundations with tangential edge constraints and temperature dependent properties. Composite Structures, 131, (2015), pp. 1028–1039. doi:10.1016/j.compstruct.2015.06.043.
H. V. Tung. Nonlinear axisymmetric response of FGM shallow spherical shells with tangential edge constraints and resting on elastic foundations. Composite Structures, 149, (2016), pp. 231–238. doi:10.1016/j.compstruct.2016.04.032.
H.-S. Shen. Postbuckling of shear deformable FGM cylindrical shells surrounded by an elastic medium. International Journal of Mechanical Sciences, 51, (5), (2009), pp. 372–383. doi:10.1016/j.ijmecsci.2009.03.006.
O. Civalek. Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches. Composites Part B: Engineering, 50, (2013), pp. 171–179. doi:10.1016/j.compositesb.2013.01.027.
C. Demir, K. Mercan, and O. Civalek. Determination of critical buckling loads of isotropic, FGM and laminated truncated conical panel. Composites Part B: Engineering, 94, (2016), pp. 1–10. doi:10.1016/j.compositesb.2016.03.031.
V. R. Kar and S. K. Panda. Postbuckling analysis of shear deformable FG shallow spherical shell panel under nonuniform thermal environment. Journal of Thermal Stresses, 40, (1), (2017), pp. 25–39. doi:10.1080/01495739.2016.1207118.