×

Nonlinear bending of FGM cylindrical panels resting on elastic foundations in thermal environments. (English) Zbl 1406.74259

Summary: A nonlinear bending analysis is presented for a simply supported, functionally graded cylindrical panel resting on an elastic foundation in thermal environments. The panel is exposed to elevated temperature and is subjected to a transverse uniform or sinusoidal load. Material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent, and graded in the thickness direction based on Mori-Tanaka micromechanics model. The formulations are based on a higher order shear deformation shell theory with a von Kármán-type of kinematic nonlinearity and include shell panel-foundation interaction and the thermal effects. A two-step perturbation technique is employed to determine the load-deflection and load-bending moment curves. The numerical illustrations concern nonlinear bending response of FGM cylindrical panels with two constituent materials resting on Pasternak elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects of the volume fraction index, temperature variation, foundation stiffness as well as the character of in-plane boundary conditions are also examined.

MSC:

74G60 Bifurcation and buckling
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74K20 Plates
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Alinia, M. M.; Ghannadpour, S. A.M., Nonlinear analysis of pressure loaded FGM plates, Compos. Struct., 88, 354-359, (2009)
[2] Duc, N. D.; Anh, V. T.T.; Cong, P. H., Nonlinear axisymmetric response of FGM shallow spherical shells on elastic foundations under uniform external pressure and temperature, Eur. J. Mech. A Solids, 45, 80-89, (2014) · Zbl 1406.74469
[3] Duc, N. D.; Quan, T. Q., Nonlinear stability analysis of double-curved shallow FGM panels on elastic foundations in thermal environments, Mech. Compos. Mat., 48, 435-448, (2012)
[4] Farid, M.; Zahedinejad, P.; Malekzadeh, P., Three-dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation using a hybrid semi-analytic, differential quadrature method, Mat. Des., 31, 2-13, (2010)
[5] Ghannadpour, S. A.M.; Alinia, M. M., Large deflection behavior of functionally graded plates under pressure loads, Compos. Struct., 75, 67-71, (2006)
[6] Gibson, L. J.; Ashby, M. F.; Karam, G. N.; Wegst, U.; Shercliff, H. R., Mechanical properties of natural materials. II. microstructures for mechanical efficiency, Proc. R. Soc. Lond. A, 450, 141-162, (1995)
[7] Hill, R., A self-consistent mechanics of composite materials, J. Mech. Phys. Solids, 13, 213-222, (1965)
[8] Khabbaz, R. S.; Manshadi, B. D.; Abedian, A., Nonlinear analysis of FGM plates under pressure loads using the higher-order shear deformation theories, Compos. Struct., 89, 333-344, (2009)
[9] Kiani, Y.; Akbarzadeh, A. H.; Chen, Z. T.; Eslami, M. R., Static and dynamic analysis of an FGM doubly curved panel resting on the Pasternak-type elastic foundation, Compos. Struct., 94, 2474-2484, (2012)
[10] Mori, T.; Tanaka, K., Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metall., 21, 571-574, (1973)
[11] Na, K.-S.; Kim, J.-H., Nonlinear bending response of functionally graded plates under thermal loads, J. Therm. Stress, 29, 245-261, (2006)
[12] Ovesy, H. R.; Ghannadpour, S. A.M., Large deflection finite strip analysis of functionally graded plates under pressure loads, Int. J. Struct. Stab. Dyn., 7, 193-211, (2007)
[13] Phung-Van, P.; Nguyen-Thoi, T.; Luong-Van, H.; Lieu-Xuan, Q., Geometrically nonlinear analysis of functionally graded plates using a cell-based smoothed three-node plate element (CS-MIN3) based on the C^{0}-HSDT, Comput. Methods Appl. Mech. Eng., 270, 15-36, (2014) · Zbl 1296.74124
[14] Praveen, G. N.; Reddy, J. N., Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, Int. J. Solids Struct., 35, 4457-4476, (1998) · Zbl 0930.74037
[15] Reddy, J. N.; Chin, C. D., Thermomechanical analysis of functionally graded cylinders and plates, J. Therm. Stress, 21, 593-629, (1998)
[16] Reddy, J. N.; Liu, C. F., A higher-order shear deformation theory of laminated elastic shells, Int. J. Eng. Sci., 23, 319-330, (1985) · Zbl 0559.73072
[17] Shen, H.-S., Kármán-type equations for a higher-order shear deformation plate theory and its use in the thermal postbuckling analysis, Appl. Math. Mech., 18, 1137-1152, (1997) · Zbl 0910.73033
[18] Shen, H.-S., Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments, Int. J. Mech. Sci., 44, 561-584, (2002) · Zbl 1022.74023
[19] Shen, H.-S., Nonlinear thermal bending response of FGM plates due to heat conduction, Compos. B Eng., 38, 201-215, (2007)
[20] Shen, H.-S., Functionally graded materials nonlinear analysis of plates and shells, (2009), CRC Press Boca Raton
[21] Shen, H.-S., A two-step perturbation method in nonlinear analysis of beams, plates and shells, (2013), John Wiley & Sons Inc
[22] Shen, H.-S.; Wang, H., Nonlinear vibration of shear deformable FGM cylindrical panels resting on elastic foundations in thermal environments, Compos. B Eng., 60, 167-177, (2014)
[23] Shen, H.-S.; Wang, Z.-X., Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations, Compos. Struct., 92, 2517-2524, (2010)
[24] Touloukian, Y. S., Thermophysical properties of high temperature solid materials, (1967), Macmillan New York
[25] Tung, H. V.; Duc, N. D., Nonlinear response of shear deformable FGM curved panels resting on elastic foundations and subjected to mechanical and thermal loading conditions, Appl. Math. Model, 38, 2848-2866, (2014)
[26] Woo, J.; Merguid, S. A., Nonlinear analysis of functionally graded plates and shallow shells, Int. J. Solids Struct., 38, 7409-7421, (2001) · Zbl 1010.74034
[27] Yang, J.; Shen, H.-S., Nonlinear analysis of functionally graded plates under transverse and in-plane loads, Int. J. Non-Linear Mech., 38, 467-482, (2003) · Zbl 1346.74116
[28] Yang, J.; Shen, H.-S., Nonlinear bending analysis of shear deformable functionally graded plates subjected to thermo-mechanical loads under various boundary conditions, Compos. B Eng., 34, 103-115, (2003)
[29] Zhao, X.; Liew, K. M., Geometrically nonlinear analysis of functionally graded shells, Int. J. Mech. Sci., 51, 131-144, (2009) · Zbl 1264.74153
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.