Effects of elastic foundation and the Poisson’s ratio on the nonlinear buckling and postbuckling behaviors of imperfect FGM plates subjected to mechanical loads
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Abstract
Abstract: This paper presents an analytical approach to investigate effects of elastic foundation and the Poisson’s ratio on the nonlinear buckling behavior of imperfect FGM plates, subjected to mechanical loads. Material properties are assumed to be temperature independent, and graded in the thickness direction according to a power law distribution in terms of volume fractions of constituents. Equilibrium and compatibility equations are derived by using classical plate theory taking into account geometrical nonlinearity, initial geometrical imperfection and elastic foundation with Pasternak model. Galerkin method is used to determine explicit expressions of buckling loads and postbuckling paths. Analysis is carried out to assess the effects of material, geometrical, elastic foundation parameters on the stability of FGM plates.
Keywords: Buckling and postbuckling, Functionally graded material, Plate, Elastic foundations, Poisson’s ratio .References
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[6] Nguyen Dinh Duc, Hoang Van Tung, Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations. J. Composite Structures, Vol. 93, p2874-2881, 2011.
[7] Nguyen Dinh Duc, Do Nam, Hoang Van Tung, Effects of elastic foundation on nonlinear stability of FGM plates under compressive and thermal loads. Proceedings of Xth National Conference on Mechanics of Deformed Solid, Thai Nguyen, Nov. 2010, p 191-197, 2010.
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[9] Javaheri R., Eslami M.R., Thermal buckling of functionally graded plates, AIAA J. 40(1), pp. 162-169, 2002.
[10] Lanhe W. , Thermal buckling of a simply supported moderately thick rectangular FGM plate, Compos. Struct. 64(2), pp. 211-218, 2004.
[11] Dao van Dung, Nguyen Thi Nga, Nonlinear Stability Analysis of Imperfect Functionally Graded Plates with the Poisson’s Ratio v=v(z) Subjected to Mechanical and Thermal Loads. Proceedings of Xth National Conference on Mechanics of Deformed Solid, Thai Nguyen, Nov. 2010, pp. 142-154, 2010.
[12] Do Nam, Stability of FGM plates on elastic foundations. Master’s thesis, Hanoi, 2011.
[13] Hoang Van Tung, Stability of FGM plates and shells. PhD’s thesis, Hanoi, 2010.
[14] Zhao X, Lee YY, Liew KM. Mechanical and thermal buckling analysis of functionally graded plates. J. Compos Struct; 90:161–71, 2009.
[15] Liew KM, Jang J, Kitipornchai S. Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading. Int J Solids Struct ;40:3869–92, 2003.
[16] Yang J, Liew KM, Kitipornchai S. Imperfection sensitivity of the post-buckling behavior of higher-order shear deformable functionally graded plates. Int J Solids Struct ;43:5247–66, 2006.
[17] Shen H-S. Postbuckling of FGM plates with piezoelectric actuators under thermo–electro-mechanical loadings. Int J Solids Struct ;42:6101–21, 2005.
[18] Shen H-S. Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties. Int J Mech Sci ;49:466–78, 2007.
[19] Lee YY, Zhao X, Reddy JN. Postbuckling analysis of functionally graded plates subject to compressive and thermal loads. Comput Methods Appl Mech Eng ;199:1645–53, 2010.
[20] Librescu L, Lin W. Postbuckling and vibration of shear deformable flat and curved panels on a non-linear elastic foundation. Int J Non-Lin Mech ;32(2):211–25, 1997
[21] Huang ZY, Lu CF, Chen WQ. Benchmark solutions for functionally graded thick plates resting on Winkler–Pasternak elastic foundations. J. Compos Struct ;85:95–104, 2008.
[22] Zenkour AM. Hygro–thermo-mechanical effects on FGM plates resting on elastic foundations. J. Compos Struct ;93:234–8, 2010.
[23] Shen H-S, Wang Z-X. Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations. J.Compos Struct ;92:2517–24, 2010
[2] Samsam Shariat B.A., Javaheri R., Eslami M.R. “Buckling of imperfect functionally graded plates under in-plane compressive loading”, Thin-Walled Struct. 43, pp. 1020-1036, 2005.
[3] Samsam Shariat B.A., Eslami M.R., “Thermal buckling of imperfect functionally graded plates”, Int. J. Solids Struct. 43, pp. 4082-4096, 2006.
[4] Samsam Shariat B.A., Eslami M.R., “Effect of initial imperfection on thermal buckling of functionally graded plates”, J. Thermal Stresses 28, pp. 1183-1198, 2005.
[5] Librescu L., Stein M., “A geometrically nonlinear theory of transversely isotropic laminated composite plates and its use in the post-buckling analysis”, Thin-Walled Struct. 11, pp. 177-201, 1991.
[6] Nguyen Dinh Duc, Hoang Van Tung, Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations. J. Composite Structures, Vol. 93, p2874-2881, 2011.
[7] Nguyen Dinh Duc, Do Nam, Hoang Van Tung, Effects of elastic foundation on nonlinear stability of FGM plates under compressive and thermal loads. Proceedings of Xth National Conference on Mechanics of Deformed Solid, Thai Nguyen, Nov. 2010, p 191-197, 2010.
[8] Javaheri R., Eslami M.R., Buckling of functionally graded plates under in-plane compressive loading, ZAMM 82(4). pp. 277-283, 2002.
[9] Javaheri R., Eslami M.R., Thermal buckling of functionally graded plates, AIAA J. 40(1), pp. 162-169, 2002.
[10] Lanhe W. , Thermal buckling of a simply supported moderately thick rectangular FGM plate, Compos. Struct. 64(2), pp. 211-218, 2004.
[11] Dao van Dung, Nguyen Thi Nga, Nonlinear Stability Analysis of Imperfect Functionally Graded Plates with the Poisson’s Ratio v=v(z) Subjected to Mechanical and Thermal Loads. Proceedings of Xth National Conference on Mechanics of Deformed Solid, Thai Nguyen, Nov. 2010, pp. 142-154, 2010.
[12] Do Nam, Stability of FGM plates on elastic foundations. Master’s thesis, Hanoi, 2011.
[13] Hoang Van Tung, Stability of FGM plates and shells. PhD’s thesis, Hanoi, 2010.
[14] Zhao X, Lee YY, Liew KM. Mechanical and thermal buckling analysis of functionally graded plates. J. Compos Struct; 90:161–71, 2009.
[15] Liew KM, Jang J, Kitipornchai S. Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading. Int J Solids Struct ;40:3869–92, 2003.
[16] Yang J, Liew KM, Kitipornchai S. Imperfection sensitivity of the post-buckling behavior of higher-order shear deformable functionally graded plates. Int J Solids Struct ;43:5247–66, 2006.
[17] Shen H-S. Postbuckling of FGM plates with piezoelectric actuators under thermo–electro-mechanical loadings. Int J Solids Struct ;42:6101–21, 2005.
[18] Shen H-S. Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties. Int J Mech Sci ;49:466–78, 2007.
[19] Lee YY, Zhao X, Reddy JN. Postbuckling analysis of functionally graded plates subject to compressive and thermal loads. Comput Methods Appl Mech Eng ;199:1645–53, 2010.
[20] Librescu L, Lin W. Postbuckling and vibration of shear deformable flat and curved panels on a non-linear elastic foundation. Int J Non-Lin Mech ;32(2):211–25, 1997
[21] Huang ZY, Lu CF, Chen WQ. Benchmark solutions for functionally graded thick plates resting on Winkler–Pasternak elastic foundations. J. Compos Struct ;85:95–104, 2008.
[22] Zenkour AM. Hygro–thermo-mechanical effects on FGM plates resting on elastic foundations. J. Compos Struct ;93:234–8, 2010.
[23] Shen H-S, Wang Z-X. Nonlinear bending of FGM plates subjected to combined loading and resting on elastic foundations. J.Compos Struct ;92:2517–24, 2010