Biaxial Buckling Analysis of Symmetric Functionally Graded Metal Cored Plates Resting on Elastic Foundation under Various Edge Conditions Using Galerkin Method
الموضوعات :
M Rezaei
1
(Department of Mechanical Engineering, School of Engineering, Yasouj University, Yasouj, Iran)
S Ziaee
2
(Department of Mechanical Engineering, School of Engineering, Yasouj University, Yasouj, Iran)
S Shoja
3
(Department of Civil Engineering, School of Engineering, Yasouj University, Yasouj, Iran)
الکلمات المفتاحية: Elastic foundation, Functionally graded material, Galerkin Method, Buckling analysis, Plate,
ملخص المقالة :
In this paper, buckling behavior of symmetric functionally graded plates resting on elastic foundation is investigated and their critical buckling load in different conditions is calculated and compared. Plate governing equations are derived using the principle of minimum potential energy. Afterwards, displacement field is solved using Galerkin method and the proposed process is examined through numerical examples. Effect of FGM power law index, plate aspect ratio, elastic foundation stiffness and metal core thickness on critical buckling load is investigated. The accuracy of this approach is verified by comparing its results to those obtained in another work, which is performed using Fourier series expansion.
Bever M.B., Duwez P.E., 1972, Gradients in composite materials, Materials Science and Engineering 10: 1-8.
[2] Singh B.N., Lal A., 2010, Stochastic analysis of laminated composite plates on elastic foundation: The cases of post-buckling behavior and nonlinear free vibration, International Journal of Pressure Vessels and Piping 87: 559-574.
[3] Li X.Y., Ding H.J., Chen W.Q., 2008, Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk, International Journal of Solids and Structures 45: 191-210.
[4] Li X.Y., Ding H.J., Chen W.Q., 2008, Axisymmetric elasticity solutions for a uniformly loaded annular plate of transversely isotropic functionally graded materials, Acta Mechanica 196: 139-159.
[5] Liu G.R., Han X., Lam K.Y., 2001, Material characterization of FGM plates using elastic waves and an inverse procedure, Journal of Composite Materials 35(11): 954-971.
[6] Zhong Z., Shang E., 2008, Closed-form solutions of three-dimensional functionally graded plates, Mechanics of Advanced Materials and Structures 15: 355-363.
[7] Kim K.D., Lomboy G.R., Han S.C., 2008, Geometrically non-linear analysis of functionally graded material (FGM) plates and shells using a four-node quasi-conforming shell element, Journal of Composite Materials 42(5): 485-511.
[8] Feldman E., Aboudi J., 1997, Buckling analysis of functionally graded plates subjected to uniaxial loading, Composite Structures 38(1-4): 29-36.
[9] Ma L.S., Wang T.J., 2004, Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory, International Journal of Solids and Structures 41: 85-101.
[10] Zhang X., Chen F., Zhang H., 2013, Stability and local bifurcation analysis of functionally graded material plate under transversal and in-plane excitations, Applied Mathematical Modelling 37(10-11): 6639-6651.
[11] Mahdavian M., 2009, Buckling analysis of simply-supported functionally graded rectangular plates under non-uniform In-plane compressive loading, Journal of Solid Mechanics 1(3): 213-225.
[12] Chen X.L., Liew K.M., 2004, Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads, Smart Materials and Structures 13: 1430-1437.
[13] Cheng Z.Q., Batra R.C., 2000, Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories, Archives of Mechanics 52(1): 143-158.
[14] Pan E., 2003, Exact solution for functionally graded anisotropic elastic composite laminates, Journal of Composite Materials 37(21): 1903-1920.
[15] Kashtalyan M., 2004, Three-dimensional elasticity solution for bending of functionally graded rectangular plates, European Journal of Mechanics - A/Solids 23(5): 853-864.
[16] Zenkour A.M., 2007, Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate, Archive of Applied Mechanics 77(4): 197-214.
[17] Zheng L., Zhong Z., 2009, Exact solution for axisymmetric bending of functionally graded circular plate, Tsinghua Science & Technology 14(2): 64-68.
[18] Vel S.S., Batra R.C., 2012, Exact solution for thermoelastic deformations of functionally graded thick rectangular plates, AIAA Journal 40(7): 1421-1433.
[19] Nguyen T.K., Sab K., Bonnet G., 2008, First-order shear deformation plate models for functionally graded materials, Composite Structures 83(1): 25-36.
[20] Hopkins D.A., Chamis C.C., 1988, A unique set of micromechanics equations for high temperature metal matrix composites, NASA TM 87154..
[21] Birman V., 1995, Stability of functionally graded hybrid composite plates, Composite Engineering 5(7): 913-921.
[22] Chen X.L., Liew K.M., 2004, Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads, Smart Materials and Structures 13(6): 1430-1437.
[23] Saidi A.R., Rasouli A., Sahraee S., 2009, Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory, Composite Structures 89(1): 110-119.
[24] Mohammadi M., Saidi A., Jomehzadeh E., 2010, Levy solution for buckling analysis of functionally graded rectangular plates, Appl Compos Mater 17(2): 81-93.
[25] Dung D.V., Thiem H.T., 2012, On the nonlinear stability of eccentrically stiffened functionally graded imperfect plates resting on elastic foundation, Proceedings of ICEMA2 Conference, Hanoi.
[26] Sobhy M., 2013, Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions, Composite Structures 99: 76-87.
[27] Naderi A., Saidi A.R., 2011, Exact solution for stability analysis of moderately thick functionally graded sector plates on elastic foundation, Composite Structures 93: 629-638.
[28] Yaghoobi H., Fereidoon A., 2014, Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: An assessment of a simple refined nth-order shear deformation theory, Composites: Part B 62: 54-64.
[29] Thai H.T., Kim S.E., 2013, Closed-form solution for buckling analysis of thick functionally graded plates on elastic foundation, International Journal of Mechanical Sciences 75: 34-44.
[30] Timoshenko S., Woinowsky-Krieger S., 1989, Theory of Shell and Plates, McGraw-Hill Book Company.
[31] Latifi M., Farhatnia F., Kadkhodaei M., 2013, Buckling analysis of rectangular functionally graded plates under various edge conditions using Fourier series expansion, European Journal of Mechanics - A/Solids 41: 16-27.
