Buckling Analysis of Simply-supported Functionally Graded Rectangular Plates under Non-uniform In-plane Compressive Loading

Document Type: Research Paper

Author

Department of Mechanical Engineering, Islamic Azad University, Arak Branch

Abstract

In this research, mechanical buckling of rectangular plates of functionally graded materials (FGMs) is considered. Equilibrium and stability equations of a FGM rectangular plate under uniform in-plane compression are derived. For isotropic materials, convergent buckling loads have been presented for non-uniformly compressed rectangular plates based on a rigorous superposition fourier solution for the in-plane Airy stress field and Galerkin’s approach for stability analysis. The results for isotropic case will be compared with reference articles and finite element method (FEM) solution. Finally, the results will be achieved for a sample of FGM material as well as the research on the effect of power law index on buckling coefficient.

Keywords


[1] Bulson P.S., 1970, The Stability of Flat Plates, Chatto and Windus, London.

[2] Yamanouchi M, Koizumi M., 1991, Functionally gradient materials, in: Proceeding of the first international symposium on functionally graded materials, Sendai, Japan.

[3] Fukui Y., 1991, Fundamental investigation of functionally graded materials, manufacturing system using centrifugal force, Japan Society of Mechanical Engineering, International Journal Series III 34(1): 144-148.

[4] Brush D.O., Almroth B.O., 1975, Buckling of Bars, Plates and Shells, McGraw-Hill, New York.

[5] Timoshenko S.P., Gere J.M., 1961, Theory of Elastic Stability, McGraw-Hill, New York.

[6] Leissa A.W., Ayoub E.F., 1988, Vibration and buckling of a simply supported rectangular plates subjected to a of in-plane concentrated forces, Journal of Sound and Vibration 127: 155-171.

[7] Khan M.Z., Walker A.C., 1972, Buckling of plates subjected to localized edge loading, Engineering 50: 225-232.

[8] Baker G., Pavlovic M.N., 1982, Elastic stability of simply supported rectangular plates under locally edge forces, ASME Transaction, Journal of Applied Mechanics 49: 177-179.

[9] Benoy M.B., 1969, An energy solution for the Buckling of rectangular plates under non-uniform in-loading, Aerospace Journal 73: 974-977.

[10] Hu H., Badir A., Abatan A., 2003, Buckling behavior of a graphite/epoxy composite plate under parabolic variation of axial loads, International Journal of Mechanical Sciences 45: 1132-1147.

[11] Bert C.W., Devarakonda K.K., 2003, Buckling of rectangular plate subjected to nonlinearly distributed in-plane loading, International Journal of Solids and Structures 40: 4097-4106.

[12] Jana P., Bhaskar K., 2004, Buckling of rectangular plates under non-uniform compression using rigorous plane stress solution, in: Proceedings of the International Conference on Theoretical, Analytical, Computational and Experimental Mechanics, IIT Kharagpur, 28-30 December.

[13] Nan C.W., Yuan R.Z., Zhang L.M., 1993, The physics of metal/ceramic functionally gradient materials, Ceramic Transactions, Functionally Gradient Materials 34: 75-82.

[14] Koizumi M., 1997, FGM Activities in Japan, Composite Part B: Engineering 28(1-2): 1-4.

[15] Javaheri R., Eslami M.R., 2002, Thermal buckling of graded plates based on higher order theory, Journal of Thermal Stresses 25(7): 603-625.

[16] Najafizadeh M.M., Eslami M.R., 2002, Buckling analysis of circular of functionally graded materials under uniform redial compression, International Journal of Mechanical Sciences 4(12): 2479-2493.

[17] Wang X., Tan M., Zhou Y., 2003, Buckling analyses of anisotropic plates and isotropic skew plates by the new version differential quadrature method, Thin-Walled Structure 41: 15-29.

[18] Praveen G.N., Reddy J.N., 1998, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, International Journal of Solids and Structures 35(33): 4457-4476.

[19] Wetherhold R.C., Seelman S., Wang J., 1996, The use of functionally graded materials to eliminate or control thermal deformation, Composites Science and Technology 56: 1099-1104.

[20] Tanigawa Y., Morishita H., Ogaki S., 1999, Derivation of system of fundamental equations for a three dimensional thermoelastic field with nonhomogeneous material properties and its application to a semi-infinite body, Journal of Thermal Stresses 22: 689-711.

[21] Timoshenko S.P., Goodier J.N., 1970, Theory of Elasticity, McGraw-Hill, New York.

[22] Ugural A.C., 1981, Stress in Plate and Shells, McGraw-Hill, New York.

[23] Reddy J.N., 2000, Analysis of functionally graded plates, International Journal of Numerical Methods in Engineering 47: 663-684.

[24] Van der Neut A., 1958, Buckling caused by thermal stresses, In: High temperature effects in aircraft structures, AGARD report 28: 215-247.