Buckling Analysis of Functionally Graded Plates Using Finite Element Analysis

Abstract

The present study aims to give critical buckling loads of rectangular functionally graded (FG) plates for various types of boundary conditions. The finite element formulation of stability of plates is introduced and the procedure is applied to obtain critical buckling loads of a plate for two types of boundary conditions: (a) CFFC: two parallel edges are clamped and free along the other two; (b) FFFC: the plate is clamped along one edge and free along all the others. Variation of mechanical properties of the FG plate along the length and the variation along the thickness have been both considered. According to the function of elasticity modulus variation, results have been obtained for various power indices of the varying function. Results compare well with those obtained using shell elements in ANSYS.

Keywords

• : FGM,Buckling of Plates,Finite Element Method,Ansys

References

1. [1] Levy, S., Bending of rectangular plates with large deflections. 1942: US Government Printing Office.
2. [2] Javaheri, R. and M. Eslami, Buckling of Functionally Graded Plates under In‐plane Compressive Loading. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik: Applied Mathematics and Mechanics, 82, 277-283, 2002
3. [3] Chen, X. and K. Liew, Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads. Smart Materials and Structures, 13, 1430, 2004
4. [4] Vel, S.S. and R. Batra, Three-dimensional exact solution for the vibration of functionally graded rectangular plates. Journal of Sound and Vibration, 272, 703-730, 2004
5. [5] Chi, S.-H. and Y.-L. Chung, Mechanical behavior of functionally graded material plates under transverse load—Part I: Analysis. International Journal of Solids and Structures, 43, 3657-3674, 2006
6. [6] Shariat, B.S. and M. Eslami, Buckling of thick functionally graded plates under mechanical and thermal loads. Composite Structures, 78, 433-439, 2007
7. [7] Birman, V. and L.W. Byrd, Modeling and analysis of functionally graded materials and structures. 2007
8. [8] Shahrjerdi, A., F. Mustapha, M. Bayat, S. Sapuan, R. Zahari, and M. Shahzamanian. Natural frequency of FG rectangular plate by shear deformation theory. in IOP conference series: materials science and engineering. 2011. IOP Publishing.

9. [9] Zhang, D.-G. and Y.-H. Zhou, A theoretical analysis of FGM thin plates based on physical neutral surface. Computational Materials Science, 44, 716-720, 2008
10. [10] Prakash, T., M. Singha, and M. Ganapathi, Influence of neutral surface position on the nonlinear stability behavior of functionally graded plates. Computational mechanics, 43, 341-350, 2009
11. [11] Mohammadi, M., A. Saidi, and E. Jomehzadeh, A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 224, 1831-1841, 2010
12. [12] Talha, M. and B. Singh, Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Applied Mathematical Modelling, 34, 3991-4011, 2010
13. [13] Pendhari, S.S., T. Kant, Y.M. Desai, and C.V. Subbaiah, Static solutions for functionally graded simply supported plates. International Journal of Mechanics and Materials in Design, 8, 51-69, 2012
14. [14] Singha, M., T. Prakash, and M. Ganapathi, Finite element analysis of functionally graded plates under transverse load. Finite elements in Analysis and Design, 47, 453-460, 2011
15. [15] Hosseini-Hashemi, S., M. Fadaee, and S.R. Atashipour, Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure. Composite Structures, 93, 722-735, 2011
16. [16] Bousahla, A.A., S. Benyoucef, A. Tounsi, and S. Mahmoud, On thermal stability of plates with functionally graded coefficient of thermal expansion. Structural Engineering and Mechanics, 60, 313-335, 2016
17. [17] Demirhan, P.A. and V. Taskin, Levy solution for bending analysis of functionally graded sandwich plates based on four variable plate theory. Composite Structures, 177, 80-95, 2017
18. [18] Mohseni, E., A. Saidi, and M. Mohammadi, Bending-stretching analysis of thick functionally graded micro-plates using higher-order shear and normal deformable plate theory. Mechanics of Advanced Materials and Structures, 24, 1221-1230, 2017
19. [19] Timoshenko, S. and J. Goodier, Theory of elasticity 3rd edition. 1970, New York, McGraw-Hill.
20. [20] Woo, J. and S. Meguid, Nonlinear analysis of functionally graded plates and shallow shells. International Journal of Solids and structures, 38, 7409-7421, 2001
21. [21] ANSYS, A., V11 Program Documentation. Ansys Inc., Canonsburg, Pennsylvania,