# Buckling of Rectangular Functionally Graded Material Plates under Various Edge Conditions

Document Type : Persian

Authors

1 M.Sc, Mechanical Engineering Department, Islamic Azad University, Khomeinishahr Branch

2 Assistant Professor, Mechanical Engineering Department, Islamic Azad University, Khomeinishahr Branch

3 Assistant Professor, Mechanical Engineering Department, Isfahan University of Technology

Abstract

In the present paper, the buckling problem of rectangular functionally graded (FG) plate with arbitrary edge supports is investigated. The present analysis is based on the classical plate theory (CPT) and large deformation is assumed for deriving stability equations. The plate is subjected to bi-axial compression loading. Mechanical properties of FG plate are assumed to vary continuously along the thickness of the plate according to different volume of fraction functions of constituents. These functions are assumed to have power law distributions. The displacement function is assumed to have the form of double Fourier series, of which derivatives are legitimized using Stokes’ transformation method. The advantage of using this method is the capability of considering effect of any possible combination of boundary conditions on the buckling loads. The out-plane displacement distribution is assumed using Fourier Sinus Series. This results in a general eigenvalue problem which can be used for evaluating the buckling load under different edge conditions, plate aspect ratios and various volume fraction functions. For generality of problem, plate is elastically restrained using some rotational and translational springs at four edges. Some numerical examples are presented and compared the to numerical results of finite element method using ABAQUS and other researchers’ results to validate the proposed method. It has been shown that there is good agreement between them

Keywords

#### References

[1] Leissa A.W, Kang J.H., Exact solutions for vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses, ASME, Vol.44,issue 9,2002, pp. 1925-1945
[2] Javaheri R., Eslami M.R., Buckling of functionally graded plates under in-plane compressive loading, Zamm .Z.Angew. Math Mech, Voll. 82, issue 4, 220, 2002, pp 277-283.
[3] Ni Q.Q., Xi J, Ivamoto M, Buckling analysis of composite laminated plates with arbitrary edge supports, Composite structures, Vol. 69, 2005, pp 209-217.
[4]
on a Higher-order Deformation Theory, J. Reinforced Plastics and Composites, Vol. 28, 2009, pp 1215-1234.
[5] Najafizadeh M.M., Mahdavian M., Superposition buckling analyses of rectangular Plates Composed of Functionally Graded materials subjected to non-uniform distributed In-plane loading, Proceedings of the Institution of Mechanical Engineers - Part C: J. Mechanical Engineering Science, Vol. 224, issue 11,2010, pp.2299-2308.
[7] Ansari R., Darvizeh M., Prediction of dynamic behaviour of FGM shells under arbitrary boundary conditions, Composite Structures, Vol. 85, 2008, pp. 284–292.
[8] Hyeong K.K., Moon S. K., An analytical method for calculating vibration characteristics of PWR fuel assembly with reactor end boundary conditions using fourier series, Transactions, SMIRT16, Washington DC, 2001,  paper No.1445.
]9[ لطیفی م.، فرهت نیا ف.، کدخدایی م.، کاربرد روش تبدیل استوکس در تحلیل سازه‌های مکانیکی، دومین کنفرانس ملی مهندسی مکانیک، دانشگاه آزاد اسلامی‌واحد خمینی شهر، 1388.
[10] Zhang D.G., Zhou Y.H., A theoretical analysis of FGM thin plates based on physical neutral surface, Computational Material Science, 44, 2008, pp. 716-720.
[11] Timoshenko S., Goodier J., Theory of elasticity, McGraw-Hill, New York, 1971.

Chen C.S., Hsu C.Y., Tzou G.J., , Vibration and Stability of Functionally Graded Plates Based