A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges

Abstract

In this article, a novel analytical method for decoupling the coupled stability equations of functionally graded (FG) rectangular plates is introduced. Based on the Mindlin plate theory, the governing stability equations that are coupled in terms of displacement components are derived. Introducing four new functions, the coupled stability equations are converted into two independent equations. The obtained equations have been solved for buckling analysis of rectangular plates with simply-supported two edges and arbitrary boundary conditions along the other edges (Levy boundary conditions). The critical buckling loads are presented for different loading conditions, various thickness to side and aspect ratios, some powers of FG materials, and various boundary conditions. The presented results for buckling of moderately thick FG plates with two simply-supported edges are reported for the first time.

Keywords

buckling functionally graded material rectangular plate Mindlin theory

Get full access to this article

View all access options for this article.

References

Nosier

Reddy

J. N.

, On vibration and buckling of symmetric laminated plates according to shear deformation theories. Acta Mech., 94, 1992, 145–169.

Javaheri

Eslami

M. R.

, Buckling of functionally graded rectangular plates under in plane compressive loading. ZAMM 82, 2002, 277–283.

Eisenberger

Alxandrov

, Buckling loads of variables thickness thin isotropic plates. Thin Walled Struct., 41, 2003, 871–889.

Lanhe

, Thermal buckling of a simply supported moderately thick rectangular FGM plate. Compos. Struct. 64, 2004, 211–218.

Chen

X. L.

Liew

K. M.

, Buckling of rectangular functionally graded materials plates subjected to nonlinearly distributed in plane edge loads. Smart Mater. Struct., 13, 2004, 1430–1437.

Xie

Iwamoto

, Buckling analysis of laminated composite plates with arbitrary edge supports. Compos. Struct., 69, 2005, 209–217.

Shufrin

Eisenberger

, Stability and vibration of shear deformable plates-first order and higher order analysis. Int. J. Solid Struct., 42, 2005, 1225–1251.

Shariat

B. A. S.

Eslami

M. R.

, Buckling of thick functionally graded plates under mechanical and thermal loads. Compos. Struct., 78, 2007, 433–439.

Shariat

B. A. S.

Eslami

M. R.

, Buckling of functionally graded plates under in plane compressive loading based on the first order plate theory. In Proceedings of the Fifth International Conference on Composite science and technology, Sharjah, UAE, 2005.

10.

Shariat

B. A. S.

Javaheri

Eslami

M. R.

, Buckling of imperfect functionally graded plates under in-plane compressive loading. Thin Walled Struct., 43, 2005, 1020–1036.

11.

T. L.

Shukla

K. K.

Huang

J. H.

, Post buckling analysis of functionally graded rectangular plates. Compos. Struct., 81, 2007, 1–10.

12.

Hosseini-Hashemi

Khorshidi

Amabili

, Exact solution for linear buckling of rectangular Mindlin plates. J. Sound Vibr., 315, 2008, 318–342.

13.

Saidi

A. R.

Rasouli

Sahraee

, Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third order shear deformation plate theory. Compos. Struct., 89, 2009, 110–119.

14.

Mirzaeifar

Shahab

Bahai

, An approximate method for simultaneous modification of natural frequencies and buckling loads of thin rectangular isotropic plates. Eng. Struct., 31, 2009, 208–215.

15.

Parkash

Singha

M. K.

Ganapathi

, Thermal postbuckling analysis of FGM skew plates. Eng. Struct., 30, 2008, 22–32.

16.

Liu

Y. G.

Pavlovic

M. N.

, A generalized analytical approach to the buckling of simply supported rectangular plates under arbitrary loads. Eng. Struct., 30, 2008, 1346–1359.

17.

Oyekoya

O. O.

Mba

D. U.

El-Zafrany

A. M.

, Buckling and vibration analysis of functionally graded composite structures using the finite element method. Compos. Struct., 89, 2009, 134–142.

18.

Mohammadi

Saidi

A. R.

Jomehzadeh

, Levy solution for buckling analysis of functionally graded rectangular plates. Appl. Compos. Mater., (2009), in press. DOI: 10.1007/s10443-009-9100-z.

19.

Brush

D. O.

Almroth

B. O.

, Buckling of bars, plates, and shells (New York, McGraw-Hill 1975).