A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

Abstract

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

Keywords

circular plate functionally graded eccentric force closed-form solution Green function asymmetric loading

Get full access to this article

View all access options for this article.

References

Reddy

J. N.

Wang

C. M.

Kitipornchai

, ‘Axisymmetric bending of functionally graded circular and annular plates’ Eur. J. Mech. A, Solids 18 (1999): 185–199.

Kawamura

Matsomoto

Tanigawa

Skrzyspek

J. J.

Hetnarski

R. B.

, ‘Multipurpose optimization problem on material composition for thermal stress relaxation type of functionally graded circular plate using genetic algorithm’ (1999).

Durodola

J. F.

Attia

, ‘Deformation and stresses in functionally graded rotating disks’ Compos. Sci. Technol. 60 7 (2000): 987–995.

L. S.

Wang

T. J.

, ‘Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory’ Int. J. Solids Struct. 41 (2004): 85–101.

Nie

Zhong

, ‘Axisymmetric bending of two-directional functionally graded circular and annular plates’ Acta Mech. Solida Sin. 20 4 (2007): 289–295.

X. Y.

Ding

H. J.

Chen

W. Q.

, ‘Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qr ^k‘ Int. J. Solids Struct. 45 (2008): 191–210.

Magnucka-Blandzi

, ‘Axi-symmetrical deflection and buckling of circular porous-cellular plate’ Thin-Walled Struct. 46 (2008): 333–337.

X. Y.

Ding

H. J.

Chen

W. Q.

, ‘Three-dimensional analytical solution for functionally graded magneto-electro-elastic circular plates subjected to uniform load’ Compos. Struct. 83 (2008): 381–390.

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 1 (2009): 110–119.

10.

Sahraee

Saidi

A. R.

, ‘Axisymmetric bending analysis of thick functionally graded circular plates using fourth-order shear deformation theory’ Eur. J. Mech. A, Solids 24 5, 974–984.

11.

Najafizadeh

M. M.

Hedayati

, ‘Refined theory for thermoelastic stability of functionally graded circular plates’ J. Therm. Stresses 27 9 (2004): 857–880.

12.

Najafizadeh

M. M.

Heydari

H. R.

, ‘Thermal buckling of functionally graded circular plates based on higher order shear deformation plate theory’ Eur. J. Mech. A, Solids 23 (2007): 1085–1100.

13.

Najafizadeh

M. M.

Eslami

M. R.

, ‘First-order-theory-based thermoelastic stability of functionally graded material circular plates’ AIAA J. 40 (2002): 1444–1450.

14.

Najafizadeh

M. M.

Eslami

M. R.

, ‘Buckling analysis of circular plates of functionally graded materials under uniform radial compression’ Int. J. Mech. Sci. 44 (2002): 2479–2493.

15.

Bassali

W. A.

, ‘Bending of a singularity loaded thin circular annulus with free boundaries’ J. Mech. Phys. Solids 8 2 (1960): 123–140.

16.

Ramakishnan

Kunukkasseril

V. X.

, ‘Asymmetric response of circular plates’ J. Sound Vib. 34 (1974): 489–504.

17.

Strozzi

, ‘Mechanical analysis of an annular plate subject to a transverse concentrated load’ J. Strain Anal. Engng. Des. 24 3 (1989): 139–149.

18.

El-Raheb

, ‘Exact solution of the asymmetric Mindlin's plate equations applied to a disk’ J. Sound Vib. 261 (2003): 153–168.

19.

Prakash

Ganapathi

, ‘Asymmetric flexural vibration and thermoelastic stability of FGM circular plates using finite element method’ Compos. B 37 (2006): 642–649.

20.

Nosier

Fallah

, ‘Reformulation of Mindlin-Reissner governing equations of functionally graded circular plates’ Acta Mech. 198 (2008): 209–233.

21.

Sahraee

, ‘Bending analysis of functionally graded sectorial plates using Levinson plate theory’ Compos. Struct. 88 4 (2009): 548–557.

22.

Jomehzadeh

Saidi

A. R.

Atashipour

S. R.

, ‘An analytical approach for stress analysis of functionally graded annular sector plates’ Mater. Des. 30 9 (2009):.

23.

Ventsel

Krauthammer

, Thin plates and shells theory, analysis and applications (New York: Marcel Dekker, Inc. 2001).