Based on the classical plate theory (CPT), we derive scaling factors between solutions of bending, buckling and free vibration of isotropic functionally graded material (FGM) thin plates and those of the corresponding isotropic homogeneous plates. The effective material properties of the FGM plate are assumed to vary piecewise continuously in the thickness direction except for the Poisson ratio that is taken to be constant. The correspondence relations hold for plates of arbitrary geometry provided that the governing equations and boundary conditions are linear. When the stretching and bending stiffnesses of the FGM plate satisfy a relation, Poisson's ratio is constant and the boundary conditions are such that the in-plane membrane forces vanish, then there exists a physical neutral surface for the FGM plate that is usually different from the plate midsurface. Example problems studied verify the accuracy of scaling factors.

References

References
1.
Qian
,
L. F.
, and
Batra
,
R. C.
,
2005
, “
Design of Bidirectional Functionally Graded Plate for Optimal Natural Frequencies
,”
J. Sound Vib.
,
280
(
1–2
), pp.
415
424
.
2.
Liu
,
D. Y.
,
Wang
,
C. Y.
, and
Chen
,
W. Q.
,
2010
, “
Free Vibration of FGM Plates With In-Plane Material Inhomogeneity
,”
Compos. Struct.
,
92
(
5
), pp.
1047
1051
.
3.
Jha
,
D. K.
,
Kant
,
T.
, and
Singh
,
R. K.
,
2013
, “
A Critical Review of Recent Research on Functionally Graded Plates
,”
Compos. Struct.
,
96
, pp.
833
849
.
4.
Swaminathan
,
K.
,
Naveenkumar
,
D. T.
,
Zenkour
,
A. M.
, and
Carrera
,
E.
,
2015
, “
Stress, Vibration and Buckling Analyses of FGM Plates—A State-of-the-Art Review
,”
Compos. Struct.
,
120
, pp.
10
31
.
5.
Yang
,
J.
, and
Shen
,
H. S.
,
2001
, “
Dynamic Response of Initially Stressed Functionally Graded Rectangular Thin Plates
,”
Compos. Struct.
,
54
(
4
), pp.
497
508
.
6.
He
,
X. Q.
,
Ng
,
T. Y.
,
Sivashanker
,
S.
, and
Liew
,
K. M.
,
2001
, “
Active Control of FGM Plates With Integrated Piezoelectric Sensors and Actuators
,”
Int. J. Solids Struct.
,
38
(
9
), pp.
1641
1655
.
7.
Javaheri
,
R.
, and
Eslami
,
M. R.
,
2002
, “
Buckling of Functionally Graded Rectangular Plates Under In-Plane Compressive Loading
,”
ZAMM
,
82
(
4
), pp.
277
283
.
8.
Samsarn Shariata
,
B. A.
,
Javaheri
,
R.
, and
Eslami
,
M. R.
,
2005
, “
Buckling of Imperfect Functionally Graded Plates Under In-Plane Compressive Loading
,”
Thin-Walled Struct.
,
43
(
7
), pp.
1020
1036
.
9.
Mohammadi
,
M.
,
Saidi
,
A. R.
, and
Jomehzadeh
,
E.
,
2010
, “
Levy Solution for Buckling Analysis of Functionally Graded Rectangular Plates
,”
Appl. Compos. Mater.
,
17
(
2
), pp.
81
93
.
10.
Chi
,
S.-H.
, and
Chung
,
Y.-L.
,
2006
, “
Mechanical Behavior of Functionally Graded Material Plates Under Transverse Load—Part I: Analysis
,”
Int. J. Solids Struct.
,
43
(
13
), pp.
3657
3674
.
11.
Chi
,
S.-H.
, and
Chung
,
Y.-L.
,
2006
, “
Mechanical Behavior of Functionally Graded Material Plates Under Transverse Load—Part II: Numerical Results
,”
Int. J. Solids Struct.
,
43
(
13
), pp.
3675
3691
.
12.
Nie
,
G. J.
, and
Batra
,
R. C.
,
2010
, “
Exact Solutions and Material Tailoring for Functionally Graded Hollow Circular Cylinders
,”
J. Elasticity
,
99
(
2
), pp.
179
201
.
13.
Zimmerman
,
R. W.
, and
Lutz
,
M. P.
,
1999
, “
Thermal Stresses and Thermal Expansion in a Uniformly Heated Functionally Graded Cylinder
,”
J. Therm. Stresses
,
22
(
2
), pp.
177
188
.
14.
Yin
,
S.-H.
,
Yu
,
T. T.
, and
Liu
,
P.
,
2013
, “
Free Vibration Analyses of FGM Thin Plates by Isogeometric Analysis Based on Classical Plate Theory and Physical Neutral Surface
,”
Adv. Mech. Eng.
,
2013
, p.
634584
.
15.
Ebrahimi
,
F.
, and
Rastgo
,
A.
,
2008
, “
An Analytical Study on the Free Vibration of Smart Thin FGM Plate Based on Classical Plate Theory
,”
Thin-Walled Struct.
,
46
(
12
), pp.
1402
1408
.
16.
Ebrahimi
,
F.
, and
Rastgo
,
A.
,
2008
, “
Free Vibration Analysis of Smart Annular FGM Plates Integrated With Piezoelectric Layers
,”
Smart Mater. Struct.
,
17
(
1
), p.
015044
.
17.
Mirtalaie
,
S.-H.
, and
Hajabasi
,
M. A.
,
2011
, “
Free Vibration Analysis of Functionally Graded Thin Annular Sector Plates Using the Differential Quadrature Method
,”
Proc. Inst. Mech. Eng., Part C
,
225
(
3
), pp.
568
583
.
18.
Hasani Baferani
,
A.
,
Saidi
,
A. R.
, and
Jomehzadeh
,
E.
,
2011
, “
An Exact Solution for Free Vibration of Thin Functionally Graded Rectangular Plates
,”
Proc. Inst. Mech. Eng., Part C
,
225
(
3
), pp.
526
536
.
19.
Vel
,
S. S.
, and
Batra
,
R. C.
,
2004
, “
Three-Dimensional Exact Solution for the Vibration of Functionally Graded Rectangular Plates
,”
J. Sound Vib.
,
272
(
3–5
), pp.
703
730
.
20.
Vel
,
S. S.
, and
Batra
,
R. C.
,
2003
, “
Three-Dimensional Analysis of Transient Thermal Stresses in Functionally Graded Plates
,”
Int. J. Solids Struct.
,
40
(
25
), pp.
7181
7196
.
21.
Vel
,
S. S.
, and
Batra
,
R. C.
,
2002
, “
Exact Solutions for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates
,”
AIAA J.
,
40
(
7
), pp.
1421
1433
.
22.
Yang
,
J.
, and
Shen
,
H.-S.
,
2003
, “
Non-Linear Analysis of Functionally Graded Plates Under Transverse and In-Plane Loads
,”
Int. J. Non-Linear Mech.
,
38
(
4
), pp.
467
482
.
23.
Woo
,
J.
,
Meguid
,
S. A.
, and
Ong
,
L. S.
, “
Nonlinear Free Vibration Behavior of Functionally Graded Plates
,”
J. Sound Vib.
,
289
(
3
), pp.
595
611
.
24.
Zhang
,
D. G.
, and
Zhou
,
Y. H.
,
2008
, “
A Theoretical Analysis of FGM Plate Based on Physical Neutral Surface
,”
Comput. Mater. Sci.
,
44
(
2
), pp.
716
720
.
25.
Batra
,
R. C.
, and
Xiao
,
J.
, “
Finite Deformations of Full Sine-Wave St.-Venant Beam Due to Tangential and Normal Distributed Loads Using Nonlinear TSNDT
,”
Meccanica
,
50
(
2
), pp.
355
365
.
26.
Cheng
,
Z. Q.
, and
Batra
,
R. C.
,
2000
, “
Deflection Relationship Between the Kirchhoff Plate Theory and Different Functionally Graded Plate Theory
,”
Arch. Mech.
,
52
(
1
), pp.
143
158
.
27.
Cheng
,
Z. Q.
, and
Kitipornchai
,
S.
,
2000
, “
Exact Bending Solution of Inhomogeneous Plates From Homogeneous Thin-Plate Deflection
,”
AIAA J.
,
38
(
7
), pp.
1289
1291
.
28.
Abrate
,
S.
,
2006
, “
Free Vibration, Buckling, and Static Deflections of Functionally Graded Plates
,”
Compos. Sci. Technol.
,
66
(
14
), pp.
2382
2394
.
29.
Abrate
,
S.
,
2008
, “
Functionally Graded Plates Behave Like Homogenous Plates
,”
Compos. Part B: Eng.
,
39
(
1
), pp.
151
158
.
30.
Reddy
,
J. N.
,
Wang
,
C. M.
, and
Kitipomchai
,
S.
,
1999
, “
Axisymmetric Bending of Functionally Graded Circular Plates
,”
Eur. J. Mech.-A/Solids
,
18
(
2
), pp.
185
199
.
31.
Ma
,
L. S.
, and
Wang
,
T. J.
,
2003
, “
Nonlinear Bending and Post-Buckling of a Functionally, Graded Circular Plate Under Mechanical and Thermal Loadings
,”
Int. J. Solids Struct.
,
40
(
13–14
), pp.
3311
3330
.
32.
Cheng
,
Z. Q.
, and
Batra
,
R. C.
,
2000
, “
Exact Correspondence Between Eigenvalues of Membranes and Functionally Graded Simply Supported Polygonal Plates
,”
J. Sound Vib.
,
229
(
4
), pp.
879
895
.
You do not currently have access to this content.