Full Text:   <3553>

CLC number: O34

On-line Access: 

Received: 2008-05-28

Revision Accepted: 2008-11-06

Crosschecked: 2009-01-09

Cited: 17

Clicked: 7994

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2009 Vol.10 No.3 P.327-336


3D thermoelasticity solutions for functionally graded thick plates

Author(s):  Ji YING, Chao-feng LÜ,, C. W. LIM

Affiliation(s):  Department of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China; more

Corresponding email(s):   lucf@zju.edu.cn

Key Words:  Functionally graded plates, Semi-analytical solutions, 3D thermoelasticity, Mori-Tanaka method

Ji YING, Chao-feng LÜ, C. W. LIM. 3D thermoelasticity solutions for functionally graded thick plates[J]. Journal of Zhejiang University Science A, 2009, 10(3): 327-336.

@article{title="3D thermoelasticity solutions for functionally graded thick plates",
author="Ji YING, Chao-feng LÜ, C. W. LIM",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T 3D thermoelasticity solutions for functionally graded thick plates
%A Chao-feng LÜ
%A C. W. LIM
%J Journal of Zhejiang University SCIENCE A
%V 10
%N 3
%P 327-336
%@ 1673-565X
%D 2009
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0820406

T1 - 3D thermoelasticity solutions for functionally graded thick plates
A1 - Ji YING
A1 - Chao-feng LÜ
A1 -
A1 - C. W. LIM
J0 - Journal of Zhejiang University Science A
VL - 10
IS - 3
SP - 327
EP - 336
%@ 1673-565X
Y1 - 2009
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A0820406

Thermal-mechanical behavior of functionally graded thick plates, with one pair of opposite edges simply supported, is investigated based on 3D thermoelasticity. As for the arbitrary boundary conditions, a semi-analytical solution is presented via a hybrid approach combining the state space method and the technique of differential quadrature. The temperature field in the plate is determined according to the steady-state 3D thermal conduction. The mori-Tanaka method with a power-law volume fraction profile is used to predict the effective material properties including the bulk and shear moduli, while the effective coefficient of thermal expansion and the thermal conductivity are estimated using other micromechanics-based models. To facilitate the implementation of state space analysis through the thickness direction, the approximate laminate model is employed to reduce the inhomogeneous plate into a homogeneous laminate that delivers a state equation with constant coefficients. The present solutions are validated by comparisons with the exact ones for both thin and thick plates. Effects of gradient indices, volume fraction of ceramics, and boundary conditions on the thermomechanical behavior of functionally graded plates are discussed.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Bellman, R.E., Casti, J., 1971. Differential quadrature and long-term integration. Journal of Mathematical Analysis and Applications, 34(2):235-238.

[2] Bian, Z.G., Chen, W.Q., Lim, C.W., Zhang, N., 2005. Analytical solutions for single- and multi-span functionally graded plates in cylindrical bending. International Journal of Solids and Structures, 42(24-25):6433-6456.

[3] Chen, W.Q., Lüe, C.F., 2005. 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported. Composite Structures, 69(1):77-87.

[4] Chen, W.Q., Lv, C.F., Bian, Z.G., 2003a. Elasticity solution for free vibration of laminated beams. Composite Structures, 62(1):75-82.

[5] Chen, W.Q., Bian, Z.G., Ding, H.J., 2003b. Three-dimensional analysis of a thick FGM rectangular plate in thermal environment. Journal of Zhejiang University SCIENCE, 4(1):1-7.

[6] Chen, W.Q., Lv, C.F., Bian, Z.G., 2004. Free vibration analysis of generally laminated beams via state-space-based differential quadrature. Composite Structures, 63(3-4):417-425.

[7] Cheng, Z.Q., Batra, R.C., 2000. Three-dimensional thermoelastic deformations of a functionally graded elliptic plate. Composites Part B: Engineering, 31(2):97-106.

[8] Ding, H.J., Chen, W.Q., Zhang, L.C., 2006. Elasticity of Transversely Isotropic Materials. Springer, Dordrecht.

[9] Hatta, H., Taya, M., 1985. Effective thermal conductivity of a Misoriented short fiber composite. Journal of Applied Physics, 58(7):2478-2486.

[10] Kashtalyan, M., 2004. Three-dimensional elasticity solution for bending of functionally graded rectangular plates. European Journal of Mechanics-A/Solids, 23(5):853-864.

[11] Koizumi, M., 1997. FGM activities in Japan. Composites Part B: Engineering, 28(1-2):1-4.

[12] Lü, C.F., Chen, W.Q., 2005. Free vibration of orthotropic functionally graded beams with various end conditions. Structural Engineering and Mechanics, 20(4):465-476.

[13] Lü, C.F., Chen, W.Q., Zhong, Z., 2006. Two-dimensional thermoelasticity solution for functionally graded thick beams. Science in China Series G: Physics, Mechanics and Astronomy, 49(4):451-460.

[14] Lü, C.F., Lim, C.W., Xu, F., 2007. Stress analysis of anisotropic thick laminates in cylindrical bending using a semi-analytical approach. Journal of Zhejiang University SCIENGE A, 8(11):1740-1745.

[15] Lü, C.F., Chen, W.Q., Xu, R.Q., Lim, C.W., 2008. Semi-analytical elasticity solutions for bi-directional functionally graded beams. International Journal of Solids and Structures, 45(1):258-275.

[16] Matsunaga, H., 2008. Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory. Composite Structures, 82(4):499-512.

[17] Mian, A.M., Spencer, A.J.M., 1998. Exact solutions for functionally graded and laminated elastic materials. Journal of the Mechanics and Physics of Solids, 46(12):2283-2295.

[18] Mori, T., Tanaka, K., 1973. Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metallurgica, 21(5):571-574.

[19] Reddy, J.N., 2000. Analysis of functionally graded plates. International Journal for Numerical Methods in Engineering, 47(1-3):663-684.

[20] Reddy, J.N., Cheng, Z.Q., 2001. Three-dimensional thermomechanical deformations of functionally graded rectangular plates. European Journal of Mechanics-A/Solids, 20(5):841-855.

[21] Rosen, B.W., Hashin, Z., 1970. Effective thermal expansion coefficients and specific heats of composite materials. International Journal of Engineering Science, 8(2):157-173.

[22] Sherbourne, A.N., Pandey, M.D., 1991. Differential quadrature method in the buckling analysis of beams and composite plates. Computers and Structures, 40(4):903-913.

[23] Shu, C., 2000. Differential Quadrature and Its Application in Engineering. Springer-Verlag, London.

[24] Tanaka, K., Tanaka, Y., Enomoto, K., Poterasu, V.F., Sugano, Y., 1993. Design of thermoelastic materials using direct sensitivity and optimization methods. Reduction of thermal stresses in functionally gradient materials. Computer Methods in Applied Mechanics and Engineering, 106(1-2):271-284.

[25] Tarn, J.Q., Wang, Y.M., 1995. Asymptotic thermoelastic analysis of anisotropic inhomogeneous and laminated plates. Journal of Thermal Stresses, 18(1):35-58.

[26] Vel, S.S., Batra, R.C., 2002. Exact solution for thermoelastic deformations of functionally graded thick rectangular plates. AIAA Journal, 40(7):1421-1433.

[27] Vel, S.S., Batra, R.C., 2003. Three-dimensional thermoelastic analysis of transient thermal stresses in functionally graded plates. International Journal of Solids and Structures, 40(25):7181-7196.

[28] Zhong, Z., Shang, E.T., 2003. Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate. International Journal of Solids and Structures, 40(20):5335-5352.

[29] Zhong, Z., Shang, E.T., 2005. Exact analysis of simply supported functionally graded piezothermoelectric plates. Journal of Intelligent Material Systems and Structures, 16(7-8):643-651.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE