In this paper, the general theoretical analysis of two-dimensional steady-state thermal stresses for a hollow thick cylinder made of functionally graded material is developed. The temperature distribution is assumed to be a function of radial and circumferential directions with general thermal and mechanical boundary conditions on the inside and outside surfaces. The material properties, except Poisson’s ratio, are assumed to depend on the variable r and they are expressed as power functions of r. The separation of variables and complex Fourier series are used to solve the heat conduction and Navier equations.
1.
Lutz
, M. P.
, and Zimmerman
, R. W.
, 1996
, “Thermal Stresses and Effective Thermal Expansion Coefficient of a Functionally Graded Sphere
,” J. Therm. Stresses
, 19
, pp. 39
–54
.2.
Zimmerman
, R. W.
, and Lutz
, M. P.
, 1999
, “Thermal Stress and Thermal Expansion in a Uniformly Heated Functionally Graded Cylinder
,” J. Therm. Stresses
, 22
, pp. 177
–188
.3.
Ootao
, Y.
, Fukuda
, T.
, and Tanigawa
, Y.
, 1989
, “Transient Thermal Stress Analysis of a Multi-Layered Composite Laminate Cylinder and Its Analytical Extension of Non-Homogeneous Materials
,” Theor Appl. Mech.
, 38
, pp. 177
–188
.4.
Ootao
, Y.
, Tanigawa
, Y.
, and Fukuda
, T.
, 1991
, “Axisymmetric Transient Thermal Stress Analysis of a Multilayered Composite Hollow Cylinder
,” J. Therm. Stresses
, 14
, pp. 201
–213
.5.
Ootao
, Y.
, Akai
, T.
, and Tanigawa
, Y.
, 1993
, “Three-Dimensional Transient Thermal Stress of Analysis Nonhomogeneous Circular Cylinder
,” Transationcs. JSME
, , 59
, pp. 1684
–1690
(in Japanese).6.
Ootao
, Y.
, Akai
, T.
, and Tanigawa
, Y.
, 1995
, “Three-Dimensional Transient Thermal Stress Analysis of a Nonhomogeneous Hollow Circular Cylinder due to a Moving Heat Source in the Axial Direction
,” J. Therm. Stresses
, 18
, pp. 497
–512
.7.
Ootao
, Y.
, Tanigawa
, Y.
, and Murakami
, H.
, 1999
, “Transient Thermal Stress and Deformation of a Laminated Composite Beam Due to Partially Distributed Heat Supply
,” J. Therm. Stresses
, 13
, pp. 193
–206
.8.
Han
, X.
, Liu
, G. R.
, and Lam
, K. Y.
, 2000
, “A Quadratic Layer Element For Analyzing Stress Waves in FGMs and Its Application in Material Characterization
,” J. Sound Vib.
, 236
(2
), pp. 307
–321
.9.
Han
, X.
, Liu
, G. R.
, and Lam
, K. Y.
, 2001
, “Transient Waves in Plates of Functionally Graded Materials
,” Int. J. Numer. Methods Eng.
, 52
, pp. 851
–865
.10.
Obata
, Y.
, and Noda
, N.
, 1993
, “Transient Thermal Stress in a Plate of Functionally Gradient Materials
,” Ceramic Transactions
, 34
, p. 403
403
.11.
Obata, Y., and Noda, N., 1995, “Transient Thermal Stresses in a Hollow Sphere of Functionally Gradient Material,” Proceedings of Thermal Stresses, Shizuola University Press, Hamamatsu, Japan, pp. 335–338.
12.
Obata, Y., and Noda, N., 1997, “Two-Dimensional Unsteady Thermal Stresses in a Partially Heated Plate Made of Functionally Graded Material,” Proceedings of Thermal Stresses, Rochester Institute of Technology, Rochester, New York, pp. 735–738.
13.
Obata, Y., Kanayama, K., Ohji, T., and Noda, N., 1999, “Two-Dimensional Unsteady Thermal Stresses in a Partially Heated Circular Cylinder Made of Functionally Graded Material,” Proceedings of Thermal Stresses, Pub. Branti Zew, Krakow, Poland, pp. 595–598.
14.
Tanigawa
, Y.
, Morishita
, H.
, and Ogaki
, S.
, 1999
, “Derivation of Systems of Fundamental Equations for a Three-Dimensional Thermoelastic Field With Nonhomogeneous Material Properties and Its Application to a Semi-Infinite Body
,” J. Therm. Stresses
, 22
, pp. 689
–711
.15.
Tanigawa
, Y.
, Ootao
, Y.
, and Kawamura
, R.
, 1991
, “Thermal Bending of Laminated Composite Rectangular Plates and Nonhomogeneous Plates due to Partial Heating
,” J. Therm. Stresses
, 14
, pp. 285
–308
.Copyright © 2003
by ASME
You do not currently have access to this content.
