This paper presents the analytical solution of one-dimensional mechanical and thermal stresses for a hollow cylinder made of functionally graded material. The material properties vary continuously across the thickness, according to the power functions of radial direction. Temperature distribution is symmetric and transient. The thermal boundary conditions may include conduction, flux, and convection for inside or outside of a hollow cylinder. The thermoelasticity equation is transient, including the moving heat source. The heat conduction and Navier equations are solved analytically, using the generalized Bessel function. A direct method of solution of Navier equation is presented.
Issue Section:
Design and Analysis
1.
Zimmerman
, R. W.
, and Lutz
, M. P.
, 1999, “Thermal Stresses and Thermal Expansion in a Uniformly Heated Functionally Graded Cylinder
,” J. Therm. Stresses
0149-5739, 22
(2
), pp. 177
–188
.2.
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
,” Theoretical Appl. Mech.
, 38
, pp. 177
–188
.3.
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 a Axial Direction
,” J. Therm. Stresses
0149-5739, 18
, pp. 497
–512
.4.
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
, Cracow
, pp. 595
–598
.5.
Tutuncu
, N.
, and Ozturk
, M.
, 2001, “Exact Solutions for Stresses in Functionally Graded Pressure Vessels
,” Composites, Part B
1359-8368, 32
(8
), pp. 683
–686
.6.
Tarn
, J. Q.
, 2001, “Exact Solutions for Functionally Graded Anisotropic Cylinders Subjected to Thermal and Mechanical Loads
,” Int. J. Solids Struct.
0020-7683, 38
(47–47
), pp. 8189
–8206
.7.
Aboudi
, J.
, Pindera
, M. J.
, and Arnolds
, S. M.
, 1996, “Thermoplasticity Theory for Bidirectionally Functionally Graded Materials
,” J. Therm. Stresses
0149-5739, 19
, pp. 809
–861
.8.
Jabbari
, M.
, Sohrabpour
, S.
, and Eslami
, M. R.
, 2002, “Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder Due to Radially Symmetric Loads
,” Int. J. Pressure Vessels Piping
0308-0161, 79
, pp. 493
–497
.9.
Jabbari
, M.
, Sohrabpour
, S.
, and Eslami
, M. R.
, 2003, “General Solution for Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder Due to Nonaxisymmetric Steady-State Loads
,” ASME J. Appl. Mech.
0021-8936, 70
, pp. 111
–118
.10.
Jabbari
, M.
, Bahtui
, A.
, and Eslami
, M. R.
, 2006, “Axisymmetric Mechanical and Thermal Stresses in Thick Long FGM Cylinders
,” J. Therm. Stresses
0149-5739, 29
(7
), pp. 643
–663
.11.
Chu
, H. S.
, Chen
, J. M.
, and Tzou
, J. H.
, 1986, “Transient Response of a Composite Hollow Cylinder Heated by a Moving Line Source With Hyperbolic Heat Conduction Equation
,” Proceedings of Int. J. Heat Transfer Conference
, Vol. 2
, pp. 621
–626
.12.
Eslami
, M. R.
, Babai
, M. H.
, and Poultangari
, R.
, 2005, “Thermal and Mechanical Stresses in a Functionally Graded Thick Sphere
,” Int. J. Pressure Vessels Piping
0308-0161, 82
(7
), pp. 522
–527
.13.
Necati Özişik
, M.
, 1980, Heat Conduction
, Wiley & Sons
.14.
Rice
, R. G.
, and Do
, D. D.
, 1995, Applied Mathematics and Modeling for Chemical Engineering
, Wiley & Sons
, New York
, pp. 131
–132
.15.
Tyn
, Myint-U
, 1980
, Partial Differential Equations of Mathematical Physics
, Elsevier
, North Holland
.16.
Ueda
, S.
, 2001, “Elastoplastic Analysis OF W–Cu Functionally Graded Materials Subjected to a Thermal Shock by Micromechanical Model
,” J. Therm. Stresses
0149-5739, 24
(7
), pp. 631
–649
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