In this paper, an analytical method is developed to obtain the solution for the two-dimensional (2D) (r,θ) transient thermal and mechanical stresses in a hollow sphere made of functionally graded (FG) material and piezoelectric layers. The FGM properties vary continuously across the thickness, according to the power functions of radial direction. The temperature distribution as a function of radial and circumferential directions and time is obtained solving the energy equation, using the method of separation of variables and Legendre series. The Navier equations are solved analytically using the Legendre polynomials and the system of Euler differential equations.

References

References
1.
Miyamoto
,
Y.
,
Kaysser
,
W. A.
,
Rabin
,
B. H.
, and
Kawasaki
,
A.
, and
Ford
,
R. G.
,
1999
,
Functionally Graded Materials: Design, Processing and Applications
,
Kluwer Academic Publishers
, Hingham, MA.
2.
Tiersten
,
H. F.
,
1969
, “
Linear Piezoelectric Plate Vibrations
,” Plenum Press, New York.
3.
Jabbari
,
M.
,
Mousavi
,
S. M.
, and
Kiani
,
M. A.
,
2016
, “
Solution for Equation of Two-Dimensional Transient Heat Conduction in FGM Hollow Sphere With Piezoelectric Internal and External Layers
,”
ASME J. Pressure Vessel Technol
,
139
(
1
), p.
011201
.
4.
Lutz
,
M. P.
, and
Zimmerman
,
R. W.
,
1996
, “
Thermal Stresses and Effective Thermal Expansion Coefficient of Functionally Graded Sphere
,”
J. Therm. Stresses
,
19
(
1
), pp.
39
54
.
5.
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
.
6.
Cheung
,
J. B.
,
Chen
,
T. S.
, and
Thirumalai
,
K.
,
1974
, “
Transient Thermal Stresses in a Sphere by Local Heating
,”
ASME J. Appl. Mech.
,
41
(
4
), pp.
930
934
.
7.
Takeuti
,
Y.
, and
Tanigawa
,
Y.
,
1982
, “
Transient Thermal Stresses of a Hollow Sphere Due to Rotating Heat Source
,”
J Therm. Stresses
,
5
(3–4), pp.
283
289
.
8.
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.
,
70
(
1
), pp.
111
118
.
9.
Poultangari
,
R.
,
Jabbari
,
M.
, and
Eslami
,
M. R.
,
2008
, “
Functionally Graded Hollow Spheres Under Non-Axisymmetric Thermo-Mechanical Loads
,”
Int. J. Pressure Vessels Piping
,
85
(
5
), pp.
295
305
.
10.
Jabbari
,
M.
,
Mohazzab
,
A. H.
, and
Bahtui
,
A.
,
2009
, “
One-Dimensional Moving Heat Source in a Hollow FGM Cylinder
,”
ASME J. Appl. Mech.
,
131
(
2
), p. 021202.
11.
Jabbari
,
M.
,
Vaghari
,
A. R.
,
Bahtui
,
A.
, and
Eslami
,
M. R.
,
2008
, “
Exact Solution for Asymmetric Transient Thermal and Mechanical Stresses in FGM Hollow Cylinders With Heat Source
,”
Int. J. Struct. Eng. Mech.
,
29
(
5
), pp.
551
565
.
12.
Ootao
,
Y.
,
Tanigawa
,
Y.
, and
Nakanishi
,
N.
,
1991
, “
Transient Thermal Stress Analysis of a Nonhomogeneous Hollow Sphere Due to Axisymmetric Heat Supply
,”
Trans. Jpn. Soc. Mech. Eng.
,
57
(539), pp.
1581
1587
.
13.
Ootao
,
Y.
, and
Tanigawa
,
Y.
,
1994
, “
Three-Dimensional Transient Thermal Stress Analysis of Nonhomogeneous Hollow Sphere With Respect to Rotating Heat Source
,”
Trans. Jpn. Soc. Mech. Eng.
,
60
(578), pp.
2273
2279
.
14.
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
(
5
), pp.
497
512
.
15.
Chen
,
L. S.
, and
Chu
,
H. S.
,
1989
, “
Transient Thermal Stresses of a Composite Hollow Cylinder Heated by a Moving Line Source
,”
Comput. Struct.
,
33
(
5
), pp.
1205
1214
.
16.
Jabbari
,
M.
,
Bahtui
,
A.
, and
Eslami
,
M. R.
,
2009
, “
Axisymmetric Mechanical and Thermal Stresses in Thick Short Length FGM Cylinder
,”
Int. J. Pressure Vessels Piping
,
86
(
5
), pp.
296
306
.
17.
Sugano
,
Y.
,
Kataoka
,
S.
, and
Tanaka
,
K.
,
1993
, “
Analysis of Transient Thermal Stresses in a Hollow Circular Cylinder of Functionally Gradient Material With Temperature-Dependent Material Properties
,”
A Hen/Trans. Jpn. Soc. Mech. Eng.
,
59
(
A562
), pp.
1505
1513
(Japanese).
18.
Fesharaki
,
J. J.
,
Fesharaki
,
V. J.
,
Yazdipoor
,
M.
, and
Razavian
,
B.
,
2012
, “
Two-Dimensional Solution for Electro-Mechanical Behavior of Functionally Graded Piezoelectric Hollow Cylinder
,”
Appl. Math. Model.
,
36
(
11
), pp.
5521
5533
.
19.
Alibeigloo
,
A.
, and
Nouri
,
V.
,
2010
, “
Static Analysis of Functionally Graded Cylindrical Shell With Piezoelectric Layers Using Differential Quadrature Method
,”
Compos. Struct.
,
92
(8), pp. 1775–1785.
20.
Li
,
X.-F.
,
Peng
,
X.-L.
, and
Lee
,
K. Y.
,
2010
, “
Radially Polarized Functionally Graded Piezoelectric Hollow Cylinders as Sensors and Actuators
,”
Eur. J. Mech. A/Solids
,
29
(4), pp. 704–713.
This content is only available via PDF.
You do not currently have access to this content.