Based on the small deformation theory and Tresca's yield criterion an axisymmetric, plane strain, elastoplastic, thermal stress analysis for a cylindrical vessel made of functionally graded elastic, perfectly plastic material is offered. Elastic modulus and yield strength coefficients are assumed to be power functions of radius and linear functions of temperature. A cylindrical vessel is taken to be composed of two or more nested fully elastic and perfectly plastic cylinders. By comparing the values of the deformation or stress components in the interfaces of the neighboring cylinders, a system of equations is formed. The interfacial boundary values of the fully elastic or perfectly plastic regions are obtained by simultaneous solution of the resulting interfacial consistency conditions. Having prepared the closed form solutions for the stress fields in purely elastic and purely plastic regions, the distribution of stress throughout the vessel can be obtained. Using this model, in some sample problems, the influences of temperature and pressure on the stress, strain, and plastic zone patterns are studied. The location of plastic zones is obtained for a class of material property compositions.

References

References
1.
Chen
,
W.
,
Ye
,
G.
, and
Cai
,
J.
,
2002
, “
Thermoelastic Stresses in a Uniformly Heated Functionally Graded Isotropic Hollow Cylinder
,”
J. Zheijang Univ. Sci.
,
3
, pp.
1
5
.10.1631/jzus.2002.0001
2.
Kahrobaiyan
,
M. H.
,
Rahaeifard
,
M.
,
Tajalli
,
S. A.
, and
Ahmadian
,
M. T.
,
2012
, “
A Strain Gradient Functionally Graded Euler–Bernoulli Beam Formulation
,”
Int. J. Eng. Sci.
,
52
, pp.
65
76
.10.1016/j.ijengsci.2011.11.010
3.
Ding
,
H. J.
,
Wang
,
H. M.
, and
Chen
,
W. Q.
,
2003
, “
A Solution of a Non-Homogeneous Orthotropic Cylindrical Shell for Axisymmetric Plane Strain Dynamic Thermoelastic Problems
,”
J. Sound Vib.
,
263
, pp.
815
829
.10.1016/S0022-460X(02)01075-1
4.
Liew
,
K. M.
,
Kitipornchai
,
S.
,
Zhang
,
X. Z.
, and
Lim
,
C. W.
,
2003
, “
Analysis of the Thermal Stress Behavior of Functionally Graded Hollow Circular Cylinders
,”
Int. J. Solids Struct.
,
40
, pp.
2355
2380
.10.1016/S0020-7683(03)00061-1
5.
Wang
,
X.
,
Pan
,
E.
, and
Roy
,
A. K.
,
2007
, “
Three-Dimensional Green's Functions for a Steady Point Heat Source in a Functionally Graded Half-Space and Some Related Problems
,”
Int. J. Eng. Sci.
,
45
, pp.
939
950
.10.1016/j.ijengsci.2007.07.003
6.
Shao
,
Z. S.
,
Wang
,
T. J.
, and
Ang
,
K.
,
2007
, “
Transient Thermomechanical Stresses of Functionally Graded Cylindrical Panels
,”
AIAA J.
,
45
, pp.
2487
2496
.
7.
Shao
,
Z. S.
, and
Ma
,
G. W.
,
2008
, “
Thermo-Mechanical Stresses in Functionally Graded Circular Hollow Cylinder With Linearly Increasing Boundary Temperature
,”
Compos. Struct.
,
83
, pp.
259
265
.10.1016/j.compstruct.2007.04.011
8.
Santos
,
H.
,
Soares
,
C. M.
,
Soares
,
C. A.
, and
Reddy
,
J. N.
,
2008
, “
A Semi-Analytical Finite Element Model for the Analysis of Cylindrical Shells Made of Functionally Graded Materials Under Thermal Shock
,”
Compos. Struct.
,
86
, pp.
10
21
.10.1016/j.compstruct.2008.03.004
9.
Hosseini
,
S. M.
,
Akhlaghi
,
M.
, and
Shakeri
,
M.
,
2008
, “
Heat Conduction and Heat Wave Propagation in Functionally Graded Thick Hollow Cylinder Base on Coupled Thermoelasticity Without Energy Dissipation
,”
Heat Mass Transfer
,
44
, pp.
1477
1484
.10.1007/s00231-008-0381-9
10.
Shao
,
Z. S.
,
Ang
,
K. K.
,
Reddy
,
J. N.
, and
Wang
,
T. J.
,
2008
, “
Nonaxisymmetric Thermomechanical Analysis of Functionally Graded Hollow Cylinders
,”
J. Therm. Stresses
,
31
, pp.
515
536
.10.1080/01495730801977879
11.
Gong
,
W.
,
Lam
,
K. Y.
, and
Reddy
,
J. N.
,
1999
, “
The Elastic Response of Functionally Graded Cylindrical Shells to Low-Velocity Impact
,”
Int. J. Impact Eng.
,
22
, pp.
397
417
.10.1016/S0734-743X(98)00058-X
12.
Tutuncu
,
N.
, and
Ozturk
,
M.
,
2001
, “
Exact Solution for Stresses in Functionally Graded Pressure Vessels
,”
Compos. Part B
,
32
, pp.
683
686
.10.1016/S1359-8368(01)00041-5
13.
Nemat-Alla
,
M.
,
Ahmed
,
K. I. E.
, and
Hassab-Allah
,
I.
,
2009
, “
Elastic-Plastic Analysis of Two-Dimensional Functionally Graded Materials Under Thermal Loading
,”
Int. J. Solids Struct.
,
46
, pp.
2774
86
.10.1016/j.ijsolstr.2009.03.008
14.
Obata
,
Y.
, and
Noda
,
N.
,
1994
, “
Steady Thermal Stresses in a Hollow Circular Cylinder and a Hollow Sphere of a Functionally Gradient Material
,”
J. Therm. Stresses
,
17
, pp.
471
487
.10.1080/01495739408946273
15.
Reddy
,
J. N.
, and
Chin
,
C. D.
,
1998
, “
Thermomechanical Analysis of Functionally Graded Cylinders and Plates
,”
J. Therm. Stresses
,
21
, pp.
593
626
.10.1080/01495739808956165
16.
Kim
,
K.
, and
Noda
,
N.
,
2001
, “
Green's Function Approach to Solution the Transient Temperature for Thermal Stresses of Functionally Graded Materials
,”
JSME Int. J. Ser. A
,
44
, pp.
31
36
.10.1299/jsmea.44.31
17.
Ye
,
G. R.
,
Chen
,
W. Q.
, and
Cai
,
J. B.
,
2001
, “
A Uniformly Heated Functionally Graded Cylindrical Shell With Transverse Isotropy
,”
Mech. Res. Commun.
,
28
, pp.
535
542
.10.1016/S0093-6413(01)00206-3
18.
Eraslan
,
A. N.
, and
Akis
,
T.
,
2006
, “
Plane Strain Analytical Solutions for a Functionally Graded Elastic-Plastic Pressurized Tube
,”
Int. J. Pressure Vessel Piping
,
83
, pp.
635
644
.10.1016/j.ijpvp.2006.07.003
19.
Shen
,
H. S.
,
2004
, “
Thermal Postbuckling Behavior of Functionally Graded Cylindrical Shells With Temperature-Dependent Properties
,”
Int. J. Solids Struct.
,
41
, pp.
1961
1974
.10.1016/j.ijsolstr.2003.10.023
20.
Yang
,
J.
,
Liew
,
K. M.
,
Wu
,
Y. F.
, and
Kitipornchai
,
S.
,
2006
, “
Thermo-Mechanical Post-Buckling of, FGM Cylindrical Panels With Temperature-Dependent Properties
,”
Int. J. Solids Struct.
,
43
, pp.
307
324
.10.1016/j.ijsolstr.2005.04.001
21.
Peng
,
X. L.
, and
Li
,
X. F.
,
2010
, “
Thermoelastic Analysis of a Cylindrical Vessel of Functionally Graded Materials
,”
Int. J. Pressure Vessel Piping
,
87
, pp.
203
210
.10.1016/j.ijpvp.2010.03.024
22.
Akis
,
T.
,
2009
, “
Elastoplastic Analysis of Functionally Graded Spherical Pressure Vessels
,”
Comput. Mater. Sci.
,
46
, pp.
545
554
.10.1016/j.commatsci.2009.04.017
23.
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 Vessel Piping
,
79
, pp.
493
497
.10.1016/S0308-0161(02)00043-1
24.
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 Vessel Piping
,
79
, pp.
493
497
.10.1016/S0308-0161(02)00043-1
25.
Wang
,
C. T.
,
1953
,
Applied Elasticity
,
McGraw-Hill Book Company
,
New York
.
You do not currently have access to this content.