In this work, a fractional-order theory of thermoelasticity by quasi-static approach is applied to the two-dimensional problem of a thin circular plate whose lower surface is maintained at zero temperature, whereas the upper surface is insulated and subjected to a constant temperature distribution. Integral transform technique is used to derive the solution in the physical domain. The corresponding thermal stresses are found using the displacement potential function.

References

References
1.
Podlubny
,
I.
,
2002
, “
Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation
,”
Fractional Calculus and Applied Analysis
,
5
(4), pp.
367
386
.https://arxiv.org/abs/math/0110241
2.
Lord
,
H.
, and
Shulman
,
Y.
,
1967
, “
A Generalized Dynamical Theory of Thermoelasticity
,”
J. Mech. Phys. Solids
,
15
(
5
), pp.
299
307
.
3.
Green
,
A. E.
, and
Lindsay
,
K. A.
,
1972
, “
Thermoelasticity
,”
J. Elasticity
,
2
(1), pp.
1
7
.
4.
Green
,
A. E.
, and
Naghdi
,
P. M.
,
1993
, “
Thermoelasticity Without Energy Dissipation
,”
J. Elasticity
,
31
(3), pp.
181
208
.
5.
Chandrasekharaiah
,
D. S.
,
1986
, “
Thermoelasticity With Second Sound: A Review
,”
ASME Appl. Mech. Rev.
,
39
(3), pp.
355
376
.
6.
Tripathi
,
J. J.
,
Kedar
,
G. D.
, and
Deshmukh
,
K. C.
,
2015
, “
Generalized Thermoelastic Diffusion Problem in a Thick Circular Plate With Axisymmetric Heat Supply
,”
Acta Mech.
,
226
(7), pp.
2121
2134
.
7.
Tripathi
,
J. J.
,
Kedar
,
G. D.
, and
Deshmukh
,
K. C.
,
2015
, “
Two Dimensional Generalized Thermoelastic Diffusion in a Half Space Under Axisymmetric Distributions
,”
Acta Mech.
,
226
(
10
), pp.
3263
3274
.
8.
Tripathi
,
J. J.
,
Kedar
,
G. D.
, and
Deshmukh
,
K. C.
,
2016
, “
A Brief Note on Generalized Thermoelastic Response in a Half Space Due to a Periodically Varying Heat Source Under Axisymmetric Distribution
,”
Int. J. Thermodyn.
,
19
(1), pp.
1
6
.
9.
Tripathi
,
J. J.
,
Kedar
,
G. D.
, and
Deshmukh
,
K. C.
,
2016
, “
Dynamic Problem of Fractional Order Thermoelasticity for a Thick Circular Plate With Finite Wave Speeds
,”
J. Therm. Stresses
,
39
(
2
), pp.
220
230
.
10.
Povstenko
,
Y.
,
2004
, “
Fractional Heat Conduction Equation and Associated Thermal Stresses
,”
J. Therm. Stresses
,
28
(1), pp.
83
102
.http://dx.doi.org/10.1080/014957390523741
11.
Povstenko
,
Y.
,
2009
, “
Thermoelasticity Which Uses Fractional Heat Conduction Equation
,”
J. Math. Sci.
,
162
(2), pp.
296
305
.
12.
Povstenko
,
Y.
,
2009
, “
Theory of Thermoelasticity Based on the Space-Time-Fractional Heat Conduction Equation
,”
Phys. Scr.
,
2009
(T136), p.
014017
.http://iopscience.iop.org/article/10.1088/0031-8949/2009/T136/014017/pdf
13.
Povstenko
,
Y.
,
2010
, “
Signaling Problem for Time-Fractional Diffusion-Wave Equation in a Half-Plane in the Case of Angular Symmetry
,”
Nonlinear Dyn.
,
59
(4), pp.
593
605
.
14.
Povstenko
,
Y.
,
2010
, “
Fractional Cattaneo-Type Equations and Generalized Thermoelasticity
,”
J. Therm. Stresses
,
34
(2), pp.
97
114
.
15.
Povstenko
,
Y.
,
2012
, “
Theories of Thermal Stresses Based on Space-Time-Fractional Telegraph Equations
,”
Comput. Math. Appl.
,
64
(10), pp.
3321
3328
.
16.
Raslan
,
W. E.
,
2015
, “
Application of Fractional Order Theory of Thermoelasticity in a Thick Plate Under Axisymmetric Temperature Distribution
,”
J. Therm. Stresses
,
38
(
7
), pp.
733
743
.
17.
Sherief
,
H.
,
El-Sayed
,
A.
, and
Abd El-Latief
,
A. M.
,
2010
, “
Fractional Order Theory of Thermoelasticity
,”
Int. J. Solids Struct.
,
47
(2), pp.
269
275
.
18.
Raslan
,
W. E.
,
2014
, “
Application of Fractional Order Theory of Thermoelasticity to a 1D Problem for a Cylindrical Cavity
,”
Arch. Mech.
,
66
(4), pp.
257
267
.http://am.ippt.pan.pl/am/article/view/v66p257
19.
Aouadi
,
M.
,
2006
, “
A Generalized Thermoelastic Diffusion Problem for an Infinitely Long Solid Cylinder
,”
Int. J. Math. Math. Sci.
,
2006
, p.
25976
.
20.
Povstenko
,
Y.
,
2016
, “
Fractional Heat Conduction in a Space With a Source Varying Harmonically in Time and Associated Thermal Stresses
,”
J. Therm. Stresses
,
39
(
11
), pp.
1442
1450
.
21.
Kulkarni
,
V. S.
,
Deshmukh
,
K. C.
, and
Warbhe
,
S. D.
,
2008
, “
Quasi-Static Thermal Stresses Due to Heat Generation in a Thin Hollow Circular Disk
,”
J. Therm. Stresses
,
31
(8), pp.
698
705
.
22.
Deshmukh
,
K. C.
,
Warbhe
,
S. D.
, and
Kulkarni
,
V. S.
,
2009
, “
Quasi-Static Thermal Deflection of a Thin Clamped Circular Plate Due to Heat Generation
,”
J. Therm. Stresses
,
32
(9), pp.
877
886
.
23.
Deshmukh
,
K. C.
,
Warbhe
,
S. D.
, and
Kulkarni
,
V. S.
,
2011
, “
Brief Note on Heat Flow With Arbitrary Heating Rates in a Hollow Cylinder
,”
J. Therm. Stresses
,
15
(
1
), pp.
275
280
.
24.
Podlubny
,
I.
,
1999
,
Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, Some Methods of Their Solution and Some of Their Applications
,
Academic Press
,
New York
.
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