In two-dimensional thermoelasticity, Green’s functions of the external force boundary value problem are derived for an infinite plane with an arbitrary shaped hole under adiabatic and isothermal boundary conditions subjected to heat sources in two cases as follows. One is the case of a heat source and a heat sink arbitrarily located within the plane, the other is the case of a heat source arbitrarily located within the plane and a heat sink at infinity. Complex stress functions, temperature function, a rational mapping function, and the thermal dislocation method are used for the analysis. In analytical examples, distributions of temperature, heat flux, and stresses are shown for an infinite plane with a rectangular hole under adiabatic and isothermal boundary conditions.

Issue Section:
Technical Papers
Topics:
Heat, Boundary-value problems, Heat sinks, Stress, Temperature, Dislocations, Heat flux, Thermoelasticity
1.
Florence
A. L.
, and
Goodier
J. N.
,
1960
, “
Thermal Stresses due to Disturbance of Uniform Heat Flow by an Insulated Ovaloid Hole
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
27
, pp.
635
–
639
.
2.
Fukui
K.
,
Fukui
T.
, and
Kaibori
H.
,
1970
, “
Thermal Stresses of the Elastic Plane With a Circular Hole, Including One Heat Source
,”
Transactions of the Japan Society of Mechanical Engineers
, Vol.
36
, No.
291
, pp.
1772
–
1776
.
3.
Fukui
T.
, and
Fukui
K.
,
1974
, “
Thermal Stresses Around Circular Inclusion Due to Heat Source and Sink One
,”
Transactions of the Japan Society of Mechanical Engineers
, Vol.
40
, No.
340
, pp.
3275
–
3283
.
4.
Hasebe
N.
, and
Ueda
M.
,
1980
, “
Crack Originating from a Corner of a Square Hole
,”
Engineering Fracture Mechanics
, Vol.
13
, pp.
913
–
923
.
5.
Hasebe
N.
, and
Inohara
S.
,
1981
, “
Stress Intensity Factor at a Bilaterally-Bent Crack in the Bending Problem of Thin Plane
,”
Engineering Fracture Mechanics
, Vol.
14
, No.
3
, pp.
607
–
616
.
6.
Hasebe
N.
,
Keer
L. M.
, and
Nemat-Nasser
S.
,
1984
, “
Stress Analysis of a Kinked Crack Initiating from a Rigid Line Inclusion, Part I: Formulation
,”
Mechanics of Materials
, Vol.
3
, pp.
131
–
145
.
7.
Hasebe
N.
,
Tomida
A.
,
and Nakamura
T.
,
1988
, “
Thermal Stresses of a Cracked Circular Hole due to Uniform Heat Flux
,”
Journal of Thermal Stresses
, Vol.
11
, pp.
381
–
391
.
8.
Hasebe
N.
,
Irikura
H.
, and
Nakamura
T.
,
1991
, “
A Solution of the Mixed Boundary Value Problem for an Infinite Plane With a Hole Under Uniform Heat Flux
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
113
, pp.
996
–
1000
.
9.
Muskhelishvili, N. I., 1963, Some Basic Problems of Mathematical Theory of Elasticity, 4th ed., Martinus Noordhoff, Dordrecht, The Netherlands.
10.
Nisitani
H.
,
Saimoto
A.
,
Noguchi
H.
, and
Chert
D. H.
,
1991
, “
Method of Analysis of Two-Dimensional Stationary Thermo-elastic Problem by a Body Force Method (1st Report, The Basic Theory)
,”
Transactions of the Japan Society of Mechanical Engineers
, Vol.
57
, No.
542
, pp.
2561
–
2567
.
11.
Yoshikawa, K., and Hasebe, N., 1998, “Heat Source in Infinite Plane with Elliptical Rigid Inclusion and Hole,” ASCE Journal of Engineering Mechanics, submitted for publication.
12.
Zhang
X.
, and
Hasebe
N.
,
1993
, “
Basic Singular Thermoelastic Solutions for a Crack
,”
International Journal of Fracture
, Vol.
62
, pp.
97
–
118
.
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