This paper gives an analytic algorithm to plane elastostatic problem of an infinite medium containing two holes of arbitrary shapes and arrangement, using Schwarz’s alternating method, and finds that the method has a very quick convergence speed even for solving a complex double hole problem.

Issue Section:
Brief Notes
Keywords:
elasticity, stress analysis, convergence of numerical methods, iterative methods
Topics:
Algorithms, Stress, Stress analysis (Engineering)
1.
Howland
,
R. C. J.
, and
Knight
,
R. C.
,
1939
, “
Stress Functions for a Plate Containing Groups of Circular Holes
,”
Philos. Trans.
,
238
, pp.
357
–
392
.
2.
Green
,
A. G.
,
1940
, “
General Biharmonic Analysis for a Plate Containing Circular Holes
,”
Proc. R. Soc. London, Ser. A
,
176
, pp.
121
–
139
.
3.
Ling
,
Chin-bing
,
1948
, “
On the Stresses in a Plate Containing Two Circular Holes
,”
J. Appl. Phys.
,
19
, pp.
77
–
82
.
4.
Ukadgaonker
,
V. G.
,
1982
, “
Stress Analysis of a Plate Containing Two Circular Holes Having Tangential Stresses
,”
AIAA J.
,
20
, pp.
125
–
128
.
5.
Hasebe
,
N.
,
Yoshikawa
,
K.
,
Ueda
,
M.
, and
Nakamura
,
T.
,
1994
, “
Plane Elastic Solution for the Second Mixed Boundary Value Problem and Its Application
,”
Archive of Applied Mechanics
,
64
, pp.
295
–
306
.
6.
Muskhelishvili, N. I., 1953, “Some Basic Problems of Mathematical Theory of Elasticity,” P. Noordhoff, Groningen, The Netherlands.
Copyright © 2001
 by ASME
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