A numerical approach for the stress concentration of periodic collinear holes in an infinite plate in tension is presented. It involves the fictitious stress method and a generalization of Bueckner's principle. Numerical examples are concluded to show that the numerical approach is very efficient and accurate for analyzing the stress concentration of periodic collinear holes in an infinite plate in tension. The stress concentration of periodic collinear square holes in an infinite plate in tension is studied in detail by using the numerical approach. The calculated stress concentration factor is proven to be accurate.

References

References
1.
Ling
,
C. B.
,
1948
, “
On the Stresses in a Plate Containing Two Circular Holes
,”
J Appl. Phys.
,
19
(
1
), pp.
77
82
.10.1063/1.1697875
2.
Atsumi
,
A.
,
1956
, “
On the Stresses In a Strip Under Tension and Containing Two Equal Circular Holes Placed Longitudinally
,”
ASME J. Appl. Mech.
,
23
, pp.
555
562
.
3.
Haddon
,
R. A.
,
1967
, “
Stresses In an Infinite Plate With Two Unequal Circular Holes
,”
Q. J. Mech. Appl. Math.
,
20
(
3
), pp.
277
291
.10.1093/qjmam/20.3.277
4.
Kienzler
,
R.
, and
Zhuping
,
D.
,
1987
, “
On the Distribution of Hoop Stresses Around Circular Holes in Elastic Sheets
,”
ASME J. Appl. Mech.
,
54
(
1
), pp.
110
114
.10.1115/1.3172943
5.
Greenwood
,
J. A.
,
1989
, “
Exact Formulate for Stresses Around Circular Holes and Inclusions
,”
Int. J. Mech. Sci.
,
31
(
3
), pp.
219
227
.10.1016/0020-7403(89)90112-4
6.
Howland
,
R. C. J.
,
1935
, “
Stress In a Plate Containing an Infinite Row of Holes
,”
Proc. R. Soc. London, Ser. A
,
148
(
864
), pp.
471
491
.10.1098/rspa.1935.0030
7.
Isida
,
M.
, and
Igawa
,
H.
,
1991
, “
Analysis of a Zig-Zag Array of Circular Holes in an Infinite Solid Under Uniaxial Tension
,”
Int. J. Solids Struct.
,
27
(
7
), pp.
849
864
.10.1016/0020-7683(91)90020-G
8.
Meguid
,
S. A.
,
Kalamkarov
,
A. L.
, and
Yao
,
J.
,
1996
, “
Analytical, Numerical, and Experimental Studies of Effective Elastic Properties of Periodically Perforated Materials
,”
ASME J. Eng. Mater. Technol.
,
118
(
1
), pp.
43
48
.10.1115/1.2805932
9.
Chen
,
Y. Z.
, and
Lin
,
X. Y.
,
2007
, “
Solution of Periodic Group Circular Hole Problems by Using the Series Expansion Variational Method
,”
Int. J. Numer. Meth. Eng.
,
69
(
7
), pp.
1405
1422
.10.1002/nme.1812
10.
Chen
,
Y. Z.
,
2011
, “
Solutions of Periodic Notch Problems With Arbitrary Configuration by Using Boundary Integral Equation and Superposition Method
,”
Acta Mech.
,
221
(
3–4
), pp.
251
260
.10.1007/s00707-011-0499-6
11.
Horii
,
H.
, and
Nemat-Nasser
,
S.
,
1985
, “
Elastic Fields of Interacting Inhomogeneities
,”
Int. J. Solids Struct.
,
21
(
7
), pp.
731
745
.10.1016/0020-7683(85)90076-9
12.
Meguid
,
S. A.
, and
Shen
,
C. L.
,
1992
, “
On the Elastic Fields of Interacting Defense and Main Hole Systems
,”
Int. J. Mech. Sci.
,
34
(
1
), pp.
17
29
.10.1016/0020-7403(92)90050-Q
13.
Ting
,
K.
,
Chen
,
K. T.
, and
Yang
,
W. S.
,
1999
, “
Boundary Element Alternating Method Applied to Analyze the Stress Concentration Problems of Multiple Elliptical Holes in an Infinite Domain
,”
Nucl. Eng. Des.
,
187
(
3
), pp.
303
313
.10.1016/S0029-5493(98)00301-X
14.
Inglis
,
E.
,
1913
, “
Stress in a Plate Due to the Presence of Cracks and Sharp Corners
,”
T. Inst. Naval Arch.
,
55
, pp.
219
242
.
15.
Crouch
,
S. L.
, and
Starfied
,
A. M.
,
1983
,
Boundary Element Method in Solid Mechanics
,
Geore Allon & Unwin
,
Bonton, London, Sydney
.
16.
Yan
,
X.
,
2006
, “
An Effective Numerical Approach for Multiple Void–Crack Interaction
,”
ASME J. Appl. Mech.
,
73
(
4
), pp.
525
535
.10.1115/1.2127955
17.
Yan
,
X.
,
2005
, “
An Efficient and Accurate Numerical Method of SIFs Calculation of a Branched Crack
,”
ASME J. Appl. Mech.
,
72
(
3
), pp.
330
340
.10.1115/1.1796449
18.
Bueckner
,
H. F.
,
1958
, “
The Propagation of Cracks and the Energy of Elastic Deformation
,”
ASME J. Appl. Mech.
,
80
, pp.
1225
1230
.
19.
Masako
,
N.
,
1986
,
Stress Concentration
,
China Machine Press
,
Beijing, China
.
20.
O'Donnell
,
W. J.
, and
Langer
,
B. F.
,
1962
, “
Design of Perforated Plates
,”
J. Eng. Ind.
,
84
(
3
), pp.
307
320
.10.1115/1.3667483
21.
Slot
,
T.
, and
O'Donnell
,
W. J.
,
1971
, “
Effective Elastic Constants of Thick Perforated Plates With Square and Triangular Penetration Patterns
,”
ASME J. Eng. Ind.
,
93
(
4
), pp.
935
942
.10.1115/1.3428087
22.
Reinhardt
,
W.
,
2000
, “
An Equivalent Solid Based Analysis of Broached Tube Support Plates
,”
ASME Press. Vessels Pip. Div.
,
400
, pp.
243
249
.
23.
Kasraie
,
B.
,
Porowski
,
J. S.
,
Badlani
,
M. L.
, and
O'Donnell
,
W. J.
,
1985
, “
Irregular Ligaments in Tubeshellts With Square Penetration Patterns
,”
ASME Press. Vessels Pip. Div.
(Publication) PVP,
98
(
2
), pp.
53
60
.
24.
Porowski
,
J.
, and
O'Donnell
,
W. J.
,
1974
, “
Effective Plastic Constants for Perforated Materials
,”
ASME Pressure Vessels and Piping Technol.
,
96
(
3
), pp.
234
241
.10.1115/1.3454173
25.
Gordon
,
J. L.
, and
Jones
,
D. P.
,
2002
, “
Application of a Sixth Order Generalized Stress Function for Determining Limit Loads for Plates With Triangular Penetration Patterns
,”
ASME Pressure Vessels and Piping Conference Division
, Vancouver, BC, Canada, Aug. 5–9, Vol.
441
, pp.
153
162
.
26.
Porowski
,
J. S.
,
O'Donnell
,
W. J.
,
Tanaka
,
T.
, and
Badlani
,
M.
,
1980
, “
Stress and Strain Concentrations in Perforated Structures Under Steady Creep Conditions
,”
ASME J. Pressure Vessel Technol.
,
102
(
4
), pp.
419
429
.10.1115/1.3263353
27.
Porowski
,
J.
, and
O'Donnell
,
W. J.
,
1975
, “
Plastic Strength of Perforated Plates With Square Penetration Patterns
,”
ASME J. Pressure Vessel Technol.
,
97
(
3
), pp.
146
154
.10.1115/1.3454288
28.
Fil'shtinskii
,
L. A.
,
1964
, “
Stresses and Displacements in an Elastic Sheet Weakened by a Doubly-Periodic Set of Equal Circular Holes
,”
J. Appl. Math. Mech.
,
28
(
3
), pp.
530
543
.10.1016/0021-8928(64)90095-4
29.
Fotoohi
,
K.
, and
Mitri
,
H. S.
,
1996
, “
Non-Linear Fault Behavior Near Underground Excavations-A Boundary Element Approach
,”
Int. J. Numer. Anal. Methods Geomech.
,
20
(
3
), pp.
173
190
.10.1002/(SICI)1096-9853(199603)20:3<173::AID-NAG814>3.0.CO;2-H
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