Abstract

An incline-loaded finite aluminum plate containing two different-size colinear round holes is stress analyzed from associated thermal data. The neighboring holes, which are aligned with the width of the plate, are sufficiently close together than their stress fields interact. While results are supported here by those from finite elements and strain gages, a motivation for the presented approach is for where finite element methods are impracticable, e.g., when loads are unreliable or unavailable. Representative of situations when applied loads are not well-known, the present finite element results, while acceptable, are not as reliable as those from strain gages. The present methodology is applicable to other geometries or loading as well as to members fabricated from nonisotropic materials. The technique can provide stress concentrations in finite perforated geometries for varying distance between holes. This ability was previously limited to infinite members. Some of the highlights are as follows: (1) Experimentally determine stresses throughout region containing different-diameter holes whose stresses interact. (2) Colinear holes in inclined finite tensile plate transversely aligned to its longitudinal direction. (3) Suitable for isotropic or anisotropic materials. (4) Valid for other loading conditions or geometries. (5) Important design implications for pressure-vessel members.

References

1.
Jindal
,
U. C.
,
1983
, “
Reduction of Stress Concentration Around a Hole in a Uniaxially Loaded Plate
,”
J. Strain Anal.
,
18
(
2
), pp.
35
141
.10.1243/03093247V182135
2.
Rhee
,
J.
,
Cho
,
H. K.
,
Marr
,
R. J.
, and
Rowlands
,
R. E.
,
2012
, “
Local Compliance, Stress Concentrations and Strength in Orthotropic Materials
,”
J. Stress Anal. Eng. Des.
,
47
(
2
), pp.
113
128
.10.1177/0309324711426517
3.
Rajaiah
,
K.
, and
Naik
,
N. K.
,
1984
, “
Hole-Shape Optimization in a Finite Plate in the Presence of Auxiliary Holes
,”
Exp. Mech.
,
24
(
2
), pp.
157
161
.10.1007/BF02324999
4.
Meguid
,
S. A.
, and
Gong
,
S. X.
,
1993
, “
Stress Concentration Around Interacting Circular Holes: A Comparison Between Theory and Experiments
,”
Eng. Fract. Mech.
,
44
(
2
), pp.
247
256
.10.1016/0013-7944(93)90049-X
5.
Howland
,
R. C. J.
, and
Knight
,
R. C.
,
1939
, “
Stress Function for Plates Containing Groups of Circular Holes
,”
Phys. Trans. R. Soc., London, Ser. A
,
238
, pp.
357
392
.10.1098/rsta.1939.0010
6.
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
7.
Savin
,
G. N.
,
1961
, “
Stress Concentrations Around Holes, Pergamon Press; Also Stress Distribution Around Holes, 1968
,” National Aeronautics and Space Administration, Washington, DC, Report No.
NASA TT F-607
.https://www.abbottaerospace.com/downloads/nasa-tt-f-607-stress-distribution-around-holes/
8.
Salerno
,
V. L.
, and
Mahoney
,
J. B.
,
1968
, “
Stress Solution for an Infinite Plate Containing Two Arbitrary Circular Holes Under Equal Biaxial Stresses
,”
ASME J. Eng. Ind.
,
90
(
4
), pp.
656
665
.10.1115/1.3604705
9.
Hulbert
,
L. E.
,
1963
, “
The Numerical Solution of Two-Dimensional Problems of Theory of Elasticity
,”
Ph.D. thesis
,
Ohio State University
,
Columbus, OH
.https://www.proquest.com/openview/6725a99cd06eac21d3b14dc501481b50/1?pqorigsite=gscholar&cbl=18750&diss=y
10.
Davies
,
G. A. O.
, and
Hoddinott
,
J. R.
,
1963
, “
Stresses in a Plate Pierced by Two Unequal Circular Holes
,”
Aeronaut. J.
,
67
, pp.
451
452
. (Published online by Cambridge University Press, July 4, 2016).10.1017/S036839310007886X
11.
Haddon
,
R. A. W.
,
1967
, “
Stresses in an Infinite Plate With Two Unequal Circular Holes
,”
Q. J. Mech. Appl. Math.
,
20
, pp.
277
291
.10.1093/qjmam/20.3.277
12.
Pilkey
,
W. D.
, and
Pilkey
,
D. F.
,
2008
,
Peterson's Stress Concentration Factors
, 3rd ed.,
Wiley
,
Hoboken, NJ
, Chart 4.31.
13.
Mori
,
K.
,
1972
, “
Stress Distribution in a Semi-Infinite Plate With a Row of Circular Holes
,”
Jpn. Soc. Mech. Eng.
,
18
(
86
), pp.
899
906
.10.1299/jsme1958.15.899
14.
Kosmodamianskii
,
A. S.
, and
Chernik
,
V. I.
,
1981
, “
Stress State of Plate Weakened by Two Elliptical Holes With Parallel Axes
,”
Sov. Appl. Mech.
,
17
(
6
), pp.
576
581
.10.1007/BF00885716
15.
Ukadgonker
,
V. G.
,
Avargerimath
,
R. R.
, and
Koranne
,
S. D.
,
1995
, “
Stress Analysis of an Infinite Plate Containing Two Unequal Collinear Elliptical Holes Under In-Plane Stresses at Infinity
,”
Indian J. Eng. Mater. Sci.
,
2
, pp.
62
79
.https://nopr.niscpr.res.in/handle/123456789/29829
16.
Zimmerman
,
R. W.
,
1988
, “
Stress Singularity Around Two Nearby Holes
,”
Mech. Res. Commun.
,
15
(
2
), pp.
87
90
.10.1016/0093-6413(88)90057-2
17.
Zimmerman
,
R. W.
,
1988
, “
Second Order Approximation for the Compression of an Elastic Plate Containing a Pair of Circular Holes
,”
ZAMM (Z. Angew., Math. Mech.)
,
68
, pp.
575
577
.10.1002/zamm.19880681122
18.
Zeng
,
X. T.
,
Lu
,
A. Z.
, and
Zhang
,
N.
,
2018
, “
Analytical Stress Solution for an Infinite Plate Containing Two Oval Holes
,”
Eur. J. Mech. – A/Solids
,
67
, pp.
291
304
.10.1016/j.euromechsol.2017.09.011
19.
Lu
,
A. Z.
,
Xu
,
Z.
, and
Zhang
,
N.
,
2017
, “
Stress Analytical Solution for an Infinite Plane Containing Two Holes
,”
Int. J. Mech. Sci.
,
128–129
, pp.
224
234
.10.1016/j.ijmecsci.2017.04.025
20.
Zeng
,
X. T.
, and
Lu
,
A. Z.
,
2019
, “
Stress Solution for an Infinite Elastic Plate Containing Two Arbitrarily Shaped Holes
,”
AIAA J.
,
57
(
4
), pp.
1691
1701
.10.2514/1.J057578
21.
Jafari
,
M.
, and
Mahmodzade Hoseyni
,
S. A.
,
2016
, “
Optimization of Infinite Orthotropic Plates With Hypotrochoid Cutout Under Tensile Loading Using Genetic Algorithm
,”
J. Reinf. Plast. Compos.
,
36
(
5
), pp.
360
376
.10.1177/0731684416676634
22.
Mirji
,
P.
,
2013
, “
Optimization of Rectangular Plate With Two Holes Subjected to In-Plane Loading
,”
Int. J. Sci. Eng. Res.
,
4
(
6
), pp.
1470
1473
.https://www.ijser.org/researchpaper/Optimization-Of-Rectangular-Plate-With-Two-Holes-Subjected-to-In-Plane-Static-Loading.pdf
23.
Khaja
,
A. A.
, and
Rowlands
,
R. E.
,
2017
, “
Stresses Associated With Multiple Holes Whose Individual Stresses Interact
,”
J. Strain Anal. Des.
,
52
(
3
), pp.
162
176
.10.1177/0309324717690282
24.
Khaja
,
A. A.
, and
Rowlands
,
R. E.
,
2022
, “
Stress Analysis of Finite Plate Containing Two Neighboring Unequal Diameter Holes Subjected to Transverse Tensile Loads
,”
Int. J. Pressure Vessels Piping
,
200
, p.
104758
.10.1016/j.ijpvp.2022.104758
25.
Samad
,
W. A.
, and
Rowlands
,
R. E.
,
2017
, “
Individual Stress Determination in Irregularly Perforated Unsymmetrically-Loaded Structures From Temperature Data
,”
J. Aerosp. Sci. Technol.
,
63
, pp.
91
99
.10.1016/j.ast.2016.12.021
26.
Lin
,
S. J.
,
2007
, “
Two-and Three-Dimensional Hybrid Photomechanical-Numerical Stress Analysis
,”
Ph.D. thesis
,
University of Wisconsin-Madison
,
Madison, WI
.https://books.google.co.in/books/about/Two_and_Three_dimensional_Hybrid_Photome.html?id=N7usAAAAMAAJ&redir_esc=y
27.
Khaja
,
A. A.
,
2012
, “
Experimentally Determined Full-Field Stress, Strain and Displacements of Perforated Finite Members
,”
Ph.D. thesis
,
University of Wisconsin-Madison
,
Madison, WI
.https://dp.la/item/00fc410d82c52a1ae3fc07d2722d4da5
28.
Greene
,
R. J.
,
Patterson
,
E. A.
, and
Rowlands
,
R. E.
,
2008
, “
Thermoelastic Stress Analysis
,”
Handbook of Experimental Solid Mechanics
,
W. M.
Sharpe
, ed.,
Springer
,
New York
, Chap.
26
.
29.
Soutas-Little
,
R. W.
,
1998
,
Elasticity
,
Dover Publications
,
Mineola, NY
.
30.
Cho
,
H. K.
, and
Rowlands
,
R. E.
,
2007
, “
Reducing Tensile Stress Concentration in Perforated Hybrid Laminate by Genetic Algorithm
,”
Compos. Sci. Technol.
,
67
, pp.
2877
2888
.10.1016/j.compscitech.2006.09.022
31.
Haj-Ali
,
R.
,
Wei
,
B. S.
,
Johnson
,
S.
, and
El-Hajjar
,
R.
,
2008
, “
Thermoelastic and Infrared-Thermography Methods for Surface Strains in Cracked Orthotropic Composite Materials
,”
Eng. Fract. Mech.
,
75
(
1
), pp.
58
75
.10.1016/j.engfracmech.2007.02.014
32.
Khaja
,
A. A.
, and
Rowlands
,
R. E.
,
2012
, “
Experimentally Determined Stresses Associated With Elliptical Holes Using Polar Coordinates
,”
Strain
,
49
(
2
), pp.
116
124
.10.1111/str.12018
33.
Dewangan
,
H. C.
,
Sharma
,
N.
, and
Panda
,
S. K.
,
2022
, “
Thermomechanical Loading and Cutout Effect on Static and Dynamic Responses of Multilayered Structure With TD Prophies
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
236
(
16
), pp.
9081
9094
.10.1177/09544062221089153
You do not currently have access to this content.