0
Research Papers

Extended Green’s Solution for the Stresses in an Infinite Plate With Two Equal or Unequal Circular Holes

[+] Author and Article Information
Son K. Hoang

School of Civil Engineering and Environmental Science, The University of Oklahoma, 100 East Boyd Street, Sarkeys Energy Center, Suite P119, Norman, OK 73019-1014; PoroMechanics Institute, The University of Oklahoma, 100 East Boyd Street, Sarkeys Energy Center, Suite P119, Norman, OK 73019-1014sonhoang@ou.edu

Younane N. Abousleiman

Mewbourne School of Petroleum and Geological Engineering, The University of Oklahoma, 100 East Boyd Street, Sarkeys Energy Center, Suite P119, Norman, OK 73019-1014; School of Geology and Geophysics, The University of Oklahoma, 100 East Boyd Street, Sarkeys Energy Center, Suite P119, Norman, OK 73019-1014; School of Civil Engineering and Environmental Science, The University of Oklahoma, 100 East Boyd Street, Sarkeys Energy Center, Suite P119, Norman, OK 73019-1014; PoroMechanics Institute, The University of Oklahoma, 100 East Boyd Street, Sarkeys Energy Center, Suite P119, Norman, OK 73019-1014yabousle@ou.edu

J. Appl. Mech 75(3), 031016 (May 02, 2008) (13 pages) doi:10.1115/1.2793803 History: Received June 09, 2007; Revised August 23, 2007; Published May 02, 2008

The distribution of stress in an isotropic and infinitely large plate perforated by circular holes has long attracted attention from both mathematical and engineering standpoints. Unfortunately, almost all existing solutions are only applicable to stress-free conditions at the boundary of the holes, which is not always the case in engineering applications. In an attempt to cover a wider range of applications, this paper presents the exact explicit solution for the stress distribution in an infinite plate containing two equal/unequal circular holes subjected to general in-plane stresses at infinity and internal pressures inside the holes, following the approach proposed by Green (1940, “General Bi-Harmonic Analysis for a Plate Containing Circular Holes  ,” Proc. R. Soc. London, Ser. A, 176(964), pp. 121–139). The newly derived general solution has been verified not only with published solutions for special cases but also qualitatively with a comparable experimental testing program. In addition, some numerical examples are also provided to offer insight into the complexity of the interplay of parameters.

Copyright © 2008 by American Society of Mechanical Engineers
Topics: Stress
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 2

Tangential stress at the boundary of either hole for different stress anisotropy (Ling’s solution for λ=1.20), identical to the results by Bargui and Abousleiman (11)

Grahic Jump Location
Figure 3

Maximum tangential stress at the boundary of the holes when only Hole 2 is pressurized (identical to the results by Iwaki and Miyao (3))

Grahic Jump Location
Figure 4

Sketch of breakout shapes. Reproduced from Papanastasiou (13-14)

Grahic Jump Location
Figure 5

Distribution of major principal stress reproducing the stress pattern in Fig. 4, Experiment 1: SH=1, Sh=1, α=0deg, P1=P2=0

Grahic Jump Location
Figure 6

Distribution of major principal stress reproducing the stress pattern in Fig. 4, Experiment 3: SH=1, Sh=0.6, α=90deg, P1=P2=0

Grahic Jump Location
Figure 10

Tangential stress at the boundary of either hole for a1=a2=1, S1=1, S2=0.8, α=30deg, P1=P2=0.2

Grahic Jump Location
Figure 11

Tangential stress at the boundary of either hole for a1=a2=1, S1=1, S2=0.8, α=60deg, P1=P2=0.2

Grahic Jump Location
Figure 12

Tangential stress at the boundary of either hole for a1=a2=1, S1=1, S2=0.8, α=90deg, P1=P2=0.2

Grahic Jump Location
Figure 18

Tangential stress at the boundary of Hole 2 for a1=a2=1, S1=1, S2=0.8, α=0deg, P1=0.2, P2=0

Grahic Jump Location
Figure 19

Tangential stress at the boundary of Hole 1 for a1=1, a2=0.5, S1=1, S2=0.8, α=0deg, P1=P2=0.2

Grahic Jump Location
Figure 22

Tangential stress at the boundary of Hole 2 for a1=1, a2=0.25, S1=1, S2=0.8, α=0deg, P1=P2=0.2

Grahic Jump Location
Figure 17

Tangential stress at the boundary of Hole 1 for a1=a2=1, S1=1, S2=0.8, α=0deg, P1=0.2, P2=0

Grahic Jump Location
Figure 16

Tangential stress at the boundary of Hole 2 for a1=a2=1, S1=1, S2=0.8, α=0deg, P1=0.2, P2=0.1

Grahic Jump Location
Figure 15

Tangential stress at the boundary of Hole 1 for a1=a2=1, S1=1, S2=0.8, α=0deg, P1=0.2, P2=0.1

Grahic Jump Location
Figure 14

Tangential stress at the boundary of either hole for a1=a2=1, S1=1, S2=0.6, α=0deg, P1=P2=0.2

Grahic Jump Location
Figure 13

Tangential stress at the boundary of either hole for a1=a2=1, S1=1, S2=0.7, α=0deg, P1=P2=0.2

Grahic Jump Location
Figure 9

Tangential stress at the boundary of either hole for a1=a2=1, S1=1, S2=0.8, α=0deg, P1=P2=0.2

Grahic Jump Location
Figure 8

Distribution of major principal stress reproducing the stress pattern in Fig. 4, Experiment 5: SH=1, Sh=0.6, α=0deg, P1=P2=0

Grahic Jump Location
Figure 7

Distribution of major principal stress reproducing the stress pattern in Fig. 4, Experiment 4: SH=1, Sh=0.6, α=45deg, P1=P2=0

Grahic Jump Location
Figure 21

Tangential stress at the boundary of Hole 2 for a1=1, a2=0.5, S1=1, S2=0.8, α=0deg, P1=P2=0.2

Grahic Jump Location
Figure 20

Tangential stress at the boundary of Hole 1 for a1=1, a2=0.25, S1=1, S2=0.8, α=0deg, P1=P2=0.2

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In