Stresses around One Hole or Two Holes Subjected to Internal Pressures in Semi-Infinite or Infinite Medium

Abstract

The formulas for the numerical determination of stresses in an infinite elastic medium having two circular holes of different diameters subjected to different hydrostatic pressures on their walls, have been deduced from the well-known Airy's stress function represented by the bipolar coordinate system.Modifying the above formulas, we can also determine the stresses in a semi-infinite elastic medium having a circular hole closed to the straight boundary, under the cases of loading on both the walls of the hole and the straight boundary, and of loading on either of them.In the present study, we calculated the stresses in an infinite or a semi-infinite medium under the above mentioned conditions using the formulas, and discussed the results of the stress analysis. Some examples of the results obtained are as follows:(1) In the case of the infinite medium having one hole subjected to hydrostatic pressure and another hole with free surface, unless the interval of their holes is extremely small, the maximum tensile stress on the wall of the hole subjected to pressure does not occur at the intersection (A) of the wall and the line through the center of their holes, but occurs at the point having the value of θ=30°∼60° (Fig. 2, ∼4).(2) In the case of the infinite medium having two holes subjected to equal pressure, the maximum tensile stress occurs at the inner intersection of the wall of the smameter diameter hole and the line through the center of two holes (Fig. 8, 9).(3) In the case of the semi-infinite medium having a hole subjected to pressure, the maximum tensile stress on the wall of the hole occurs at the point having the value of θ=80°∼90° (Fig. 11).