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

Abstract

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 (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.