Revisit of two-circular-holes problem subject to anti-plane remote shear

Abstract

In this paper, we derive the solution of anti-plane deformation for two circular cylindrical holes embedded in an elastic matrix of infinite extent under remote shears. The two holes may have different radii and distance between each other. The matrix is subjected to arbitrary direction of remote shears. The solution is obtained via the boundary integral formulation in conjunction with the degenerate kernel of bipolar coordinates instead of M & ouml;bius transformation using complex variables. Several examples are revisited to compare with those data of Honein et al. Three differences between the present result and those of Morse and Feshbach and Lebedev et al. are discussed.