Shrinkage Fitting of Circular Discs into Two Similar Circular Holes in Infinite Plate

Abstract

In cases where two circular inserts with the same elastic constants are shrink-fitted into two similar circular holes in an infinite plate, the stress concentration has been investigated by using the dimensionless principal stress, on the basis of the uniform compressible stress acting on the interface of a single hole with the shrinkage insert, and the followng conclusions can be made concerning the tendency of <N_m>^^^⌒ or <N_τm>^^^⌒ which shows the dimensionless maximum value of the maximum principal stress or of double the maximum shearing stress respectively : 1. <N_m>^^^⌒ and <N_τm>^^^⌒ on the plate and on the inserts are generated on the symmetrical axis connecting the centers of the two circular holes. 2. <N_m>^^^⌒ and <N_τm>^^^⌒ on the plate are mainly functions of the following two values : (1) the ratio of Young's moduli of the plate and the inserts (α'), and (2) the ratio of the distance between the two centers and the diameter of the circular holes (coshξ₁). The values of <N_m>^^^⌒ and <N_τm>^^^⌒ become greater as the value of ξ₁ approaches zero, and the value of <N_m>^^^⌒ increases proportionally as the value of α' is further apart from a particular value. The values of <N_m>^^^⌒ and <N_τm>^^^⌒ generated on the inserts increase proportionally as the value of α' or ξ₁ approaches zero, and the value of <N_τm>^^^⌒ on the inserts is fairly smaller than that on the plate.