Stress Solutions for an Infinite Plate With Triangular Inlay

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Abstract
The method of solving two-dimensional problems in elasticity by means of the functions of complex variable, essentially developed by É. Goursat (1), and N. I. Muskhelishvili (2-4), has been applied to the following cases: (a) An infinite plate with a rigid triangular inlay under uniform tension at infinity; (b) A concentrated force; and (c) a moment acting on a triangular inlay in an infinite plate. All these problems are second boundary-value problems; i.e., the displacements are prescribed on the boundary. The first boundary-value problem for a triangular opening in an infinite plate was treated by Hu-Nan Chu (7). The mapping function used in this paper is z = ω ( ζ ) = K ( ζ + n ζ 2 ) , K is real, and 0 < n < 1/2 and real, and it maps an exterior of a triangle with rounded corners, Fig. 1, in the z-plane into an exterior of a unit circle in the ζ-plane [for detailed discussion of this mapping refer to (4)].

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