Stresses in an Infinite Plate under Two Concentrated Forces in the Vicinity of the Hole

Abstract

This paper contains an exact solution for the stress distributions in an elastic infinite plate under the two equal and opposite concentrated forces, or the two equal and same directional concentrated couples, applied at the points in the neighbourhood of a circular hole, an elliptical hole or two circular holes. The circular, the elliptical and the bipolar coordinates were used in the solutions, and the basic stress functions were expanded in the Fourier series. The complete stress functions in a plate with the hole were constructed in a form, in which the basic stress function was added to the auxiliary one. The parametric coefficients involved in the solutions were adjusted so as to satisfied the conditions at the hole. The formulas of the stress along the edge of the hole were derived, and the stress distributions were computed by them.