Stress Solution for an Infinite Plate Containing Two Arbitrary Circular Holes Under Equal Biaxial Stresses

Abstract

A method of successive approximations utilizing analytic stress functions of the complex variable z, in the manner of the Schwartz Alternating Method, has been used to obtain the solution of the stress distribution around two circular holes of unequal radii in an equal biaxial stress field of an infinite plate. The stress functions up to a third approximation are obtained in all detail for one numerical example and a chart for a wide range of hole and distance parameters is developed for practical use. It is believed that this basic solution for two holes is a preliminary attempt toward the solution of stress concentration problems in the perforated components in pressure vessels in the area of reactor structures. It is also believed that this solution may be used to obtain solutions to more complicated hole patterns.