Two Unequal Inclusions in Infinite Plate

Abstract

An analytical solution is presented for the stress distribution in an infinite plate which is pierced by two inclusions of rigid circular discs of different diameters. The inclusions are assumed to produce uniform normal pres sure along the circular boundaries. The first fundamental boundary value problem is formulated in complex plane in terms of complex stress functions and then the Schwarz's alternating method is used for obtaining the solution. The complex stress functions are determined for the case of a single circular hole, neglecting the effect of the other hole. These leave some residual stresses at the edge of the second hole, which are corrected by assuming suitable additional stresses there. The new stress functions a recomputed, which, in general, don't satisfy the boundary condition at the edge of the first hole. These are corrected again and the procedure is repeated with the two holes alternately. Thus the successive approximations to the st res s functions are obtained. Numerical results of the stress field are computed upto the second approximation by the use of computer. The stress concentration factors for the tangential stresses at the boundaries of the holes are obtained by varying distances, internal pressures and hole diameter ratios. The variation of stress distribution along the radial direction are plotted for different angular coordinates. It is found that the maximum stress concentration occurs at a point on the edge of the smaller hole nearest to the larger one.