An analytical solution, using complex variable methods, is given for the problem of the stress distribution due to an elliptical hole, reinforced around its boundary, in a plane sheet subjected at infinity either to an arbitrary constant stress system or to a bending type stress system. Numerical results were obtained for a wide range of parameters, including three different shapes of ellipse, and ten different amounts of reinforcement. Poisson's ratio was assumed to be 1/3.

A slender ducted body of arbitrary cross section is studied. This possesses an annular, side or “scoop” type of intake at some streamwise station. The parts of the body forward of and behind the intake are both permitted to have discontinuities of longitudinal profile slope at streamwise stations widely separated both from each other and from the intake. The external flow is taken to be entirely supersonic and it is assumed that the intake lip is sharp and that there is no “spill over” due to choking of the internal flow, which must be supersonic for a short distance inside the duct.

General expressions are obtained for the stress distribution in a flat plate end-loaded by equal principal stresses and containing a circular hole reinforced by an annular plate. The reinforcement is placed on one side of the plate only so that the other side remains flush. It is shown that the effect of an asymmetrically placed reinforcement is to induce, in the plate and rein-forcement, bending stresses which are not negligible compared with the externally applied direct stress. From particular examples it is found that reinforcements having practical dimensions can give rise to stress concentrations in the same order of magnitude as those in a similarly loaded plate containing an unreinforced hole. For practical purposes, data have been obtained which enable the designer to determine quickly the stress distributions associated with reinforcements and plates having a reasonably wide range of dimensions.