Neutral holes in plane sheet reinforced holes which are elastically equivalent to the uncut sheet

Abstract

It is shown that, in a plane sheet under any particular loading system, certain reinforced holes may be made which do not alter the stress distribution in the main body of the sheet. These reinforced holes (hereafter called neutral holes) necessarily have exactly the same stiffness and at least the same strength as the portion of the sheet that has been cut out. The weight of the reinforcement is usually greater than the weight of the sheet that has been cut out, though there are cases where it is less. The Airy stress function is used throughout because it admits of great generality and because the properties of a neutral hole can be expressed simply in terms of the function and its derivatives. Indeed, the stress function assumes a new and special significance in determining the shape of a neutral hole.