Cutouts in Shallow Shells

Integral representations of general solutions to the shallow shell equations are obtained by means of the Betti-Rayleigh principle. With the aid of these integral representations the cutout problem of shallow shells is reduced to a system of four coupled integral equations. The cutout can have an arbitrary shape. Cutouts with reinforced edges and other boundary-value problems for shallow shells can be reduced to integral equations by the method developed in the paper.