The Shell with Double Curvature Considered as a Plate on an Elastic Foundation

From the differential equation of the doubly curved shell in terms of the displacement components u, v and w it is apparent that, in so far as the flexural phenomena are concerned, the shell can be considered as a flat plate on an elastic foundation, at a~y rate in a region of sufficiently small size to be regarded as quasi-Euclidean around the vertex of the osculating paraboloid. The modulus of the elastic foundation is dependent on the shell thickness and the principal curvatures of the middle surface. The actual load on the plate must, however, be increased by a diformation load depending on the displacements u and v in the middle surface. Various aspects of this approach to the problem are verified by riference to simple examples and to the results of tests on a large model of an equilateral hyperbolic paraboloid shell.