Differential Properties of the Operator of the Geometrically Nonlinear Problem of a Sandwich Plate Bending

Abstract

The geometrically nonlinear bending problem of a sandwich plate with a transversally soft core in a one-dimensional formulation is considered. A generalized formulation of the problem in the form of an operator equation in Sobolev space is obtained. The differential properties of the operator of this equation are investigated. It is proved that the operator of the equation is differentiate according to Gâlteaux. It is established that the Gâlteaux derivative is a continuous operator. Therefore, the operator is also differentiate Frechet derivative wherein the Gato derivative coincides with the Frechet derivative.