Gâteaux and Fréchet derivatives of the operator of geometrically nonlinear bending problem of sandwich plate

Abstract

© Published under licence by IOP Publishing Ltd. The geometrically nonlinear problem of bending of sandwich plates with a transversally soft core in a one-dimensional statement is considered. Mathematically, the problem is formulated as an integral identity generating an operator equation in the Sobolev space. The Gâteaux derivative of the operator is calculated and it is proved that it coincides with the Fréchet derivative.