The stability of three-layer nonhomogeneous rectangular plates in anisotropic resisting medium

The paper investigates the problem of stability of three-layer nonhomogeneous rectangular plates in an anisotropic resisting medium, the layers of which are made of various continuously nonhomogeneous materials. It is assumed that the elastic characteristics of the layer material are continuous functions of the plate thickness coordinate. Using the Kirchhoff-Love hypotheses for the entire thickness of the element, expressions for the forces and moments were obtained, and the generalized stiffness characteristics for the considered three-layer nonhomogeneous plate were determined. In general, plate deflection stability equation systems and stress functions were obtained. In the case of the hinged support of the plate edges, a solution to the problem was constructed and the formula for determining the critical load of the plate was found. During the numerical calculations, the elastic properties of the layer material were taken as linear functions of the thickness coordinates.Analysis of the numerical calculations shows that the plate layer material nonhomogeneity can significantly affect the critical param­eters of the plate.