Generalization of discrete and continuous structural approaches to elaboration of a mathematical model of laminated plates and masses

A mathematical model of laminated plates and masses in the form of bands was elaborated using an iterative approach. A system of differential equations was written relative to the unknown functions found on face surfaces. This allows dividing the structure into several bands by thickness if necessary. The stress-strain state of each one is described by the proposed system of differential equations. It is possible to attain a high accuracy of determination of the components of the displacement vector and stress tenser. However, for most of the problems of calculation of both plates and masses analyzed, it is totally sufficient to examine one band. The analogy in the differential operators relative to the unknown function significantly facilitates the realization of such a model.