Abstract
A new class of boundary value problems is presented. These problems are described by related equations of different nature and possess such properties as the appearance of highest derivatives in boundary conditions. Such problems appear to model common engineering constructions composed of elements of different mechanical natures like plates, shells, membranes, or three-dimensional elastic bodies. Two problems are considered in detail, namely a three-dimensional elastic body with flat elements taken as a plate or a membrane, and a plate-membrane system. The existence-uniqueness theorems for the corresponding boundary value problems are established and an application of a conforming FEM is justified.
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