The Theory of Thin Elastic Plates–History and Current State of the Problem

The article is an analytical review and is devoted to the theory of thin, isotropic elastic plates. The basic relations of the theory based on the kinematic hypothesis are presented, according to which tangential displacements are distributed linearly over the thickness of the plate, and its deflection does not depend on the normal coordinate. As a result, a system of sixth-order equations was obtained for two potential functions: the penetrating potential, which determines the deflection of the plate, and the edge potential, which makes it possible to set three boundary conditions on the edge of the plate and eliminate the well-known contradiction in the theory of Kirchhoff plates. Problems that do not have a correct solution within the framework of Kirchhoff’s theory are considered - cylindrical bending of a plate with a free edge, bending of a rectangular plate with a non-classical hinge, torsion of a square plate by moments distributed along the contour, bending of a plate with a rigid stamp. In conclusion, a brief historical review of works devoted to the theory of plate bending is presented.