Technical Theory of Bending of Elastic Rectangular Plate Pivotally Supported on the Perimeter or Pinched Along Two Adjacent Sides

Abstract

There is a need to improve methods for calculating elements of engineering structures and equipment for strength and stiffness, which directly affects the safety of nuclear power facilities. For the first time the theory of pure bending of rectangular plates pivotally supported at corner points is generalized to the case of their bending both when the plates are hinged around the perimeter and when a rectangular plate is pinched on two adjacent sides. It should be noted that the obtained system of equilibrium equations does not allow satisfying the equilibrium equations exactly, but only in the sense of the average integral value. However, the authors think this method of solving the deflection problem is much more mathematically and physically justified in comparison with the use of Kirchhoff hypotheses, which lead to contradictions when zero shear forces are assumed to be nonzero, only in order to obtain a deliberately equilibrium equation. The proposed approach allows us to evaluate the deflection of the plate in the case when the main vector of forces applied to the plate can be applied to its geometric center. The article indicates the conditions for the distribution of the transverse load under which it can be assumed that the main vector of forces can be applied to the geometric center of the plate. As examples, the problems of deflection of a rectangular plate under its own weight have been solved both when hinged around the perimeter and when pinched on two adjacent sides.