Problem of Plate Bending in the Moment Asymmetric Theory of Elasticity

Abstract

For a number of materials used in modern practice, calculations according to the classical theory of elasticity give incorrect results. To ensure the reliable operation of structures, there is a need for new theories. At present, of particular interest for practical applications is the asymmetric moment theory of elasticity. In the work, by the method of hypotheses, the three-dimensional equations of the moment asymmetric theory of elasticity are reduced to the equations of the theory of plates. The hypotheses of the theory of plates in the moment theory of elasticity are formulated on the basis of previously obtained our results of the reduction of three-dimensional equations to two-dimensional theories by a mathematical method. Just as in the classical theory of elasticity, the complete problem of the moment theory of plates is divided into two problems - a plane problem and a problem of plate bending. The equations of the plane problem have been obtained in many papers. The situation is different with the construction of the theory of plate bending in the moment theory of elasticity. In this work, for the first time, substantiated hypotheses are formulated and a consistent theory of plate bending is presented. A numerical calculation of the bending of a rectangular hinged plate is carried out according to the obtained applied theory. The calculation results are presented in the form of graphs.