Mixed method for calculations of plates with complex boundary conditions

Abstract

The paper presents new possibilities of using a mixed method for calculating bendable plates with complex boundary conditions. When composing resolving equations, it is sufficient to have an expression to determine the deflections of a plate with a normal pinched at the origin. Such solutions are given in the authors’ previously published works for plates of various shapes. On the basis of these solutions, the canonical equations of the mixed method are compiled, where the unknown forces of the method are the forces in the support links, the displacement method is linear and angular displacement of the pinching introduced at the origin. After determining the unknown forces of the method, according to the generally accepted formulas of the mixed method, the deflections of the plate are determined, according to which, in turn, internal forces are determined. Two examples of calculating plates in Cartesian and polar coordinates are given. Numerical implementation of the proposed methodology and algorithm for elastic calculation of bendable plates with complex boundary conditions is carried out using the Wolfram Mathematica 11.3 computer program.