On the calculation of the rectangular finite element of the plate

Abstract

On the calculation of the rectangular finite element of the plate The article is devoted to the study of the thin plate bending by the finite element method. The application of the finite element method to solving the problem of the plate bending leads to the necessity of studying the rectangular finite element of the plate. All deformation and statics characteristics of the plate are functions of the displacement in the direction of the normal to the middle surface of the plate, which is determined by the deflection function. In the article, the formation of the plate deflection function in explicit form is carried out. The ways for finding the deflection function by division of the variables in the equilibrium equation of the plate, through an incomplete fourth-degree polynomial and in the form of Hermite polynomials are presented. The article is focused mainly on mechanics, engineers and scientific employees of technical specialties.

On the finite element method for calculation of rectangular plates

“…where f 1 (x), ..., f 4 (x), ϕ 1 (y), ..., ϕ 4 (y) are coordinate functions for bending beams, and taking into account that the plate coordinate functions are equal to [14]…”

“…These packages of computer programs implement the computational process of the finite element method, and also have a convenient interface for input of initial data, control of the calculation process and processing of calculation results [15]. 14 Статья посвящена исследованию задач изгиба прямоугольных пластин, которые имеют большое прикладное значение и встречаются повсеместно в самых различных отраслях науки и техники. Расчет изгиба пластин выполнен методом конечных элементов.…”