STUDY ON THE STRESS-DEFORMED STATE OF RECTANGULAR PLATE WITH VARIABLE THICKNESS ACCORDING TO THE NON-CLASSICAL THEORY

Abstract

This paper presents a method to calculate the stress-deformed state of a rectangular plate with variable cross-section according to non-classical theory. The equation of state of the plate is built on the basis of the three dimensional elastic theory. Displacements in the direction perpendicular to the mean plane of the plate are represented as polynomials which are 2 orders higher than the classical theory of Kirchhoff-Love. The system of  equilibrium equations and the boundary conditions are obtained using the Lagrange variation method. Using Levi's method for an isotropic rectangular plate of variable thickness, a system of differential equations with variable coefficients is obtained. To solve this problem, the author used the finite difference method. Based on the calculation results for rectangular plate whose thickness varies, a comparison of the results obtained by classical and non-classical theory has been made.