PLANE STATE PROBLEM ANALYSIS WITH FINITE-DIFFERENCE METHOD

Abstract

This paper presents a finite-difference analysis of stresses and displacements of the plane elastic problems of orthotropic materials. Starting from the Airy stress function, we assume that in the case of orthotropic materials there is a function Ψ(x, y) the partial derivatives of which determine the specific deformations with the material equations. We also use a potential function of the displacements, the partial derivatives of which lead to the stress fields with the help of the material equations. This will make the prescription of the mixed boundary conditions possible. Therefore, the description of the boundary conditions under the form of prescribed stresses (of the load distribution on the boundary) becomes possible, because there is a direct relation (differential equations) between the displacements and stresses.