Generalized finite difference approach verification on circular plates

Abstract

The best-known method, finite differences (abbreviated in text as - FDM), consists of replacing each derivative by a difference algebraic quotient in the classic formulation. It is that discretization method which simple to code and economic to compute. In a sense, a finite difference formulation offers a more direct approach to the numerical solution of partial differential equations (abbreviated in text as - PDE) than does a method based on other formulations. The main drawback of the finite difference methods is the flexibility. Standard finite difference methods requires more regularity of the solution and triangulation (e.g. uniform meshing). Difficulties also arise in imposing boundary conditions.Nowadays, FDM predominates the numerical solutions of PDE not less in pair with the method of finite elements (abbreviated in text as - FEM).In This paper, an advanced static structural-deflection analysis procedure of circular plates through generalized (modernized) finite difference method is presented. The generalized approach considers a lot of parameters been regarded-less by the classical one. The thing which negatively affects the accuracy (convergence to the exact solution values) and consequently; tendency of results it generates. Besides, the newly presented can be easily applied to many cases that the classical even fails to solve. A theoretical mathematical statement been reviewed containing all the necessary explanatories, graphs and indications followed by verification testing problems simultaneously with a comparison been held among variety of results generated via different techniques. The verification comparison indicates the powerfulness of the innovated approach relative to the classical one and the easiness and precision it offers in relevant to the others.