A Meshless Method For Kirchoff Plate Model.

Abstract

In this work we describe and analyze the application of a meshless method to static
and dynamic calculation of Kirchhoff thin plate problems. The method is based on the use of
blurred derivatives. Briefly, blurred derivatives allow to transform differential equations into
an integral equation which does no contain derivatives of the unknown function. The final
expression is an updating formula which only has physical meaning in a limit known as a
functional integral, so that the technique is designated as the Functional Integral
Formulation (FIM) of continuous problems.
The application of this meshless method for modeling plate problems offers a number of
advantages over the traditional finite element method. It considerably simplifies data
preparation in highly irregular structures and allows to use “p-refinement” without
modifying the net of nodes.
In this work we first describe the basics of the method and its computational
implementation. The method is the applied to a static problem comparing its performance
with rectangular finite elements. Finally, its feasibility for calculation of free vibrations of
plates is demonstrated.