Solving the Kirsch Problem with Mesh-free Elements Using Radial Base Interpolation Functions

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Fabio H Realpe
Yasser H Ochoa
Francisco Franco
Pedro J Díaz


Mfree, Mfree (Elementos Libres de Malla), Mesh-free elements, RPIM (Método de interpolación de puntos radiales), RPIM, MQ (Multi-cuadráticas)., Radial Point Interpolation Method, RBF, Radio Basis Functions Multi-quadratics


The problem of Kirsch published in 1898, is used as a basis for corroborating the relative precision of numerical methods developed in the mechanics of solids. For this reason, the solution of this problem is used to evaluate the accuracy of the Mfree numerical method with a function of form using the radial points of interpolation, in the mesh-free numerical method. The radial points of interpolation method (RPIM) is an interpolation technique used to construct form functions with locally distributed nodes in a weak formulation that allows the representation of the problem as a system of equations. The most common type of functions are the polynomial functions or MQ radial basis functions (RBF), which was used for the stability it presents at the moment of solving the problem numerically. The most common type of functions are the polynomial functions or radial basis functions (RBF), which was used for the stability it presents at the moment of solving the problem numerically. To make the comparison we used the analytical solution given by Kirsch and the numerical solution developed in the present work, obtained an error of 0.00899%, which shows that the Mfree technique with radial bases of interpolation MQ are accurate and reliable when used as a numerical method of analysis. 


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