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espanolEl problema de Kirsch publicado en 1898, es utilizado como base para corroborar la precision relativa de los metodos numericos desarrollados en la mecanica de solidos. Por esta razon se utiliza la solucion de este problema para evaluar la precision del metodo numerico Mfree con una funcion de forma utilizando los puntos radiales de interpolacion, en el metodo numerico libre de malla. El metodo de puntos radiales de interpolacion es una tecnica de interpolacion utilizada para construir funciones de forma con nodos distribuidos localmente en una formulacion debil la cual permite representar el problema como un sistema de ecuaciones. El tipo de funciones mas usuales son las funciones polinomiales o funciones de base radial MQ (RBF, radio basis functions), la cual fue utilizada por la estabilidad que presenta al momento de solucionar el problema numericamente. Para hacer la comparacion se uso la solucion analitica dada por Kirsch y la solucion numerica desarrollada en el presente trabajo, obtenido un error del 0.00899% lo que muestra que la tecnica Mfree con bases radiales de interpolacion MQ son precisas y confiables al momento de ser utilizadas como metodo numerico de analisis. EnglishThe 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.

Solución del problema de Kirsch mediante elementos libres de malla, utilizando funciones de interpolación de base radial