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Natural elements’ methods applied to structural problems
Aplicación del método de elementos naturales a problemas estructurales
DOI:
https://doi.org/10.15446/ing.investig.v28n1.14862Keywords:
meshless method, natural element method, finite element method, natural neighbour interpolation (en)métodos sin malla, método de elementos naturales, método de elementos finitos, interpolación por vecinos naturales (es)
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This paper was aimed at reviewing the theory and numerical implementations of the natural elements method (NEM, meshless method) used for resolving structural problems. An exact analytical solution and the finite element method were used for comparing the results obtained for two lineal-elastic structural problems in two spatial dimensions. The interpolation procedure used by the method for obtaining the trial functions and the most important features of the standard NEM are described. The results of two simulations concerning structural problems are presented using a code written in Matlab 6.5 for resolving differential lineal elasticity equations in two dimensional domains it was found that NEM is similar to the finite element method in terms of stability and convergence, having the advantage of mesh being automatically produced and the approximated solution not depending on the distribution of the node cloud, thereby defining the geometric domain.
El objetivo del presente artículo se enmarca en la revisión de la teoría y la implementación numérica de uno de los métodos numéricos sin malla usados para la solución de problemas de tipo estructural, el método de los elementos naturales (MEN), junto con la contrastación de los resultados obtenidos para dos problemas estructurales elásticolineales en dos dimensiones con la solución analítica exacta y la aproximada por el método de los elementos finitos (MEF). Se describe la técnica de interpolación usada por el MEN para obtener las funciones de forma y se presentan las características más importantes del método en su forma estándar. Se presentan los resultados de dos simulaciones de problemas estructurales realizadas usando un código escrito en Matlab 6.5 para la solución de ecuaciones diferenciales de elasticidad lineal en dominios bidimensionales. Se concluye que el método de los elementos naturales es similar al de los elementos finitos en cuanto a estabilidad y convergencia, con la ventaja de que la malla es generada automáticamente y la no dependencia de la solución aproximada con la distribución de la nube de puntos que define la geometría.
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Copyright (c) 2008 Libardo Andrés González Torres, Diego Alexander Garzón Alvarado, Máximo Alejandro Roa Garzón
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