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Utilización de matrices dispersas en el Método de los Elementos Finitos
DOI:
https://doi.org/10.15446/ing.investig.n27.20759Keywords:
Método de los elementos finitos, Matrices dispersas, Esfuerzos (es)Finite element method, Sparse matrices, Efforts (en)
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El presente es el primero de una serie de artículos relacionados con el tema de los Elementos Finitos y su aplicación en el campo de la ingeniería, y en particular de la Ingeniería Geotécnica, que publicaremos en esta sección.
En el primero de ellos estamos presentando el método ilustrándolo con un ejemplo muy sencillo en el que se determinan los esfuerzos de una viga constituida por un material CHILE bajo el supuesto de deformaciones planas y esfuerzos biaxiales.
La finalidad de este primer artículo es mostrar las ventajas que ofrecen las matrices dispersas para el manejo de la matriz banda que genera un tipo de problemas como el planteado, frente a los sistemas tradicionales de Choleski-Jordan y Gauss-Seidel, entre otros.
Posteriores artículos ilustraran el método para materiales CHOLE (Continuos, Homogéneos, Ortotrópicos y linealmente elásticos) y otros tipos de materiales en donde el comportamiento elástico no cumple con la linearidad.
This paper is the first of a series of articles relating with the topic of Finite Elements and their application to the engineering field and in particular to geotechnical engineering, which will be published in this section. In this first article we are presenting the method, ilustrating a very simple example in wich the stresses are determined in a beam made with a CHILE material (continuos, homogeneous, isotropic, linearly elastic), under the assumption of planar deformations and biaxial stresses. The objetive of the this first article is to show the advantages that the disperse matrices offer in the handling of the banded matrices that is generated by the type of problem presented, with respect to the traditional methods of Choleski-Jordan and Gauss-Seidel, amongst others. Future articles will illustrate the method for CHOLE materials (Continuos, homogeneous, orthotropic and linearly elastic) and other type of materials where the elastic behaviour does not comply with linearity.
References
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Copyright (c) 1992 Gino Natale Primero, Jesús Rafael García Núñez, Alvaro Correa Arroyave
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