Hermosillo et al 2016a - Revision history

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Rimni: Rimni moved page Draft Samper 697204568 to Hermosillo et al 2016a

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← Older revision		Revision as of 14:13, 3 September 2020
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	In this paper an automatic remeshing algorithm of triangular finite elements is presented. It is well known that the element sizes of the mesh play an important role in modeling the continuum, particularly when notable material properties differences exist in contiguous areas of the medium. In such cases, the mesh must be fine enough in such areas in order to obtain reliable results. Therefore, in this paper is advanced an algorithm to carry out automatic remeshing of local areas where the “remeshing” criteria is activated to refine the mesh accordingly. Herein the proposed algorithm integrated into a two dimensional finite element computer program is used to analyze a classical geotechnical problem to show the importance of locally refining the mesh and to demonstrate that regardless of the geometric characteristics of the initial mesh, the algorithm yields practically equal results. Computations with the proposed method are compared with the corresponding close form solutions, whenever available, to show the usefulness and reliability of the remeshing algorithm. Furthermore, to show the algorithm’s versality, the initial loading boundary conditions considered for the cases included in this paper are modified in order to show how the automatic local remeshing is capable of adapting the initial mesh configuration into a new one as a function of the new boundary conditions. As shown in the paper, the final resulting meshes for both load boundary conditions considered are appreciably dissimilar from each other, which leads to somehow different results.		In this paper an automatic remeshing algorithm of triangular finite elements is presented. It is well known that the element sizes of the mesh play an important role in modeling the continuum, particularly when notable material properties differences exist in contiguous areas of the medium. In such cases, the mesh must be fine enough in such areas in order to obtain reliable results. Therefore, in this paper is advanced an algorithm to carry out automatic remeshing of local areas where the “remeshing” criteria is activated to refine the mesh accordingly. Herein the proposed algorithm integrated into a two dimensional finite element computer program is used to analyze a classical geotechnical problem to show the importance of locally refining the mesh and to demonstrate that regardless of the geometric characteristics of the initial mesh, the algorithm yields practically equal results. Computations with the proposed method are compared with the corresponding close form solutions, whenever available, to show the usefulness and reliability of the remeshing algorithm. Furthermore, to show the algorithm’s versality, the initial loading boundary conditions considered for the cases included in this paper are modified in order to show how the automatic local remeshing is capable of adapting the initial mesh configuration into a new one as a function of the new boundary conditions. As shown in the paper, the final resulting meshes for both load boundary conditions considered are appreciably dissimilar from each other, which leads to somehow different results.
		+
		+	'''Keywords''': Finite element, automatic remeshing, geotechnics, shallow strip foundation, numerical analysis

	==Resumen==		==Resumen==

@@ Line 1: / Line 1: @@
 ==Resumen==
@@ Line 4: / Line 8: @@
 '''Palabras Clave''': Elemento finito, remallado automático, geotecnia, cimentación superficial flexible, análisis numérico.
 ==1  Introduction==

@@ Line 1: / Line 1: @@
-===Resumen===
+==Resumen==
 En este trabajo se presenta un algoritmo de refinamiento automático de elementos finitos triangulares. Es bien sabido que los tamaños de los elementos de la malla juegan un papel importante en el modelado de un medio continuo, particularmente cuando existen diferencias notables en las propiedades de los materiales en zonas contiguas del medio. En tales casos, la malla debe ser lo suficientemente fina en tales áreas con el fin de obtener resultados fiables. Por lo tanto, en este artículo se presenta un algoritmo para llevar a cabo el remallado automático de áreas locales donde se activa el refinamiento  de la malla acordemente a los criterios de "remallado". Aquí el algoritmo propuesto, integrado en un programa de computadora de elementos finitos en dos dimensiones, se utiliza para analizar un problema clásico de geotecnia para mostrar la importancia de refinar localmente la malla y para demostrar que, independientemente de las características geométricas de la malla inicial, los resultados del algoritmo son prácticamente iguales. Los cálculos obtenidos con el método propuesto se comparan con la correspondiente solución cerrada del problema, para mostrar la utilidad y fiabilidad del algoritmo de remallado. Por otra parte, con el fin de mostrar la versatilidad del algoritmo, en los casos incluidos en este trabajo se alteran las condiciones de frontera (de carga) consideradas inicialmente con el fin de mostrar cómo el remallado automático local es capaz de adaptar la configuración inicial de la malla en una nueva como una función de las nuevas condiciones de frontera. Como se muestra en el documento, las mallas resultantes obtenidas para ambas condiciones de frontera son sensiblemente diferentes entre sí, lo que conduce a resultados diferentes.
@@ Line 5: / Line 5: @@
 '''Palabras Clave''': Elemento finito, remallado automático, geotecnia, cimentación superficial flexible, análisis numérico.
-===Abstract===
+==Abstract==
 In this paper an automatic remeshing algorithm of triangular finite elements is presented. It is well known that the element sizes of the mesh play an important role in modeling the continuum, particularly when notable material properties differences exist in contiguous areas of the medium. In such cases, the mesh must be fine enough in such areas in order to obtain reliable results. Therefore, in this paper is advanced an algorithm to carry out automatic remeshing of local areas where the “remeshing” criteria is activated to refine the mesh accordingly. Herein the proposed algorithm integrated into a two dimensional finite element computer program is used to analyze a classical geotechnical problem to show the importance of locally refining the mesh and to demonstrate that regardless of the geometric characteristics of the initial mesh, the algorithm yields practically equal results. Computations with the proposed method are compared with the corresponding close form solutions, whenever available, to show the usefulness and reliability of the remeshing algorithm. Furthermore, to show the algorithm’s versality, the initial loading boundary conditions considered for the cases included in this paper are modified in order to show how the automatic local remeshing is capable of adapting the initial mesh configuration into a new one as a function of the new boundary conditions. As shown in the paper, the final resulting meshes for both load boundary conditions considered are appreciably dissimilar from each other, which leads to somehow different results.
 ==1  Introduction==
@@ Line 234: / Line 233: @@
 ==References==
 [1] Hu Y., Randolph M.F. H-adaptive FE analysis of elasto-plastic non-homogeneous soil with large deformation. Computers and Geotechnics, 23:61-83, 1988.
@@ Line 277: / Line 277: @@
 [22] Poulos H.G., Davis E.H. Elastic Solutions for soil and rock mechanics. Centre for Geotechnical Research. University of Sidney, 1991.

@@ Line 1: / Line 1: @@
-'''Resumen'''
+===Resumen===
 En este trabajo se presenta un algoritmo de refinamiento automático de elementos finitos triangulares. Es bien sabido que los tamaños de los elementos de la malla juegan un papel importante en el modelado de un medio continuo, particularmente cuando existen diferencias notables en las propiedades de los materiales en zonas contiguas del medio. En tales casos, la malla debe ser lo suficientemente fina en tales áreas con el fin de obtener resultados fiables. Por lo tanto, en este artículo se presenta un algoritmo para llevar a cabo el remallado automático de áreas locales donde se activa el refinamiento  de la malla acordemente a los criterios de "remallado". Aquí el algoritmo propuesto, integrado en un programa de computadora de elementos finitos en dos dimensiones, se utiliza para analizar un problema clásico de geotecnia para mostrar la importancia de refinar localmente la malla y para demostrar que, independientemente de las características geométricas de la malla inicial, los resultados del algoritmo son prácticamente iguales. Los cálculos obtenidos con el método propuesto se comparan con la correspondiente solución cerrada del problema, para mostrar la utilidad y fiabilidad del algoritmo de remallado. Por otra parte, con el fin de mostrar la versatilidad del algoritmo, en los casos incluidos en este trabajo se alteran las condiciones de frontera (de carga) consideradas inicialmente con el fin de mostrar cómo el remallado automático local es capaz de adaptar la configuración inicial de la malla en una nueva como una función de las nuevas condiciones de frontera. Como se muestra en el documento, las mallas resultantes obtenidas para ambas condiciones de frontera son sensiblemente diferentes entre sí, lo que conduce a resultados diferentes.
-'''Abstract'''
+'''Palabras Clave''': Elemento finito, remallado automático, geotecnia, cimentación superficial flexible, análisis numérico.
 In this paper an automatic remeshing algorithm of triangular finite elements is presented. It is well known that the element sizes of the mesh play an important role in modeling the continuum, particularly when notable material properties differences exist in contiguous areas of the medium. In such cases, the mesh must be fine enough in such areas in order to obtain reliable results. Therefore, in this paper is advanced an algorithm to carry out automatic remeshing of local areas where the “remeshing” criteria is activated to refine the mesh accordingly. Herein the proposed algorithm integrated into a two dimensional finite element computer program is used to analyze a classical geotechnical problem to show the importance of locally refining the mesh and to demonstrate that regardless of the geometric characteristics of the initial mesh, the algorithm yields practically equal results. Computations with the proposed method are compared with the corresponding close form solutions, whenever available, to show the usefulness and reliability of the remeshing algorithm. Furthermore, to show the algorithm’s versality, the initial loading boundary conditions considered for the cases included in this paper are modified in order to show how the automatic local remeshing is capable of adapting the initial mesh configuration into a new one as a function of the new boundary conditions. As shown in the paper, the final resulting meshes for both load boundary conditions considered are appreciably dissimilar from each other, which leads to somehow different results.
 ==1  Introduction==

@@ Line 1: / Line 1: @@
 '''Resumen'''
 En este trabajo se presenta un algoritmo de refinamiento automático de elementos finitos triangulares. Es bien sabido que los tamaños de los elementos de la malla juegan un papel importante en el modelado de un medio continuo, particularmente cuando existen diferencias notables en las propiedades de los materiales en zonas contiguas del medio. En tales casos, la malla debe ser lo suficientemente fina en tales áreas con el fin de obtener resultados fiables. Por lo tanto, en este artículo se presenta un algoritmo para llevar a cabo el remallado automático de áreas locales donde se activa el refinamiento  de la malla acordemente a los criterios de "remallado". Aquí el algoritmo propuesto, integrado en un programa de computadora de elementos finitos en dos dimensiones, se utiliza para analizar un problema clásico de geotecnia para mostrar la importancia de refinar localmente la malla y para demostrar que, independientemente de las características geométricas de la malla inicial, los resultados del algoritmo son prácticamente iguales. Los cálculos obtenidos con el método propuesto se comparan con la correspondiente solución cerrada del problema, para mostrar la utilidad y fiabilidad del algoritmo de remallado. Por otra parte, con el fin de mostrar la versatilidad del algoritmo, en los casos incluidos en este trabajo se alteran las condiciones de frontera (de carga) consideradas inicialmente con el fin de mostrar cómo el remallado automático local es capaz de adaptar la configuración inicial de la malla en una nueva como una función de las nuevas condiciones de frontera. Como se muestra en el documento, las mallas resultantes obtenidas para ambas condiciones de frontera son sensiblemente diferentes entre sí, lo que conduce a resultados diferentes.
 '''Abstract'''
 In this paper an automatic remeshing algorithm of triangular finite elements is presented. It is well known that the element sizes of the mesh play an important role in modeling the continuum, particularly when notable material properties differences exist in contiguous areas of the medium. In such cases, the mesh must be fine enough in such areas in order to obtain reliable results. Therefore, in this paper is advanced an algorithm to carry out automatic remeshing of local areas where the “remeshing” criteria is activated to refine the mesh accordingly. Herein the proposed algorithm integrated into a two dimensional finite element computer program is used to analyze a classical geotechnical problem to show the importance of locally refining the mesh and to demonstrate that regardless of the geometric characteristics of the initial mesh, the algorithm yields practically equal results. Computations with the proposed method are compared with the corresponding close form solutions, whenever available, to show the usefulness and reliability of the remeshing algorithm. Furthermore, to show the algorithm’s versality, the initial loading boundary conditions considered for the cases included in this paper are modified in order to show how the automatic local remeshing is capable of adapting the initial mesh configuration into a new one as a function of the new boundary conditions. As shown in the paper, the final resulting meshes for both load boundary conditions considered are appreciably dissimilar from each other, which leads to somehow different results.
 ==1  Introduction==

← Older revision	Revision as of 15:36, 28 April 2017
(No difference)

@@ Line 253: / Line 253: @@
 ==References==
-[1] Hu Y. and Randolph M.F. H-adaptive FE analysis of elasto-plastic non-homogeneous soil with large deformation. Computers and Geotechnics, 23:61-83, 1988.
+[1] Hu Y., Randolph M.F. H-adaptive FE analysis of elasto-plastic non-homogeneous soil with large deformation. Computers and Geotechnics, 23:61-83, 1988.
-[2] Belitchko T. and Tabaraa M. H-Adaptivity finite element methods for dynamic problems, with emphasis of location. Int. J. Numer. Meth. Engng. 36:4245-4265, 1993.
+[2] Belitchko T., Tabaraa M. H-Adaptivity finite element methods for dynamic problems, with emphasis of location. Int. J. Numer. Meth. Engng. 36:4245-4265, 1993.
 [3] Lo S.H. Delaunay Triangulation of non-convex planer domains. Int. J. Numer. Meth. Engng., 28(11):2695, 1989.
-[4] George P.L. and Hermeline F. Delaunay’s mesh of a convex polyhedron in dimension d. Application to arbitrary polyhedra. Int. J. Numer. Meth. Engng, 33:975–995, 1992.
+[4] George P.L., Hermeline F. Delaunay’s mesh of a convex polyhedron in dimension d. Application to arbitrary polyhedra. Int. J. Numer. Meth. Engng, 33:975–995, 1992.
 [5] Lo S.H. A new mesh generation scheme for arbitrary planar domains. Int. J. Numer. Meth. Engng, 21:1403–1426, 1985.
@@ Line 265: / Line 265: @@
 [6] Lo S.H. Automatic mesh generation and adaptation by using contours. Int. J. Numer. Meth. Engng, 31:689–707, 1991.
-[7] Lo S.H. and Lau T.S. Generation of hybrid finite element mesh. Microcomputers in Civil Engineering, 7:235–241, 1992.
+[7] Lo S.H., Lau T.S. Generation of hybrid finite element mesh. Microcomputers in Civil Engineering, 7:235–241, 1992.
 [8] Shephard M.S. Approaches to the automatic generation and control of finite element meshes. Applied Mechanics Reviews, 41:169–185, 1988.
@@ Line 273: / Line 273: @@
 [10] Oysu C. Finite element and boundary element contact stress analysis with remeshing technique. Applied Mathematical Modelling, 31:2744–2753, 2007.
-[11] Castelló W.B. and Flores F.G. A triangular finite element with local remeshing for the large strain analysis of axisymmetric solids. Comput. Methods Appl. Mech. Engrg., 198:332–343, 2008.
+[11] Castelló W.B., Flores F.G. A triangular finite element with local remeshing for the large strain analysis of axisymmetric solids. Comput. Methods Appl. Mech. Engrg., 198:332–343, 2008.
-[12] Hamel V., Roelandt J.M., Gacel J.N. and Schmit F. Finite element modeling of clinch forming with automatic remeshing. Computers & Structures, 77:185-200, 2000.
+[12] Hamel V., Roelandt J.M., Gacel J.N., Schmit F. Finite element modeling of clinch forming with automatic remeshing. Computers & Structures, 77:185-200, 2000.
 [13] Plaza A. The fractal behaviour of triangular refined/derefined meshes. Commun. Num. Meth. Engng.,  12:295-302, 1996.
@@ Line 281: / Line 281: @@
 [14] Rivara, M.-C. A grid generator based on 4-triangles conforming mesh-refinement algorithms. Int. J. Numer. Meth. Engng., 24(7):1343–1354, 1987.
-[15] Rivara, M.-C. and Iribarren G. The 4-triangles longest-side partition of triangles and linear refinement algorithms. Mathematics of Computation,  65(216):1485-1502, 1996.
+[15] Rivara, M.-C., Iribarren G. The 4-triangles longest-side partition of triangles and linear refinement algorithms. Mathematics of Computation,  65(216):1485-1502, 1996.
-[16] Bova S.W.  and Carey G.F. Mesh generation/refinement using fractal concepts and iterated function systems. Int. J. Numer. Meth. Engng, 33:287-305, 1992.
+[16] Bova S.W. , Carey G.F. Mesh generation/refinement using fractal concepts and iterated function systems. Int. J. Numer. Meth. Engng, 33:287-305, 1992.
-[17] Ferragut L., Montenegro R. and Plaza A. Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems. Commun. Num. Meth. Engng., 10:403-412, 1994.
+[17] Ferragut L., Montenegro R., Plaza A. Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems. Commun. Num. Meth. Engng., 10:403-412, 1994.
-[18] Padrón M.A., Suárez J.P. and Plaza Á. Adaptive techniques for unstructured nested meshes. Applied Numerical Mathematics, 51:565–579, 2004.
+[18] Padrón M.A., Suárez J.P., Plaza Á. Adaptive techniques for unstructured nested meshes. Applied Numerical Mathematics, 51:565–579, 2004.
 [19] Hermosillo A. Refinamiento automático de mallas de elemento finito mediante teoría de fractales y su aplicación en problemas geotécnicos. Tesis de Maestría, DEPFI, UNAM, 2006. ([http://132.248.9.195/pd2006/0603573/Index.html http://132.248.9.195/pd2006/0603573/Index.html])
-[20] Magaña, R., Pérez M. and Romo M. Uso de fractales en el refinamiento continuo de mallas de elemento finito. XXI Congreso Nacional de Ingeniería Sísmica, Guadalajara Jalisco, 2001.
+[20] Magaña, R., Pérez M., Romo M. Uso de fractales en el refinamiento continuo de mallas de elemento finito. XXI Congreso Nacional de Ingeniería Sísmica, Guadalajara Jalisco, 2001.
-[21] Magaña, R., Pérez M., Hermosillo A. and Romo M. Comparative studies between methods of classic remeshing and fractal approaches. Int. Conf. on Adaptive Modeling and Simulation, ADMOS 2003, Göteborg, Sweden, September, 2003.
+[21] Magaña, R., Pérez M., Hermosillo A., Romo M. Comparative studies between methods of classic remeshing and fractal approaches. Int. Conf. on Adaptive Modeling and Simulation, ADMOS 2003, Göteborg, Sweden, September, 2003.
-[22] Poulos H.G. and Davis E.H. Elastic Solutions for soil and rock mechanics. Centre for Geotechnical Research. University of Sidney, 1991.
+[22] Poulos H.G., Davis E.H. Elastic Solutions for soil and rock mechanics. Centre for Geotechnical Research. University of Sidney, 1991.

@@ Line 8: / Line 8: @@
-<span style="font-size: 75%;">Received: 14 June 2016<br />
+<span style="font-size: 85%;">'''Received''': 14 June 2016<br />
-Accepted: 13 December 2016<br />
+'''Accepted''': 13 December 2016<br />
-Published: July 2017</span>
+'''Published''': July 2017</span>