Hermosillo-Arteaga et al 2020a - Revision history

Rimni at 13:05, 17 November 2020

2020-11-17T13:05:19Z

AHermosilloA: AHermosilloA moved page Draft Hermosillo-Arteaga 666480963 to Hermosillo-Arteaga et al 2020a

2020-11-17T11:00:57Z

AHermosilloA moved page Draft Hermosillo-Arteaga 666480963 to Hermosillo-Arteaga et al 2020a

Rimni at 11:14, 23 October 2020

2020-10-23T11:14:29Z

Rimni at 11:46, 4 September 2020

2020-09-04T11:46:17Z

Rimni at 11:30, 4 September 2020

2020-09-04T11:30:18Z

Rimni: /* References */

2020-09-03T14:32:48Z

‎References

Rimni at 14:20, 3 September 2020

2020-09-03T14:20:08Z

Rimni: /* 5. Conclusions */

2020-09-03T13:53:40Z

‎5. Conclusions

Rimni at 13:52, 3 September 2020

2020-09-03T13:52:08Z

Rimni: /* =4.5 Load boundary condition effects on FE results */

2020-09-03T12:49:20Z

‎=4.5 Load boundary condition effects on FE results

@@ Line 109: / Line 109: @@
 {| style="text-align: center; margin:auto;width: 100%;"
 |-
-| <math>{Z}_{T}=2{d}_{1}^{2}{d}_{3}^{2}{{d}_{5}^{2}d}_{6}^{2}+2{d}_{1}^{2}{{d}_{2}^{2}d}_{4}^{2}{d}_{6}^{2}+</math><math>2{d}_{2}^{2}{d}_{3}^{2}{d}_{4}^{2}{d}_{5}^{2}-{d}_{1}^{4}{d}_{6}^{4}-{d}_{3}^{4}{d}_{5}^{4}-</math><math>{{d}_{2}^{4}d}_{4}^{4}</math>
+| <math>{Z}_{T}=2{d}_{1}^{2}{d}_{3}^{2}{d}_{5}^{2}{d}_{6}^{2}+2{d}_{1}^{2}{d}_{2}^{2}{d}_{4}^{2}{d}_{6}^{2}+</math><math>2{d}_{2}^{2}{d}_{3}^{2}{d}_{4}^{2}{d}_{5}^{2}-{d}_{1}^{4}{d}_{6}^{4}-{d}_{3}^{4}{d}_{5}^{4}-</math><math>{d}_{2}^{4}{d}_{4}^{4}</math>
 |}
 |  style="text-align: right;width: 5px;text-align: right;white-space: nowrap;"|(5)

@@ Line 648: / Line 648: @@
 ==References==
 [1]  Hermosillo A.,  Romo M.,   Magaña R.,  Carrera J. Automatic remeshing algorithm of triangular elements during finite element analyses. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 34(1), 4, 2018. [https://doi.org/10.23967/j.rimni.2017.5.003 https://doi.org/10.23967/j.rimni.2017.5.003]
@@ Line 710: / Line 713: @@
 [31] Poulos H.G.,  Davis E.H. Elastic solutions for soil and rock mechanics. Centre for Geotechnical Research, University of Sidney, 1991.

@@ Line 669: / Line 669: @@
 [10] Shephard M.S. Approaches to the automatic generation and control of finite element meshes. Applied Mechanics Reviews, 41:169–185, 1988.
-[11] Lo S.H. Finite element mesh generation and adaptative meshing. Prog Struct. Engng. Mater., 4(4):381-399, 2002 https://onlinelibrary.wiley.com/doi/abs/10.1002/pse.135(DOI: 10.1002/pse.135).
+[11] Lo S.H. Finite element mesh generation and adaptative meshing. Prog Struct. Engng. Mater., 4(4):381-399, 2002. [https://onlinelibrary.wiley.com/doi/abs/10.1002/pse.135 doi: 10.1002/pse.135]
-[12] Oysu Cuneyt. Finite element and boundary element contact stress analysis with remeshing technique. Applied Mathematical Modelling. 31:2744–2753, 2007.
+[12] Oysu C. Finite element and boundary element contact stress analysis with remeshing technique. Applied Mathematical Modelling, 31:2744–2753, 2007.
-[13] Castelló Walter B. and Flores Fernando 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.
+[13] 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.
-[14] Hamel V., Roelandt J.M., Gacel J.N. and Schmit F. Finite element modeling of clinch forming with automatic remeshing. Computers and Structures. 77:185-200, 2000.
+[14] Hamel V., Roelandt J.M., Gacel J.N.,  Schmit F. Finite element modeling of clinch forming with automatic remeshing. Computers and Structures, 77:185-200, 2000.
-[15] Plaza A. The fractal behaviour of triangular refined/derefined meshes. Communications in numerical methods in engineering, 12:295-302, 1996.
+[15] Plaza A. The fractal behaviour of triangular refined/derefined meshes. Communications in Numerical Methods in Engineering, 12:295-302, 1996.
-[16] Rivara María-Cecilia. A grid generator based on 4-triangles conforming mesh-refinement algorithms. International Journal of Numerical Methods, 24(7):1343–1354, 1987.
+[16] Rivara M.C. A grid generator based on 4-triangles conforming mesh-refinement algorithms. International Journal of Numerical Methods, 24(7):1343–1354, 1987.
-[17] Rivara María-Cecilia and Iribarren Gabriel. The 4-triangles longest-side partition of triangles and linear refinement algorithms. Mathematics of Computation, 65(216):1485-1502, 1996.
+[17] 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.
-[18] Bova S. W. and Carey G. F. Mesh generation/refinement using fractal concepts and iterated function systems, Int. J. Numer. Methods Eng., 33:287-305, 1992.
+[18] Bova S.W., Carey G.F. Mesh generation/refinement using fractal concepts and iterated function systems, Int. J. Numer. Methods Eng., 33:287-305, 1992.
-[19] Ferragut L., Montenegro R. and Plaza A. “Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems”. Communications in Numerical Methods in Engineering, 10:403-412, 1994.
+[19] Ferragut L., Montenegro R., Plaza A. Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems. Communications in Numerical Methods in Engineering, 10:403-412, 1994.
-[20] Padrón Miguel A., Suárez J P., Plaza Ángel. Adaptive techniques for unstructured nested meshes. Applied Numerical Mathematics, 51:565–579, 2004.
+[20] Padrón M.A., Suárez J.P., Plaza Á. Adaptive techniques for unstructured nested meshes. Applied Numerical Mathematics, 51:565–579, 2004.
 [21] Dunyach M., Vanderhaeghe D., Barthe L., Botsch M. Adaptive remeshing for real-time mesh deformation. EUROGRAPHICS 2013 / M.A. Otaduy, O. Sorkine, 2013.
-[22] You Y.H., Kou X.Y. and Tan S.T. Adaptive meshing for finite element analysis of heterogeneous materials. Computer-Aided Design, 62:176–189, 2015.
+[22] You Y.H., Kou X.Y., Tan S.T. Adaptive meshing for finite element analysis of heterogeneous materials. Computer-Aided Design, 62:176–189, 2015.
-[23] Alnaes M. S., Blechta J., Hake J., Johansson A., Kehlet B., Logg A., Richardson C., Ring J., Rognes M. E., Wells G. N. The FEniCS Project Version 1.5. Archive of Numerical Software (3), 2015.  [https://fenicsproject.org/ https://fenicsproject.org/]
+[23] Alnaes M.S., Blechta J., Hake J., Johansson A., Kehlet B., Logg A., Richardson C., Ring J., Rognes M. E., Wells G.N. The FEniCS Project Version 1.5. Archive of Numerical Software (3), 2015.  [https://fenicsproject.org/ https://fenicsproject.org/]
-[24] Fiedler M. Geometrie simplexu v En. Casopis Pêst Mat., XII:297-320, 1954.
+[24] Fiedler M. Geometrie simplexu v <math>E_n</math> I. Casopis Pêst Mat., 79(4):297-320, 1954.
-[25] Onelab. Open Numerical Engineering LABoratory, 2018. [http://onelab.info/ http://onelab.info/],
+[25] Onelab. Open Numerical Engineering LABoratory, 2018. [http://onelab.info/ http://onelab.info/]
 [26] Karban P., Mach F., Kůs P., Pánek D., Doležel I. Numerical solution of coupled problems using code Agros2D. Computing, Volume 95, Issue 1 Supplement: 381-408, 2013. 10.1007/s00607-013-0294-4. [http://www.agros2d.org/ http://www.agros2d.org/]
-[27] Brandts J., Korotov S.,  Krizek M. A geometric toolbox for tetrahedral finite element partitions. Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations, 103-122, 2011.
+[27] Brandts J., Korotov S.,  Krizek M. A geometric toolbox for tetrahedral finite element partitions. In Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations, O. Axelsson and J. Karatson (eds.), pp. 103-122, 2011.
 [28] Golias N.A., Tsiboukis T.D. An approach to reﬁning three-dimensional tetrahedral meshes based on Delaunay transformations. Internat J. Numer. Methods Engrg., 37:793-812, 1994.

@@ Line 659: / Line 659: @@
 [5] Lo S.H. Delaunay triangulation of non-convex planer domains. International Journal for Numerical Methods in Engineering, 28(11):2695–2707, 1989.
-[6] George PL and Hermeline F. Delaunay’s mesh of a convex polyhedron in dimension d. Application to arbitrary polyhedra. International Journal for Numerical Methods in Engineering. 33:975–995, 1992.
+[6] George P.L.,  Hermeline F. Delaunay’s mesh of a convex polyhedron in dimension d. Application to arbitrary polyhedra. International Journal for Numerical Methods in Engineering, 33:975–995, 1992.
-[7] Lo S H. A new mesh generation scheme for arbitrary planar domains. International Journal for Numerical Methods in Engineering. 21:1403–1426, 1985.
+[7] Lo S.H. A new mesh generation scheme for arbitrary planar domains. International Journal for Numerical Methods in Engineering, 21:1403–1426, 1985.
-[8] Lo SH. Automatic mesh generation and adaptation by using contours. International Journal for Numerical Methods in Engineering. 31:689–707, 1991.
+[8] Lo S.H. Automatic mesh generation and adaptation by using contours. International Journal for Numerical Methods in Engineering, 31:689–707, 1991.
-[9] Lo SH and Lau TS. Generation of hybrid finite element mesh. Microcomputers in Civil Engineering. 7:235–241, 1992.
+[9] Lo S.H.,  Lau T.S. Generation of hybrid finite element mesh. Microcomputers in Civil Engineering, 7:235–241, 1992.
-[10] Shephard M. S. Approaches to the automatic generation and control of finite element meshes. Applied Mechanics Reviews. 41:169–185, 1988.
+[10] Shephard M.S. Approaches to the automatic generation and control of finite element meshes. Applied Mechanics Reviews, 41:169–185, 1988.
-[11] Lo S H. Finite element mesh generation and adaptative meshing. Prog Struct. Engng. Mater 4: 381-399, 2002 (DOI: 10.1002/pse. 135).
+[11] Lo S.H. Finite element mesh generation and adaptative meshing. Prog Struct. Engng. Mater., 4(4):381-399, 2002 https://onlinelibrary.wiley.com/doi/abs/10.1002/pse.135(DOI: 10.1002/pse.135).
 [12] Oysu Cuneyt. Finite element and boundary element contact stress analysis with remeshing technique. Applied Mathematical Modelling. 31:2744–2753, 2007.

@@ Line 651: / Line 651: @@
 [1]  Hermosillo A.,  Romo M.,   Magaña R.,  Carrera J. Automatic remeshing algorithm of triangular elements during finite element analyses. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 34(1), 4, 2018. [https://doi.org/10.23967/j.rimni.2017.5.003 https://doi.org/10.23967/j.rimni.2017.5.003]
-[2] Hermosillo A., Romo M., Magaña R. and Carrera J. Adaptive Refining Method for 2D Triangular-Element Meshesfor Finite Element Analyses. Serie Investigación y Desarrollo 702, Instituto de Ingeniería, UNAM, 2018.
+[2] Hermosillo A., Romo M., Magaña R. and Carrera J. Adaptive refining method for 2D triangular-element meshes for finite element analyses. Serie Investigación y Desarrollo 702, Instituto de Ingeniería, UNAM, 2018.
-[3] 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.
+[3] 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.
-[4] Belitchko T. and Tabaraa M. H-Adaptivity finite element methods for dynamic problems, with emphasis of location. International Journal of Numerical Methods in Engineering. 36:4245-4265, 1993.
+[4] Belitchko T., Tabaraa M. H-Adaptivity finite element methods for dynamic problems, with emphasis of location. International Journal of Numerical Methods in Engineering, 36:4245-4265, 1993.
-[5] Lo S H. Delaunay Triangulation of non-convex planer domains. International Journal for Numerical Methods in Engineering 28(11):2695 – 2707, 1989.
+[5] Lo S.H. Delaunay triangulation of non-convex planer domains. International Journal for Numerical Methods in Engineering, 28(11):2695–2707, 1989.
 [6] George PL and Hermeline F. Delaunay’s mesh of a convex polyhedron in dimension d. Application to arbitrary polyhedra. International Journal for Numerical Methods in Engineering. 33:975–995, 1992.

← Older revision	Revision as of 11:00, 17 November 2020
(No difference)

@@ Line 647: / Line 647: @@
 Authors wish to thank “Dirección General de Cómputo y de Tecnologías de Información y Comunicación, UNAM” for providing computer time in the Miztli system.
-==7 References==
+==References==
-[1] A. Hermosillo, M. Romo, R. Magaña and J. Carrera, Automatic remeshing algorithm of triangular elements during finite element analyses, Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (2016).
+[1]  Hermosillo A.,  Romo M.,   Magaña R.,  Carrera J. Automatic remeshing algorithm of triangular elements during finite element analyses. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería, 34(1), 4, 2018. [https://doi.org/10.23967/j.rimni.2017.5.003 https://doi.org/10.23967/j.rimni.2017.5.003]
-−
-DOI [https://doi.org/10.23967/j.rimni.2017.5.003 https://doi.org/10.23967/j.rimni.2017.5.003]
-−
-URL [https://www.scipedia.com/public/Hermosillo_et_al_2016a https://www.scipedia.com/public/Hermosillo_et_al_2016a]
 [2] Hermosillo A., Romo M., Magaña R. and Carrera J. Adaptive Refining Method for 2D Triangular-Element Meshesfor Finite Element Analyses. Serie Investigación y Desarrollo 702, Instituto de Ingeniería, UNAM, 2018.
-[3] 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.
+[3] 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.
-[4] Belitchko T. and Tabaraa M. H-Adaptivity finite element methods for dynamic problems, with emphasis of location. International Journal of Numerical Methods in Engineering. 36: 4245-4265, 1993.
+[4] Belitchko T. and Tabaraa M. H-Adaptivity finite element methods for dynamic problems, with emphasis of location. International Journal of Numerical Methods in Engineering. 36:4245-4265, 1993.
-[5] Lo S H. Delaunay Triangulation of non-convex planer domains. International Journal for Numerical Methods in Engineering 28(11): 2695 – 2707, 1989.
+[5] Lo S H. Delaunay Triangulation of non-convex planer domains. International Journal for Numerical Methods in Engineering 28(11):2695 – 2707, 1989.
-[6] George PL and Hermeline F. Delaunay’s mesh of a convex polyhedron in dimension d. Application to arbitrary polyhedra. International Journal for Numerical Methods in Engineering. 33: 975–995, 1992.
+[6] George PL and Hermeline F. Delaunay’s mesh of a convex polyhedron in dimension d. Application to arbitrary polyhedra. International Journal for Numerical Methods in Engineering. 33:975–995, 1992.
-[7] Lo S H. A new mesh generation scheme for arbitrary planar domains. International Journal for Numerical Methods in Engineering. 21: 1403–1426, 1985.
+[7] Lo S H. A new mesh generation scheme for arbitrary planar domains. International Journal for Numerical Methods in Engineering. 21:1403–1426, 1985.
-[8] Lo SH. Automatic mesh generation and adaptation by using contours. International Journal for Numerical Methods in Engineering. 31: 689–707, 1991.
+[8] Lo SH. Automatic mesh generation and adaptation by using contours. International Journal for Numerical Methods in Engineering. 31:689–707, 1991.
-[9] Lo SH and Lau TS. Generation of hybrid finite element mesh. Microcomputers in Civil Engineering. 7: 235–241, 1992.
+[9] Lo SH and Lau TS. Generation of hybrid finite element mesh. Microcomputers in Civil Engineering. 7:235–241, 1992.
-[10] Shephard M. S. Approaches to the automatic generation and control of finite element meshes. Applied Mechanics Reviews. 41: 169–185, 1988.
+[10] Shephard M. S. Approaches to the automatic generation and control of finite element meshes. Applied Mechanics Reviews. 41:169–185, 1988.
 [11] Lo S H. Finite element mesh generation and adaptative meshing. Prog Struct. Engng. Mater 4: 381-399, 2002 (DOI: 10.1002/pse. 135).
-[12] Oysu Cuneyt. Finite element and boundary element contact stress analysis with remeshing technique. Applied Mathematical Modelling. 31: 2744–2753, 2007.
+[12] Oysu Cuneyt. Finite element and boundary element contact stress analysis with remeshing technique. Applied Mathematical Modelling. 31:2744–2753, 2007.
-[13] Castelló Walter B. and Flores Fernando 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.
+[13] Castelló Walter B. and Flores Fernando 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.
-[14] Hamel V., Roelandt J.M., Gacel J.N. and Schmit F. Finite element modeling of clinch forming with automatic remeshing. Computers and Structures. 77: 185-200, 2000.
+[14] Hamel V., Roelandt J.M., Gacel J.N. and Schmit F. Finite element modeling of clinch forming with automatic remeshing. Computers and Structures. 77:185-200, 2000.
-[15] Plaza A. The fractal behaviour of triangular refined/derefined meshes. Communications in numerical methods in engineering, vol. 12: 295-302, 1996.
+[15] Plaza A. The fractal behaviour of triangular refined/derefined meshes. Communications in numerical methods in engineering, 12:295-302, 1996.
-[16] Rivara María-Cecilia. A grid generator based on 4-triangles conforming mesh-refinement algorithms. International Journal of Numerical Methods. Volume 24, Issue 7 (July): 1343–1354, 1987.
+[16] Rivara María-Cecilia. A grid generator based on 4-triangles conforming mesh-refinement algorithms. International Journal of Numerical Methods, 24(7):1343–1354, 1987.
-[17] Rivara María-Cecilia and Iribarren Gabriel. The 4-triangles longest-side partition of triangles and linear refinement algorithms. Mathematics of computation volume 65, number 216 October: 1485-1502, 1996.
+[17] Rivara María-Cecilia and Iribarren Gabriel. The 4-triangles longest-side partition of triangles and linear refinement algorithms. Mathematics of Computation, 65(216):1485-1502, 1996.
-[18] Bova S. W. and Carey G. F. Mesh generation/refinement using fractal concepts and iterated function systems, Int. J. Numer. Methods Eng., 33: 287-305, 1992.
+[18] Bova S. W. and Carey G. F. Mesh generation/refinement using fractal concepts and iterated function systems, Int. J. Numer. Methods Eng., 33:287-305, 1992.
-[19] Ferragut L., Montenegro R. and Plaza A. “Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems”. Communications in numerical methods in engineering, vol. 10: 403-412, 1994.
+[19] Ferragut L., Montenegro R. and Plaza A. “Efficient refinement/derefinement algorithm of nested meshes to solve evolution problems”. Communications in Numerical Methods in Engineering, 10:403-412, 1994.
-[20] Padrón Miguel A., Suárez J P., Plaza Ángel. Adaptive techniques for unstructured nested meshes. Applied Numerical Mathematics 51: 565–579, 2004.
+[20] Padrón Miguel A., Suárez J P., Plaza Ángel. Adaptive techniques for unstructured nested meshes. Applied Numerical Mathematics, 51:565–579, 2004.
-[21] Dunyach Marion, Vanderhaeghe David, Barthe Loïc and Botsch Mario. Adaptive Remeshing for Real-Time Mesh Deformation. EUROGRAPHICS 2013 / M. A. Otaduy, O. Sorkine, 2013.
+[21] Dunyach M., Vanderhaeghe D., Barthe L., Botsch M. Adaptive remeshing for real-time mesh deformation. EUROGRAPHICS 2013 / M.A. Otaduy, O. Sorkine, 2013.
-[22] You Y.H., Kou X.Y. and Tan S.T. Adaptive meshing for finite element analysis of heterogeneous materials. Computer-Aided Design. 62: 176–189, 2015.
+[22] You Y.H., Kou X.Y. and Tan S.T. Adaptive meshing for finite element analysis of heterogeneous materials. Computer-Aided Design, 62:176–189, 2015.
-[23] Alnaes M. S., Blechta J., Hake J., Johansson A., Kehlet B., Logg A., Richardson C., Ring J., Rognes M. E. and Wells G. N. The FEniCS Project Version 1.5. Archive of Numerical Software (3), 2015. [DOI] [https://fenicsproject.org/ https://fenicsproject.org/]
+[23] Alnaes M. S., Blechta J., Hake J., Johansson A., Kehlet B., Logg A., Richardson C., Ring J., Rognes M. E., Wells G. N. The FEniCS Project Version 1.5. Archive of Numerical Software (3), 2015.  [https://fenicsproject.org/ https://fenicsproject.org/]
-[24] Fiedler M. Geometrie simplexu v En. Casopis Pêst Mat; XII: 297-320, 1954.
+[24] Fiedler M. Geometrie simplexu v En. Casopis Pêst Mat., XII:297-320, 1954.
 [25] Onelab. Open Numerical Engineering LABoratory, 2018. [http://onelab.info/ http://onelab.info/],
-[26] Karban P., Mach F., Kůs P., Pánek D., Doležel I. Numerical solution of coupled problems using code Agros2D. Computing, Volume 95, Issue 1 Supplement: 381-408, 2013. DOI 10.1007/s00607-013-0294-4. [http://www.agros2d.org/ http://www.agros2d.org/]
+[26] Karban P., Mach F., Kůs P., Pánek D., Doležel I. Numerical solution of coupled problems using code Agros2D. Computing, Volume 95, Issue 1 Supplement: 381-408, 2013. 10.1007/s00607-013-0294-4. [http://www.agros2d.org/ http://www.agros2d.org/]
-[27] Brandts J., Korotov S., and Krizek M. A Geometric Toolbox for Tetrahedral Finite Element Partitions. Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations. 103-122, 2011.
+[27] Brandts J., Korotov S.,  Krizek M. A geometric toolbox for tetrahedral finite element partitions. Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations, 103-122, 2011.
-[28] Golias NA and Tsiboukis TD. An approach to reﬁning three-dimensional tetrahedral meshes based on Delaunay transformations. Internat J Numer Methods Engrg. 37: 793-812, 1994.
+[28] Golias N.A., Tsiboukis T.D. An approach to reﬁning three-dimensional tetrahedral meshes based on Delaunay transformations. Internat J. Numer. Methods Engrg., 37:793-812, 1994.
-[29] Gruau Cyril and Coupez Thierry. 3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric. Comput. Methods Appl. Mech. Engrg. 194: 4951–4976, 2005.
+[29] Gruau C.,  Coupez T. 3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric. Comput. Methods Appl. Mech. Engrg., 194:4951–4976, 2005.
-[30] Damy J. Integración de las superficies de Boussinesq, Westergaard y Frölich, sobre superficies poligonales de cualquier forma, cargadas con fuerzas verticales uniformemente repartidas”. Rev. Ingeniería, No. 1, Facultad de Ingeniería, UNAM, México, 1985.
+[30] Damy J. Integración de las superficies de Boussinesq, Westergaard y Frölich, sobre superficies poligonales de cualquier forma, cargadas con fuerzas verticales uniformemente repartidas. Rev. Ingeniería, No. 1, Facultad de Ingeniería, UNAM, México, 1985.
-[31] Poulos H. G. and Davis E. H. Elastic Solutions for soil and rock mechanics. Centre for Geotechnical Research. University of Sidney, 1991.
+[31] Poulos H.G.,  Davis E.H. Elastic solutions for soil and rock mechanics. Centre for Geotechnical Research, University of Sidney, 1991.

@@ Line 635: / Line 635: @@
 The results included in this paper show that the algorithm can refine the elements maintaining their shape ratio under a specified threshold, same results are obtained when various thresholds are considered. Accordingly, finite element users can define very rough meshes (even not worrying about zones of stress/strain concentrations) and the proposed algorithm will adequate the mesh elements to achieve a reliable solution of the particular problem.
-The discretization of the refined mesh is dependent on the boundary conditions, as well as the loading conditions, as it was shown in the section 4.5. Henceforth, it can be concluded that if the load conditions in a problem change, the mesh used must be modified accordingly.
+The discretization of the refined mesh is dependent on the boundary conditions, as well as the loading conditions, as it was shown in the Section 4.5. Henceforth, it can be concluded that if the load conditions in a problem change, the mesh used must be modified accordingly.
 It could be argued that the automatic remeshing proposed in this paper allows optimization of the computing resources because only some areas of the analyzed medium are refined, avoiding the use of overly dense meshes defined on the basis of previous experiences. This may become important when an extended program of parametric analyses of a particularly complex problem is needed.

@@ Line 616: / Line 616: @@
-The remeshing-dependence of the load boundary conditions is clear. Local refinement allows to define more clearly the stress contours. These results indicate that the finite element meshes should be modified according to the ongoing load boundary conditions. In Figure 23 the normalized normal stresses &#x03c3;<sub>z</sub>/q computed along axes below the corner (indicated in Figure 22(a) using the initial mesh and the meshes obtained after three iterations are compared with the closed form solution.
+The remeshing-dependence of the load boundary conditions is clear. Local refinement allows to define more clearly the stress contours. These results indicate that the finite element meshes should be modified according to the ongoing load boundary conditions. In [[#img-23|Figure 23]]  the normalized normal stresses <math>\sigma_z /q</math> computed along axes below the corner (indicated in [[#img-22|Figure 22]](a) using the initial mesh and the meshes obtained after three iterations are compared with the closed form solution.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id='img-23'></div>
- [[Image:Draft_Hermosillo-Arteaga_666480963-image32.png|414px]] </div>
+{| style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: auto;max-width: auto;"
 It is clear that the remeshing considering the present loading conditions has a significant effect from the ground surface down to a depth equal to the foundation width. Therefore, the results obtained in this investigation seem to indicate that whenever the elements of the initial mesh are not modified as a function of the ongoing load conditions, the results could lead to biased conclusions regarding the problem under consideration. Hence, '''meshes defined for particular loading conditions are not generally suited for the same problem whenever the load boundary conditions (and hence the stress state) are modified'''.
-. '''Conclusions'''
+==5. Conclusions==
 The results of the simple examples included in this paper clearly indicate that there is a close relationship between the load boundary conditions and the mesh needed to obtain trustworthy results. The impact that this issue can have on actual problems throughout their life expectancy can undoubtedly be larger than shown in this paper, whenever the problem complexity increases. Usual problems that lead to this condition are, for example, consolidation of a clay soil deposit (without or with drains to accelerate the consolidation, and even worse when water withdrawal from the deposit is underway, urban and in general road tunnels, any type of earth and rockfill dams, etc.).
@@ Line 638: / Line 641: @@
 Finally, it is worthwhile to mention that where sharp edges of stiff material interact with softer materials, the size of the elements to properly discretize the continuum in the surrounding area is so small that it would be practically impossible to carry out this task manually without mishaps.
-. '''Acknowledgements'''
+==Acknowledgements==
 This work was supported by UNAM-PAPIIT <IT102719>

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 |}
-===4.5 Load boundary condition effects on FE results==
+===4.5 Load boundary condition effects on FE results===
 It is common practice that finite element analyses be carried out keeping unchanged the original mesh defined for analyzing the problem at hand, regardless of the potential time variations of loading boundaries and/or stress states (''i.e.'' dam reservoir filling, water withdrawal from saturated soils leading to their consolidation, etc.). It is worth mentioning that Ferragut and Plaza [19] recognized this shortcoming and studied this issue for heat time-variation in plates. Herein, to show the influence of modifying the load boundary conditions on the induced shear stresses, the loading condition of the slab on the ground surface example was modified by adding a horizontal load. Therefore, the load boundary condition includes vertical (existing) and horizontal (added) loading, where
@@ Line 614: / Line 614: @@
 | colspan="2" style="padding:10px;"| '''Figure 22'''. Slab on the ground surface. Half mesh visualized. Stresses in kg<math>_f</math>/m<math>^2</math>
 |}