Idelsohn et al 2007a - Revision history

Cinmemj: Cinmemj moved page Draft Samper 571268946 to Idelsohn et al 2007a

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Cinmemj moved page Draft Samper 571268946 to Idelsohn et al 2007a

Cinmemj at 10:48, 7 May 2019

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 <div id="cite-11"></div>
-[[#citeF-1|[11]]]    S. Koshizuka, H. Tamko, Y. Oka, A particle method for   incompressible viscous flow with fluid fragmentation. ''Comp. Fluid Dynamic   Journal'', 4, (1), 29&#8211;46, (1995).
+[[#citeF-11|[11]]]    S. Koshizuka, H. Tamko, Y. Oka, A particle method for   incompressible viscous flow with fluid fragmentation. ''Comp. Fluid Dynamic   Journal'', 4, (1), 29&#8211;46, (1995).
 <div id="cite-12"></div>

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-<!-- metadata commented in wiki content
+Published in ''Variational Formulations in Mechanics: Theory and Applications'', E. Taroco, E.A. de Souza Neto and A.A. Novotny (Eds.), CIMNE, Barcelona, Spain, 2007
-==A UNIFIED SYMMETRICAL FORMULATION FOR  INTERACTIONS BETWEEN ELASTIC SOLIDS AND  INCOMPRESSIBLE FLUIDS ==
-−
 '''
-S.R. Idelsohn,<math>^{\scriptstyle *}</math> and E. Oñate<math>^{\scriptstyle 1}</math>
-J. Marti<math>^{\scriptstyle 2}</math>  '''
-−
-{|
-|-
-| <math>^{\scriptstyle *}</math> ICREA Research Professor at (1)
-|-
-| <math>^{\scriptstyle 1}</math> International Center for Numerical
-|-
-| Methods in Engineering (CIMNE)
-|-
-| Universidad Politecnica de Cataluna
-|-
-| Campus Norte UPC, 08034 Barcelona, Spain
-|-
-| Web page: [http://www.cimne.com http://www.cimne.com]
-<math>^{\scriptstyle 2}</math> International Center for Computational
-|-
-| Method in Engineering (CIMEC)
-|-
-| Universidad Nacional del Litoral
-|-
-| and CONICET
-|-
-| Güemes 3450, Santa Fe, Argentina
-|}
--->
-−
 ==Abstract==

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_571268946-Figure_collapse2.png|500px|Collapse of a water column with an elastic obstacle]]
+|[[Image:Draft_Samper_571268946-Figure_collapse2.png|600px|Collapse of a water column with an elastic obstacle]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 7:''' Collapse of a water column with an elastic obstacle
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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_571268946-Figs9.png|351px|3D collapse of a water column with an elastic cylindrical obstacle]]
+|[[Image:Draft_Samper_571268946-Figs9.png|500px|3D collapse of a water column with an elastic cylindrical obstacle]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 9:''' 3D collapse of a water column with an elastic cylindrical obstacle

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_571268946-Figure_collapse2.png|351px|Collapse of a water column with an elastic obstacle]]
+|[[Image:Draft_Samper_571268946-Figure_collapse2.png|500px|Collapse of a water column with an elastic obstacle]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 7:''' Collapse of a water column with an elastic obstacle

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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_571268946-Grafico5.png|400px|Collapse of a water column with an elastic obstacle: History of   the displacement and comparison with Ref. 26]]
+|[[Image:Draft_Samper_571268946-Grafico5.png|500px|Collapse of a water column with an elastic obstacle: History of   the displacement and comparison with Ref. <span id='citeF-26'></span>[[#cite-26|[26]]]]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="1" | '''Figure 8:''' Collapse of a water column with an elastic obstacle: History of   the displacement and comparison with Ref. 26
+| colspan="1" | '''Figure 8:''' Collapse of a water column with an elastic obstacle: History of   the displacement and comparison with Ref. <span id='citeF-26'></span>[[#cite-26|[26]]]
 |}

← Older revision	Revision as of 11:14, 7 May 2019
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 |}
-Figure [[#img-7|7]] represents the same problem but with a elastic obstacle with density <math display="inline">\rho = 2500 [kg/m^3]</math>, Young's modulus <math display="inline">E=10^6 [kg/s^2m]</math> and Poisson's ratio <math display="inline">\nu =0</math>. The geometry of the more slender obstacle is of width <math display="inline">h= 1.2 [cm]</math> and height <math display="inline">20/3\cdot h</math>. This example was also solved in Ref. 26 with a staggered and level-set method for the free surface flow. A unified formulation for incompressible flow and for the flexible obstacle has been used in this paper. No experimental results have been found for this example, but the shape of the deformation of the elastic beam as well as the free surface perturbation seems to be in agreement with the physics of the problem.
+Figure [[#img-7|7]] represents the same problem but with a elastic obstacle with density <math display="inline">\rho = 2500 [kg/m^3]</math>, Young's modulus <math display="inline">E=10^6 [kg/s^2m]</math> and Poisson's ratio <math display="inline">\nu =0</math>. The geometry of the more slender obstacle is of width <math display="inline">h= 1.2 [cm]</math> and height <math display="inline">20/3\cdot h</math>. This example was also solved in Ref. <span id='citeF-26'></span>[[#cite-26|[26]]] with a staggered and level-set method for the free surface flow. A unified formulation for incompressible flow and for the flexible obstacle has been used in this paper. No experimental results have been found for this example, but the shape of the deformation of the elastic beam as well as the free surface perturbation seems to be in agreement with the physics of the problem.
-The left upper corner of the solid first gets a defection to the left when the water acts on its lower part and moves to the right while the water rises. It obtains its maximum deflection (mark (a) in Figure [[#img-8|8]]) when the water jet passes the top and is fully attached to the left side of the solid. Finally, the impact of the fluid causes the thin solid to start oscillating (b). This oscillation  is damped (c) by the water located left and right of the wall. The results obtained in Ref. 26 are also presented in Figure [[#img-8|8]].
+The left upper corner of the solid first gets a defection to the left when the water acts on its lower part and moves to the right while the water rises. It obtains its maximum deflection (mark (a) in Figure [[#img-8|8]]) when the water jet passes the top and is fully attached to the left side of the solid. Finally, the impact of the fluid causes the thin solid to start oscillating (b). This oscillation  is damped (c) by the water located left and right of the wall. The results obtained in Ref. <span id='citeF-26'></span>[[#cite-26|[26]]] are also presented in Figure [[#img-8|8]].
 Finally, Figure [[#img-9|9]] shows a 3D solution with a cylindrical elastic obstacle. The figure shows the elastic deflection of the beam at different time steps. Experimental results are not finished for this example, but the results seems to be in agreement with the physical of the problem.
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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_571268946-Grafico5.png|600px|Collapse of a water column with an elastic obstacle: History of   the displacement and comparison with Ref. 26]]
+|[[Image:Draft_Samper_571268946-Grafico5.png|400px|Collapse of a water column with an elastic obstacle: History of   the displacement and comparison with Ref. 26]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 8:''' Collapse of a water column with an elastic obstacle: History of   the displacement and comparison with Ref. 26

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-|[[Image:Draft_Samper_571268946-Fig11a.png|360px|]]
+|[[Image:Draft_Samper_571268946-Fig11a.png|300px|]]
-|[[Image:Draft_Samper_571268946-dam011.png|360px|]]
+|[[Image:Draft_Samper_571268946-dam011.png|300px|]]
 |-
-|[[Image:Draft_Samper_571268946-Fig11c.png|360px|]]
+|[[Image:Draft_Samper_571268946-Fig11c.png|300px|]]
-|[[Image:Draft_Samper_571268946-dam021.png|360px|]]
+|[[Image:Draft_Samper_571268946-dam021.png|300px|]]
 |-
-|[[Image:Draft_Samper_571268946-Fig11e.png|360px|]]
+|[[Image:Draft_Samper_571268946-Fig11e.png|300px|]]
-|[[Image:Draft_Samper_571268946-dam031.png|360px|]]
+|[[Image:Draft_Samper_571268946-dam031.png|300px|]]
 |-
-|[[Image:Draft_Samper_571268946-Fig11g.png|360px|]]
+|[[Image:Draft_Samper_571268946-Fig11g.png|300px|]]
-|[[Image:Draft_Samper_571268946-dam041.png|360px|]]
+|[[Image:Draft_Samper_571268946-dam041.png|300px|]]
 |-
-|[[Image:Draft_Samper_571268946-Fig11i.png|360px|]]
+|[[Image:Draft_Samper_571268946-Fig11i.png|300px|]]
-|[[Image:Draft_Samper_571268946-dam101.png|360px|Comparison between experimental and numerical results of the collapse of a water column with an obstacle]]
+|[[Image:Draft_Samper_571268946-dam101.png|300px|Comparison between experimental and numerical results of the collapse of a water column with an obstacle]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" | '''Figure 5:''' Comparison between experimental and numerical results of the collapse of a water column with an obstacle

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 ===7.2 Impact of  waves on elastic and rigid objects===
-The collapse of a water column illustrated in Figure [[#img-4|4]] is calculated using the present formulation and  compared with experiment results obtained by S. Koshizuka.<math display="inline">^{11}</math> Figure [[#img-5|5]] shows the experimental and the numerical results at different characteristic time step.
+The collapse of a water column illustrated in Figure [[#img-4|4]] is calculated using the present formulation and  compared with experiment results obtained by S. Koshizuka. <span id='citeF-11'></span>[[#cite-11|[11]]] Figure [[#img-5|5]] shows the experimental and the numerical results at different characteristic time step.
 At time 0.1 sec, the right surfaces of the water start the disturbance due to the obstacle. At time 0.2 sec, the water surface is completely disturbed by the obstacle. The results compare very well with the experimental results. At 0.3 sec. the collapsed water crashes to the right wall. At 0.4 sec, the water goes up along the right wall with separations and several drops. Finally, at 1,0 sec, the water along the right wall falls down and a new breaking wave will soon occur on the left wall.
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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Samper_571268946-dam.png|600px|Initial geometry of the water column]]
+|[[Image:Draft_Samper_571268946-dam.png|400px|Initial geometry of the water column]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="1" | '''Figure 4:''' Initial geometry of the water column