Franci et al 2015b - Revision history

Cinmemj: Cinmemj moved page Draft Samper 722607179 to Franci et al 2015b

2018-04-25T11:20:47Z

Cinmemj moved page Draft Samper 722607179 to Franci et al 2015b

Cinmemj at 11:12, 25 April 2018

2018-04-25T11:12:27Z

Cinmemj at 11:08, 25 April 2018

2018-04-25T11:08:57Z

Cinmemj at 11:05, 25 April 2018

2018-04-25T11:05:42Z

Cinmemj at 11:01, 25 April 2018

2018-04-25T11:01:38Z

Cinmemj at 10:57, 25 April 2018

2018-04-25T10:57:48Z

Cinmemj at 10:54, 25 April 2018

2018-04-25T10:54:56Z

Cinmemj at 10:34, 25 April 2018

2018-04-25T10:34:27Z

Cinmemj at 10:04, 25 April 2018

2018-04-25T10:04:03Z

Cinmemj at 09:12, 25 April 2018

2018-04-25T09:12:12Z

@@ Line 5,833: / Line 5,833: @@
 |}
 For the V, VP and VPS the percentage errors for the tip displacement with respect to the reference solution are 5.68%, 0.707 % and 0.791%, respectively.
@@ Line 7,189: / Line 7,188: @@
 |}

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 | style="border-right: 1px solid;" | 1.57E-04
 |}
-−
-Simply supported beam.  Cauchy stress XX-component and maximum vertical displacement for different discretizations.
 In the examples presented in this section, for the convergence analysis the percentage error is computed versus the solution obtained with the finest discretization as
@@ Line 2,557: / Line 2,556: @@
 The convergence curves are given in  Figure [[#img-13|13]]. <div id='img-13'></div>
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 |}
 For the present analysis the limit load obtained is <math display="inline">P_{lim}=264.27</math>, the relative percentage errors with respect the solutions given in [115] and [74] are 1.37% and 1.76%, respectively.
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 |}
 The four curves of Figure [[#img-23|23]] are the converged time evolution of the top corner vertical displacement obtained with the V-element in 3D, the VP-element in 2D and 3D and the reference solution [8]. The curves corresponding to the V and VP elements are almost superposed and they match the reference solution.
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 |}
 The problem has been solved also for the 3D problem for a structured mesh of 4-noded tetrahedra with average size 0.125.

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 |}
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 |}
-Material data for the rod components at different temperatures. MatDataRodT
 Concerning the plate and the corium, the material properties are the ones already introduced for the basic model (Figures [[#table-12|12]], [[#table-13|13]] and [[#table-14|14]]). As for the basic model, it has been assumed that the corium keeps the same temperature (<math display="inline">{T = 2000K}</math>)  for all the duration of the analysis.

@@ Line 7,196: / Line 7,196: @@
 |}
-Material data for the corium at T=2000K. MatDataCorium
 Concerning the steel plate, the material data at <math display="inline">{T=293 K}</math> are collected in  Table [[#table-13|6.2]]. These material properties are comparable to those of the stainless steels and they can represent a Stainless Steel 309.
@@ Line 7,234: / Line 7,234: @@
 |}
 The thermal influence on the material properties has been taken into account by multiplying the Young modulus <math display="inline">{E}</math>, the heat conductivity <math display="inline">{ k}</math>, the specific heat <math display="inline">{c_v}</math> and the yield stress <math display="inline">{\sigma _Y}</math> by the coefficients <math display="inline">{C_E}</math>, <math display="inline">{ C_k}</math>, <math display="inline">{C_c}</math> and <math display="inline">{C_Y}</math>, respectively. Hence:
@@ Line 7,380: / Line 7,379: @@
 |}
 ===6.3.2 Preliminary study===

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 <div class="center" style="font-size: 75%;">'''Table 6.1'''. Material data for the corium at T=2000K.</div>
-{| class="wikitable" style="text-align: center; margin: 1em auto;"
+{| class="wikitable" style="text-align: center; margin: 1em auto;font-size:85%;"
 |- style="border-top: 2px solid;"
 | style="border-left: 2px solid;border-right: 2px solid;" | <math display="inline">{\rho }</math>
@@ Line 7,203: / Line 7,203: @@
 <div class="center" style="font-size: 75%;">'''Table 6.2'''. Material data for the plate at T=293 K.</div>
-{| class="wikitable" style="text-align: center; margin: 1em auto;"
+{| class="wikitable" style="text-align: center; margin: 1em auto;font-size:85%;"
 |- style="border-top: 2px solid;"
 | style="border-left: 2px solid;border-right: 2px solid;" | <math display="inline">{\rho }</math>
@@ Line 7,283: / Line 7,283: @@
 <div class="center" style="font-size: 75%;">'''Table 6.3'''. Thermal coefficients for the plate.</div>
-{| class="wikitable" style="text-align: center; margin: 1em auto;"
+{| class="wikitable" style="text-align: center; margin: 1em auto;font-size:85%;"
 |- style="border-top: 2px solid;"
 | colspan='2' style="border-left: 2px solid;border-right: 2px solid;border-left: 2px solid;border-right: 2px solid;" | Temperature

← Older revision	Revision as of 11:20, 25 April 2018
(No difference)

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 | (f) <math>t=15.47s</math>
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 146:''' Melting of an ice block. Zoom on the piece of ice at different time steps.
+| colspan="3" | '''Figure 146:''' Melting of an ice block. Zoom on the piece of ice at different time steps.
 |}

@@ Line 6,401: / Line 6,401: @@
 | (f) <math>t = 7.320 s</math>
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 124:''' Filling of an elastic container with  a viscous fluid (<math>\mu=50 Pa \cdot s</math>). Snapshots at different instants of the 2D simulation. Pressure contours  depicted  over the solid domain.
+| colspan="3" | '''Figure 124:''' Filling of an elastic container with  a viscous fluid (<math>\mu=50 Pa \cdot s</math>). Snapshots at different instants of the 2D simulation. Pressure contours  depicted  over the solid domain.
 |}

@@ Line 6,427: / Line 6,427: @@
 | <math>t = 7.320 s</math>
 |- style="text-align: center; font-size: 75%;"
-| colspan="2" | '''Figure 125:''' Filling of an elastic container with  a viscous fluid (<math>\mu=100 Pa \cdot s</math>). Snapshots at different instants of the 2D simulation. Pressure contours depicted  over the solid domain.
+| colspan="3" | '''Figure 125:''' Filling of an elastic container with  a viscous fluid (<math>\mu=100 Pa \cdot s</math>). Snapshots at different instants of the 2D simulation. Pressure contours depicted  over the solid domain.
 |}

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 ===3.4.1 The Particle Finite Element Method===
-The ''Particle Finite ElementMethod (PFEM)'' is a Lagrangian finite element procedure ideated and developed by Idelsohn and Oñate and their work group [66-68,88]. The PFEM addresses those problems where severe changes of topology occur. This may happen in free surface fluid dynamics, in non-linear solid mechanics, in FSI problems or in thermal coupled problems. The essential idea of the PFEM is to follow the topology of the deformed bodies by moving the nodes of the mesh according to the equations of motion in a Lagrangian way. In other words, in the PFEM the  mesh nodes are treated as particles and they transport their momentum together with all their physical properties. All this produces the deformation of the finite elements discretization that needs to be rebuilt whenever a threshold value for the distortion is reached. Remeshing is one of the most characteristic points of the PFEM [61]. This operation is performed via an efficient combination of the  Delaunay Tessellation  [40,111] and the Alpha Shape method [39]. Once the mesh is generated, the differential problem is integrated again over the new mesh in the classical FEM fashion.
+The ''Particle Finite Element Method (PFEM)'' is a Lagrangian finite element procedure ideated and developed by Idelsohn and Oñate and their work group [66-68,88]. The PFEM addresses those problems where severe changes of topology occur. This may happen in free surface fluid dynamics, in non-linear solid mechanics, in FSI problems or in thermal coupled problems. The essential idea of the PFEM is to follow the topology of the deformed bodies by moving the nodes of the mesh according to the equations of motion in a Lagrangian way. In other words, in the PFEM the  mesh nodes are treated as particles and they transport their momentum together with all their physical properties. All this produces the deformation of the finite elements discretization that needs to be rebuilt whenever a threshold value for the distortion is reached. Remeshing is one of the most characteristic points of the PFEM [61]. This operation is performed via an efficient combination of the  Delaunay Tessellation  [40,111] and the Alpha Shape method [39]. Once the mesh is generated, the differential problem is integrated again over the new mesh in the classical FEM fashion.
 In the following parts of this section the essential points of the PFEM will be highlighted. Specifically, first the remeshing procedure will be described, then the basic steps of the PFEM will be summarized and finally the advantages and disadvantages of the technique will be highlighted.