Santasusana et al 2016a - Revision history

Scipediacontent at 09:57, 15 June 2018

2018-06-15T09:57:32Z

Scipediacontent at 09:54, 15 June 2018

2018-06-15T09:54:40Z

Scipediacontent at 09:52, 15 June 2018

2018-06-15T09:52:46Z

Scipediacontent at 09:51, 15 June 2018

2018-06-15T09:51:09Z

Scipediacontent at 09:47, 15 June 2018

2018-06-15T09:47:44Z

Scipediacontent at 09:45, 15 June 2018

2018-06-15T09:45:31Z

Scipediacontent at 09:43, 15 June 2018

2018-06-15T09:43:21Z

Scipediacontent at 09:37, 15 June 2018

2018-06-15T09:37:27Z

Scipediacontent at 09:23, 15 June 2018

2018-06-15T09:23:02Z

Scipediacontent at 09:14, 15 June 2018

2018-06-15T09:14:32Z

@@ Line 5,291: / Line 5,291: @@
 |- style="text-align: center; font-size: 75%;"
 | (a) Simulation set-up
-| (b) Displacement at time $t=23.4s$. 2D view
+| (b) Displacement at time <math display="inline">t=23.4s</math>. 2D view
 |-
 | colspan="2"|[[Image:draft_Samper_371275574-4_pendulum_3d.png|462px|Displacement at time $t=23.4s$. 3D view]]
 |- style="text-align: center; font-size: 75%;"
-|  colspan="2" | (c) Displacement at time $t=23.4s$. 3D view
+|  colspan="2" | (c) Displacement at time <math display="inline">t=23.4s</math>. 3D view
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" | '''Figure 74:''' Pendulum-like prism interacting with several spherical DEs

@@ Line 4,661: / Line 4,661: @@
 |[[Image:draft_Samper_371275574-4_sudden_force2.png|264px|Contact at a time $t_2>t_1$]]
 |- style="text-align: center; font-size: 75%;"
-| (a) Contact at a time $t_1$
+| (a) Contact at a time <math display="inline">t_1</math>
-| (b) Contact at a time $t_2>t_1$
+| (b) Contact at a time <math display="inline">t_2>t_1</math>
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" | '''Figure 63:''' Particle colliding a plane of a deformable body

@@ Line 2,725: / Line 2,725: @@
 |[[Image:draft_Samper_371275574-Fig11b.png|180px|$C_{\pi^m}$ outside the facet]]
 |- style="text-align: center; font-size: 75%;"
-| (a) $C_{\pi^m}$ inside the facet
+| (a) <math>C_{\pi ^m}</math> inside the facet
-| (b) $C_{\pi^m}$ outside the facet
+| (b) <math>C_{\pi ^m}</math> outside the facet
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" | '''Figure 34:''' Example of projection <math>C_{\pi ^m}</math> inside and outside the FE facet

@@ Line 2,319: / Line 2,319: @@
 |[[Image:draft_Samper_371275574-Fig5b.png|450px|$FE_{BBX} \in \Omega_{I}$]]
 |- style="text-align: center; font-size: 75%;"
-| (a) Evolution of $\Omega_{I}$
+| (a) Evolution of <math display="inline">\Omega _{I}</math>
-| (b) $FE_{BBX} \in \Omega_{I}$
+| (b) <math>FE_{BBX} \in \Omega _{I}</math>
 |-
 |[[Image:draft_Samper_371275574-Fig5c.png|228px|Bins over FEs $ \in \Omega_{I}$]]
 |[[Image:draft_Samper_371275574-Fig5d.png|228px|Hash table]]
 |- style="text-align: center; font-size: 75%;"
-| (c) Bins over FEs $ \in \Omega_{I}$
+| (c) Bins over FEs <math display="inline"> \in \Omega _{I}</math>
 | (d) Hash table
 |-
@@ Line 2,331: / Line 2,331: @@
 |[[Image:draft_Samper_371275574-Fig5f.png|228px|Intersection cells]]
 |- style="text-align: center; font-size: 75%;"
-| (e) $DE_{BBX} \in \Omega_{I}$
+| (e) <math>DE_{BBX} \in \Omega _{I}</math>
 | (f) Intersection cells
 |-

@@ Line 1,534: / Line 1,534: @@
 |- style="text-align: center; font-size: 75%;"
 | (a) Setup of the example
-| (b) Position evolution for $\Delta t = 0.03275$
+| (b) Position evolution for <math display="inline">\Delta t = 0.03275</math>
 |-
 |[[Image:draft_Samper_371275574-2_0_003.png|294px|Position evolution for $\Delta t = 0.00300$]]
 |[[Image:draft_Samper_371275574-2_0_0001no.png|294px|Position evolution for $\Delta t = 0.00010$]]
 |- style="text-align: center; font-size: 75%;"
-| (c) Position evolution for $\Delta t = 0.00300$
+| (c) Position evolution for <math display="inline">\Delta t = 0.00300</math>
-| (d) Position evolution for $\Delta t = 0.00010$
+| (d) Position evolution for <math display="inline">\Delta t = 0.00010</math>
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" | '''Figure 19:''' Setup and results for the position of the sphere between the plates

@@ Line 3,303: / Line 3,303: @@
 |[[Image:draft_Samper_371275574-Fig21d.png|132px|Contact $\boldsymbol{f}^{2}$]]
 |- style="text-align: center; font-size: 75%;"
-| (a) Contact $\boldsymbol{f}^{1}$
+| (a) Contact <math display="inline">\boldsymbol{f}^{1}</math>
-| (b) Contact $\boldsymbol{e}$
+| (b) Contact <math display="inline">\boldsymbol{e}</math>
-| (c) Contact $\boldsymbol{e}$
+| (c) Contact <math display="inline">\boldsymbol{e}</math>
-| (d) Contact $\boldsymbol{f}^{2}$
+| (d) Contact <math display="inline">\boldsymbol{f}^{2}</math>
 |- style="text-align: center; font-size: 75%;"
 | colspan="4" | '''Figure 50:''' Force applied by the surface and the edge to the sphere at different instants of the simulation

@@ Line 2,779: / Line 2,779: @@
 When contact with the edge <math display="inline">\boldsymbol{e}^a</math> is found the check at the lower level for the vertices associated to it, <math display="inline">\boldsymbol{\mathrm{v}}^a</math> and <math display="inline">\boldsymbol{\mathrm{v}}^{a+1}</math>, is discarded (fig. [[#17.1.2 Edge level|17.1.2]]). The contact check with the following edges can not be discarded, however, since they are at the same hierarchy level in terms of Contact Type.  The Distance Hierarchy will determine the validity of the new contact and eliminate or substitute previous ones. This is a key difference with the Fast Intersection Test where the check automatically stops once a contact entity is found.
-Contact with edge. Vertices belonging to that edge are discarded
+{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
+|-
-Weights for an edge contact in a triangle
+|[[Image:Santasusana_et_al_2016a_3802_monograph-Fig13.png|200px|Contact with edge. Vertices belonging to that edge are discarded]]
 The nodal weights can be obtained from the <math display="inline">\eta </math> parameter (equation [[#eq-110|110]]) at the edge <math display="inline">\boldsymbol{e}^a</math>. Fig. [[#17.1.2 Edge level|17.1.2]] shows graphically how <math display="inline">\eta </math> is determined,

@@ Line 218: / Line 218: @@
 |[[Image:draft_Samper_371275574-2_bins.png|252px|]]
 |[[Image:draft_Samper_371275574-2_tree.png|252px|]]
 |}

@@ Line 5,636: / Line 5,636: @@
 |[[Image:draft_Samper_371275574-3ddempack.png|426px|Plot $\kappa$ \emph{versus} $\nu$ in 3D. Taken from: Labra \cite{Labra2012}]]
 |- style="text-align: center; font-size: 75%;"
-| (a) Plot <math>\kappa </math> versus <math>\nu </math> in 2D. Taken from: Labra [101]
+| (a) Plot <math>\kappa </math> versus <math>\nu </math> in 2D. Taken from: Labra <span id='citeF-101'></span>[[#cite-101|[101]]]
-| (b) Plot <math>\kappa </math> versus <math>\nu </math> in 3D. Taken from: Labra [101]
+| (b) Plot <math>\kappa </math> versus <math>\nu </math> in 3D. Taken from: Labra <span id='citeF-101'></span>[[#cite-101|[101]]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" | '''Figure 82:''' Poisson's ratio for different values of <math>\kappa </math> in a UCS test on a concrete specimen

@@ Line 92: / Line 92: @@
 |- style="text-align: center; font-size: 75%;"
 | (a) Particle-Structure
-| (b) Two-scale. Taken from: Labra [101]
+| (b) Two-scale. Taken from: Labra <span id='citeF-101'></span>[[#cite-101|101]]
 |-
 |[[Image:draft_Samper_371275574-3_DEFE_mapping_final.png|240px|Projection onto a FE mesh]]
@@ Line 98: / Line 98: @@
 |- style="text-align: center; font-size: 75%;"
 | (c) Projection onto a FE mesh
-| (d) Embedded particles. Taken from: Zárate and Oñate [8]
+| (d) Embedded particles. Taken from: Zárate and Oñate <span id='citeF-8'></span>[[#cite-8|8]]
 |-
 | colspan="2"|[[Image:draft_Samper_371275574-3_DEFE_Discretized.png|240px|Discretized DE. Taken from: Gethin et al. \cite{Gethin2001}]]
 |- style="text-align: center; font-size: 75%;"
-|  colspan="2" | (e) Discretized DE. Taken from: Gethin et al. [9]
+|  colspan="2" | (e) Discretized DE. Taken from: Gethin ''et al.'' <span id='citeF-9'></span>[[#cite-9|9]]
 |- style="text-align: center; font-size: 75%;"
 | colspan="2" | '''Figure 2:''' Examples of different techniques that combine FE and DE methods