"$ygradualdiv" 修訂間的差異

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(未顯示由 2 位使用者於中間所作的 12 次修訂)
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The second column ''r'' should be filled in a real number.
 
The second column ''r'' should be filled in a real number.
 
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<br>
 
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[[File:Mesh2.png|600px]]
 
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<br>
 
{| class="wikitable"
 
{| class="wikitable"
 
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Then <math>l = a\frac{r^{N}-1}{r-1} </math>
 
Then <math>l = a\frac{r^{N}-1}{r-1} </math>
   
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<br>
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If the total layer thickness is <math>l </math> and i=2, then if the smallest separation distance is a
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<math>l/2 = a+ar+ar^{2}+ar^{3}+ar^{4}+...+ar^{N/2} </math>
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where N is the total grid number defined in [[$ydiv]]
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Then <math>l = 2 \cdot a\frac{r^{N/2}-1}{r-1} </math>
   
 
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: Example
 
: Example
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$ynode
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0.0
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0.5
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2.0
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3.0
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$ydiv
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25
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30
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60
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$ygradualdiv
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0
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1 1.1
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2 0.9
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<br>'''<big><big>The $ygradualdiv setting in GUI interface is here</big></big>''' <br>
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1. After setting up the Y-nodes, press '''Edit the nodes'''.<br>
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2. Choose the 1<sup>st</sup> node and set the Method to '''Uniform''' with a Mesh ratio of 0.00.<br>
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[[檔案:2D_ygradualdiv_fig1.jpg|1200px]]<br><br>
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3. Choose the 2<sup>nd</sup> node and set the Method to '''Gradual change''' with a Mesh ratio of 1.10.<br>
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[[檔案:2D_ygradualdiv_fig2.jpg|1200px]]<br><br>
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4. Choose the 3<sup>rd</sup> node and set the Method to '''Bump''' with a Mesh ratio of 0.90.<br>
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[[檔案:2D_ygradualdiv_fig3.jpg|1200px]]<br><br>
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[[檔案:2D_ygradualdiv_fig4.jpg|1200px]]
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<br><br>
 
<br><br>
 
: Related commands
 
: Related commands
:; [[$xgradualdiv]]
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:; [[$xgradualdiv]],[[$ynode]],[[$ydiv]]

於 2024年10月21日 (一) 17:42 的最新修訂

This function is to determine how the segment is divided. There are two columns to fill in. The first column i should be filled in an integer 0, 1, or 2.

i = 0: Uniform. This means the segment is divided equally with the same spacing.
i = 1: Gradual. This means the segment is divided whether from small spacing to large spacing or in the opposite way. The spacing is distributed like a geometric progression
i = 2: Bump. This means the segment can be divided into two forms small-large-small or large-small-large.

The second column r should be filled in a real number.
Mesh2.png

If r < 1 If r = 1 If r > 1
Uniform (0) uniform uniform uniform
Gradual (1) large -> small uniform small -> large
Bump (2) large -> small -> large uniform small -> large -> small


If the total layer thickness is l  and i=1, then if the smallest separation distance is a 
l = a+ar+ar^{2}+ar^{3}+ar^{4}+...+ar^{N} 
where N is the total grid number defined in $ydiv
Then   l = a\frac{r^{N}-1}{r-1} 


If the total layer thickness is l  and i=2, then if the smallest separation distance is a 
l/2 = a+ar+ar^{2}+ar^{3}+ar^{4}+...+ar^{N/2} 
where N is the total grid number defined in $ydiv
Then   l = 2 \cdot a\frac{r^{N/2}-1}{r-1} 


Example
$ynode
0.0
0.5
2.0
3.0
$ydiv
25
30
60
$ygradualdiv
0
1 1.1
2 0.9


The $ygradualdiv setting in GUI interface is here
1. After setting up the Y-nodes, press Edit the nodes.
2. Choose the 1st node and set the Method to Uniform with a Mesh ratio of 0.00.
2D ygradualdiv fig1.jpg

3. Choose the 2nd node and set the Method to Gradual change with a Mesh ratio of 1.10.
2D ygradualdiv fig2.jpg

4. Choose the 3rd node and set the Method to Bump with a Mesh ratio of 0.90.
2D ygradualdiv fig3.jpg

2D ygradualdiv fig4.jpg




Related commands
$xgradualdiv,$ynode,$ydiv