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Mesh Quality Tutorial

Figure 1: The MeshQuality model. See Figure 2 for close-up ofbottom-right area

This tutorial will illustrate the importance of Mesh Quality in

PHASE2. This tutorial will also show how to identify a poor

quality mesh, and explain how to improve the quality.

Mesh Refinement is a new feature and is only available in

PHASE2version 5.0. Mesh Quality locates and indicates the

poor quality elements with blue rectangular boxes and red

hatching (see Figure 2).

Poor quality elements are undesirable because they negativelyaffect the results. A poor quality mesh can display results that

are more mesh dependant than model dependent. This will be

shown in the third section. In extreme cases, when theelements are of very poor quality, the computation may not

converge and no results will be available.

This tutorial is divided into three parts:

Identifying poor quality elements

Improving the mesh quality

Results: before and after improving the mesh quality


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Figure 2: Located poor quality elements. Note the extremely slendersliver elements on the right-hand side. See Figure 1 for larger view.

Identifying Poor Quality Elements

Figure 3:Triangular mesh element

showing the longest side, shortestside, maximum interior angle and theminimum interior angle.

By default, poor quality elements are those elements with one

(or more) of the following (see Figure 3):

Ratio of maximum side length to minimum side length islarger than 10

Minimum interior angle is smaller than 20 degrees

Maximum interior angle is larger than 120 degrees

In this tutorial, we will examine a staged circular excavation of

about 14 metres in diameter. This model has a number of

different stage boundaries that intersect each other and the

excavation. The method that was used to construct the model,

which created several vertices that are very close to each other,

generated a few extremely poor quality elements.

If you have not already done so, run the PHASE2MODEL

program and open the MeshQuality.fea data file located in the

examples folder in your PHASE2installation folder.

Mesh Refinement

We will begin by zooming in on the excavation. This helps you

to see the area we will be interested in.

Select: ViewZoomZoom Excavation

Now, locate the poor quality elements b y selecting the Show

Mesh Quality option within the Mesh Menu.

Select: MeshMesh RefinementShow Mesh Quality


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Figure 4: Poor quality elements are highlighted.

You should get something like Figure 4. The poor quality

elements are hatched in red and are bounded by blue rectangles.

You can have a better view by zooming in to each individual

element that has been highlighted.

For the purpose of this tutorial, we will concentrate on the

elements on the right-hand side of the lower horizontal stage

boundary, where it intersects the excavation (the elements in the

lower right in Figure 4).

Select: ViewZoomZoom Window

Zoom in on the poor quality elements on the right side of the

lowest horizontal stage boundary, where it intersects the

excavation at around coordinate (155, 345).

Figure 5:Close-up of poor quality elements in lower-right

In Figure 5, the 4 selected elements have a side length ratio

greater than 10. Lets zoom in on the two on the right (seeFigure 6).


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Figure 6:ExamineSliver elements in MeshQuality.fea

These two elements are so narrow that they are not even visible

unless you focus on them particularly, thus producing

significant errors in the computation.

If you zoom in close enough, you can see that the two vertices

on the shortest side of the elements are very close to each other

(approximately 5 mm apart). The upper vertex is from the

evenly distributed vertices of the circular excavation when the

excavation was created. The lower vertex was created by the

intersection of the excavation and the horizontal stage boundary.

Another way of finding poor quality elements is to read the info

viewer.

Select: FileInfo Viewer

Under the section of Mesh Quality, you can see the detailedreport on the statistics of all the mesh elements in this project(see Chart 1).

You cant locate poor quality elements with the Info Viewer, but

you can examine the quantity and distribution of these elements.

This helps to analyze the situation. Not all poor quality

elements can have significant negative affect to the results. In

general, the worse the shape of the element, the more it will

affect the results, so it is most important to remove the worst

shaped elements.


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Chart 1: Mesh Quality info for MeshQuality.fea

Define Mesh Quality

You can also define your own criteria for poor quality elements

with Define Mesh Quality.

Select: MeshMesh RefinementDefine Mesh Quality

Figure 7:The default input for Mesh Quality

As shown in Figure 7, you can change the criteria for poor

elements, and whether to high light poor quality elements on the

mesh or not. You can also change the number of divisions forstatistics in Info Viewer. By default, the elements are separated

into ten groups (see Chart 1). You can narrow down the result

by entering a larger number of divisions.

Mesh Quality14 of 5006 Elements ( 0.3 % of elements) are poor quality elements

5 of 5006 Elements ( 0.1 % of elements) are poor quality elements because of theside length ratio

14 of 5006 Elements ( 0.3 % of elements) are poor quality elements because of theminimum interior angle

1 of 5006 Elements ( 0.0 % of elements) are poor quality elements because of themaximum interior angle

(elements can be of poor quality for more than one reason)

Mesh Quality StatisticsThe worst element has (ratio = 100.58), (min angle = 0.56) (max angle = 123.91)

10.0% of elements have: (ratios > 2.0), (min angles < 30.2) (max angles > 91.8)20.0% of elements have: (ratios > 1.7), (min angles < 35.6) (max angles > 88.2)





Poor quality elements are those with:

(maximum side length) / (minimum side length) > 10.00Minimum interior angle < 20.0 degrees

Maximum interior angle > 120.0 degrees


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Improving Mesh Quality

The best way to reduce the number of poor quality elements isto adjust the boundaries by moving or deleting the vert ices.

First, zoom in to the group of poor quality elements on the right

side of the lowest horizontal stage boundary (see Figure 5).

Moving Vertices

The two poor quality elements on the left were created because

the two vertices on the minimum length side are too close. One

way to fix this problem is to move one of the vertices further

away from the other. In this situation, it is easier to move the

lower vertex because this vertex is only on one boundary.

Select: EditVerticesMove Vertices

Meshing

Now, discretize and mesh the model.

Select: MeshDiscretize

All of the model boundaries will be discretized, and then

generate the mesh by selecting the Mesh option within the Mesh

menu.

Select: MeshMesh

The mesh will be generated, based on the discretizations of the

boundaries.

Show mesh quality again.


Select Vertices to move [Enter=done, esc=quit]:

u se t h e mo us e t o cl i c k on t h e l o wer l e f t v er t e x

a t a r o u nd 155 . 8 , 3 46 . 0 2

Select Vertices to move [Enter=done, esc=quit]:p r e s s En t e r

Enter base point [esc=quit]: use ve r t e x snap

( r i ght - c l i c k and s el ec t v er t ex snap) t o c l i c k

on t he same ver t ex

To point [esc=quit]: use t he mouse t o c l i c k on

any poi nt t hat i s c l os e t o t h e mi dpoi nt of t he

or i gi nal l i ne segment ( t r y t o sel ec t a poi nt

t hat wi l l k eep t h e s egment a st r ai ght l i ne)


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Figure 8: The highlighted region no longer has any poor qualityelements.

As you can see in Figure 8, the two elements (highlighted region

in the figure) are no longer considered poor quality elements.

Deleting Vertices

Now, zoom into the two poor quality elements on the right inFigure 5 (see Figure 6).

The two vertices on the minimum length side are so close that

you cant really see the two elements unless you zoom in a lot.

You can simply fix this problem by deleting one of the vertices.

In this case, it is better to remove the vertex that exists only on

the excavation, rather than the vertex at the intersection of the

stage boundary and the excavation boundary. This is to avoid

modifying the geometry of the stage boundary. Therefore, we

will remove the upper vertex.

Select: EditVerticesDelete Vertices

To see the result, discretize and mesh the model.

Meshing

Select: MeshDiscretize

All of the model boundaries will be discretized. Then generate

the mesh by selecting the Mesh option within the Mesh menu.

Select: MeshMesh

Select vertices to delete [enter=done,esc=quit]: Use mous e t o c l i c k o n t h e v e r t e x at

a r ound 144 . 7 , 346 . 02

Select vertices to delete [enter=done,

esc=quit]: p r es s En t e r


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Show mesh quality again.


The two poor quality elements are not there anymore.

Repeat the steps of moving or deleting vertices to fix all the

poor quality elements. Save the file as MeshQualityFixed.fea

Results: Before and After Improving the Mesh Quality

Open the file MeshQualityFixed.fea. Run COMPUTE to

analyze the model. To view the results of the analysis:

Select: FileInterpret

This will start the PHASE2INTERPRET program.

Open the file MeshQuality.fea once again.

Now there are two files open in the INTERPRET. Tile the two

windows (see Figure 9).

Select: WindowTile Horizontally

You are now viewing the Sigma 1 contours for Stage 1.

Toggle around with different data types at different stages and

compare the results.

Figure 9: The Strength Factor Contour for Stage 4. The top graph isbefore improving the mesh quality, and the bottom graph is after

improving the mesh quality.


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6. Click on the first radio button and select OK on the dialog

box.

7. The values correspond to the stage and the data type you

are viewing. Select the stage tabs, and observe the change

in the values.

8. Click on the window MeshQuality.fea and repeat the

above steps to create another query for the data before

mesh refinement.

9. Select different data types (eg. Sigma 1, Strength Factor)

at different stages for the two files and observe the

differences in the values (see Figure 12).

Figure 12: Queries on Total Displacement for Stage 4. The top graph

is before improving the mesh quality, and the bottom graph is afterimproving the mesh quality.

Graphing Queries from Different Files

Switch the data type back to viewing Total Displacement at

Stage 4 for both windows. Make sure the window of

MeshQuality: Total Displacement is selected.

1. Select: QueryWrite Query File

2. You will be prompted to select queries to write to a file.

Left click on the query (i.e. anywhere along the stage

boundary), then right-click and select Write Selected.

3. In the Save As dialog, save the query in a file called

MeshQuality


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4. You will see another dialog, allowing you to add a

comment which identifies the file. This is optional, but

you can put in Before Mesh Refinement, and select Add

Comment.

5. Now select the window of MeshQualityFixed.fea: Total

Displacement.

6. Select: GraphGraph Material Queries.

7. You will be prompted to select queries. Select the query

with a left mouse click.

8. Right-click the mouse and select Add From File.

9. In the Open file dialog, open the MeshQuality file that

you saved in step 3.

10. You should see an information dialog, informing you that

the query was successfully read. Select OK.

11. Right-click the mouse again, and select Graph Selected.Make sure stage 4 is checked. Then press create plot.

You should see the graph in Figure 13.

0.2

0.22

0.24

0.26

0.28

0.3

0.32

0.34

0.36

0 2 4 6 8 10 12

Distance (m)

TotalDisplacmenet(m)

Figure 13: Total Displacement in Stage 4, before and after MeshRefinement. The plot line with triangular markers is after improving

mesh quality. The plot line with square markers is before improvingmesh quality.

Info Viewer

Another way to analyze the results is to examine the info

viewer. In the model of the two files:

Select: FileInfo Viewer

Open the INFO VIEWER for both the MeshQuality.fea and

MeshQualityFixed.fea files. Tile the two windows vertically.


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Figure 14:Using vertex snap tochoose vertices for the stage boundary

Select: WindowTile Vertically

Chart 2: Mesh Quality Info for MeshQualityFixed.fea

Comparing Chart 1 and Chart 2, you can see that all elements

are of good quality after mesh refinement and the number and

quality of the elements before mesh refinement.

Tips

To avoid unnecessary work, you should check mesh

quality directly after meshing and before any support is

added. This will save you the effort of having to re-assign

material properties and to re-add support because any

added support and material assignments will be lost when

you discretize and mesh the model again.

The most frequent locations to find poor quality elements

are near boundary intersections, especially when there are

arcs around. For an arc, the vertices are generated so that

they are evenly distributed along the arc, thus the

positions of the vertices are not easily monitored. It is

very possible to have two vertices very close to each

other.

It is also recommended to use Vertex Snap when

selecting vertices for the stage boundary (see Figure 14).Many of the poor quality elements exist at the

intersections of stage boundaries and excavation

boundaries. Vertex snap ensures the exact selectio n of a

vertex on the circle, thus preventing vertices that are too

close to each other.

Custom Discretize allows you to set the number ofvertices on the selected boundary segments. You can

reduce the number of vertices in a particular boundary

segment, thus reducing the possibility of having two

vertices too close to each other.

Mesh Quality

All elements are of good qualityPoor quality elements are those with:

(maximum side length) / (minimum side length) > 10.00

Minimum interior angle < 20.0 degreesMaximum interior angle > 120.0 degrees

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