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Poor 2D mapped mesh quality

[ Edited ]

My goal is to create the 2D mapped quadrilateral mesh on a sphere in such a way, that triangular elements will appear near the poles of a sphere (it should look like the grid on the Earth, comprised of parallels and meridians). For implementing this I split my sphere into eight pieces and create the mesh on each of them. But the mesh obtained is slightly nonuniform near the one of the edges of each piece of the sphere (see picture with NX printscreen). The Edge Mapping option is switched on. However, as the book about CAE by Goncharov, Artamonov et al. shows (see another picture, which is extracted from the book), it is possible to create a uniform mesh on a spherical surface.

 

Therefore, I was wondering if someone could tell me how to solve my problem and why it happens in such a way.

 

Thanks in advance. 

 

 

4 REPLIES
Solution
Solution
Accepted by topic author magicmusic
‎01-22-2017 09:07 AM

Re: Poor 2D mapped mesh quality

Well, I decided my problem by using isoparametric curves. I built a set of curves on my sphere and splitted it along the direction of each isoparametric line. Then  I generated 2D mapped mesh on surface elements obtained and it became the one I desired. 

 

But if anyone knows why my mesh, obtained by the way i described in previous post, turned out to be biased, please, write there.

 

Thanks in advance.

Solution
Solution
Accepted by topic author magicmusic
‎01-22-2017 09:07 AM

Betreff: Poor 2D mapped mesh quality

[ Edited ]

Hello magicmusic,

 

if you are only interested in a even spaced spherical surface mesh having latitudes and logitudes you sould use the mesh revolve function.

 

1. First mesh a side surface of your cutted sphere with mapped meshing usind 2nd order quad elements (Quad8) without property and without export to solver but option "midside node: curved".

 

2. Then revolve that mesh by using axis "center of sphere - northern pole" and an element density and angle you wish to have. You should create a solid mesh full of bricks, wedges at centerline and tetrahedrons at northern pole.

 

3. Then create a surface coat mesh using your spherical surface area, provided by your hexa-mesh.

 

4. At last delete you solid mesh and side surface mesh.

TST_Meridian_Sphere_prt1_fem1.png

 

 

Thats all. You have the mesh you wanted to have. The only disadvantage ist having no geometry underneath your mesh for updating.

 

Using a revolving 1D-Mesh does not bring the same results as being not curved and having no elements at northern pole.

 

Hope, I could help you.

 

Best wishes, Michael

Betreff: Poor 2D mapped mesh quality

Hello, Michael,

Thank you for your reply, I'll bear that method in mind for the next time when I will need to solve such a problem.

Betreff: Poor 2D mapped mesh quality

MagicMusic,

 

I could find such problems you described already before, too.

I believe its a problem of polynomial algorithms of polygone body.

 

Sometimes the things which are primitive in an obvious way change into something really unpredictable like primitiy bodies and their meshes ;-)

 

Where did you create your sphere?

Did  you build an iPart?

Where did you split your sphere in part or iPart?

 

Try to change the method of creation of the surface you want to mesh.

Create your polygon bodies without a primitive sphere but by using an circle line with revolution or vice versa.

Change the method you choose for splitting.

 

Best wishes, Michael