Gridgenerator Trapezoids?

[Earl Fairall]

Hi everyone,

I am playing with the grid generator functions and I don't see one for trapezoids. Is that correct? Perhaps I am missing something.

I am trying to build a gear shaped geometry. Perhaps there is an easier way to do this?

Earl

[David Wells]

Hi Earl,

I think the best way to do generate a trapezoidal grid would be to use GridGenerator::general_cell. That function gives you a one-cell grid with caller-specified vertices.

> I am trying to build a gear shaped geometry. Perhaps there is an easier way to do this?

The answer depends on how many gears or their spacing, but I would try to solve this problem in the following way:

1. Generate a disk grid and refine it until we have enough boundary faces to reasonably place teeth around it. For example, if there should be four teeth, then we should refine the (2D) grid once so we have eight boundary faces.

2. Convert the refined triangulation into a triangulation with only coarse cells. There must be a better way to do this, but saving the grid to some external format (like GMSH) and then loading it again should work.

3. Use GridGenerator::merge_triangulation to attach the teeth to the disk grid. That can only merge two grids at once, so it will (wastefully) generate a lot of temporary Triangulations, but it should work.

This is an interesting problem. I hope you will post the grid you get as a result!

Thanks,

David Wells

[Earl Fairall]

Hi David, 

Thanks for the detailed response.

Yes, my plan was to generate the tooth geometry and use merge triangulations. Hopefully this is not too computationally expensive, but that is what I am testing to discover. 

Sure, I can post it if I can achieve a result. There are many applications which open up if I can get deal.ii to do some not unreasonably  complex axisymmetric geometries.

I hadn’t considered the general cell, but that looks like an excellent suggestion. I was attempting simplexes merged with a square, but this is probably better. 

I was having some issues yesterday getting my simplexes to generate, but let me look into this and report back.

Any other comments are welcome

Kind regards,

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Earl Fairall
p. 815.419.8690
efai...@gmail.com

[Earl Fairall]

This isn't exactly what I am hoping for in the end, but it is a good start using general_cell:

I should be able to parameterize this and I think it will work fairly well. It seems general_cell trapezoids can have curved edges too. Not the result I was expecting to get, but that's an important feature, too.

Earl Fairall
p. 815.419.8690
efai...@gmail.com

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