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Periodic boundary conditions on a non square area

Submitted by Andreas.Ferber on

 Hi all,

I have a Problem concerning periodic boundary conditions. The problem is

that the periodic repeating area is not a square one but has an

arbitrary shape. An example is attached to the here:

http://dl.dropbox.com/u/4920002/Bild1.png



One Problem is there are no well defined vertices for the special

treatment. Well I see there are 2 pairs of corners that have a

periodicity of three. I mean when going from one point a periodic length

in x-direction I get a second point and in a second step going a

periodic length in y-direction I get another so this point has three

occurrences on the boundary of the area. These are connected by the

red/green lines in the picture.

Another Problem is the edge between the corners with periodicity of

three. How to couple them with the auxiliary coupling nodes. They are

indicated by an question mark,

Best Regards,

Andreas Talmon l'Armée

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Mikael Öhman

I dont think periodicity is well defined for arbitrary domains. The "square" domain can be mathematically described as a flat torus (however, this doesn´t mean only square domains work).

I dont see the problem with dealing with this domain. If it is a matter of a finite element analysis, then just let one of each color be the master node, and the other slave nodes. The edges with questions mark would be no different either. Just choose a master edge and a slave edge. The same goes for every other edge-pair.

Wed, 11/23/2011 - 11:03 Permalink
Andreas.Ferber

Hi,

First thanks for your answer.

I didn't intend to use periodicity on arbitrary domain. What I tried to say was that I would like to use periodicity on domains other than square ones.

My problem is a matter of finite element analysis. I am working with Ansys and up to now I used a square region and constraint equations to establish periodic boundary conditions.

I think first I have to do some research on master and slave nodes and the use in Ansys before I can make a statement if it ist possible to use them for my specific problem.

Thanks,

 Andreas 

Wed, 11/23/2011 - 11:37 Permalink
Mikael Öhman

I'm not familiar with what Ansys does. Since arbitrary domains do not work, it is quite hard to write code that can deal with strange user input even if it makes up a periodic structure.

I'm guessing the red and green lines are something you add to in ansys to couple this, and if ansys doesn't let you match up edge-edge instead, then one option could be to use slave-nodes on one side instead (assuming your mesh matches on both edges).That would be equivalent to strong periodicity.

Wed, 11/23/2011 - 15:21 Permalink