periodic boundary conditions

[Xuannamdo-danang]

Dear Admins,
Dear FEAPER,

I would like to impose periodic boundary conditions for a Y-shape geometry. However, when reading Section 5.6.6 in Manual of FEAP8.4 I really do not know whether it is feasible for such a geometry?

Could you please tell me, if feasible, how to declare periodic boundary conditions for a Y-shape geometry in the input file?

Thank you so much in advance

Sincerely yours,
Nam Do

[Prof. S. Govindjee]

Can you write out the mathematical statement of what you would like to impose and post it?

[Xuannamdo-danang]

Dear Prof. Govindjee,

Firstly, I would like to thank for your answer

In fact, I would like to impose periodic boundary conditions for a Y-shape geometry (see attachment below) subjected to homogeneous displacement-controlled tension applied at the free-end of two wings of Y-structure. From there, I can compare results obtained from periodicity and non-periodicity of the same Y-shape unit cell of a hexagonal lattice.

However, I am not sure FEAP could do for this kind of non-rectangular geometry. Thus, I am writing to ask you about this

Thank you so much

Sincerely yours,
Nam Do

[Prof. R.L. Taylor]

You can use the displacement form for periodic as long as you can identify which DOF's satisfy the periodic condition.  I assume each arm of the Y has a mesh. 

It may be easier to use a full hexagon.

[Prof. S. Govindjee]

Are you analyzing just the Y or the interior of the hexagon?  If it is the hexagon, then you can mesh the hexagon and link the opposite faces with the LINK command.  If it is the Y that you are analyzing then I still do not understand the boundary conditions that you want to use; you will need to provide some equations for us to look at.

[Xuannamdo-danang]

Dear Prof. Govindjee,

I enclose a clarifying picture for the coupling conditions to be written: so if (assuming) there are ten nodes on each of the 3 surfaces SB, ST1, ST2, equation (1) (see in attachment) has to be written along Y1 (for pairs of nodes on SB; ST1) and along Y2 (for pairs of nodes in SB, ST2)

Sincerely yours,
Nam Do

[Prof. S. Govindjee]

You will need to link the nodes on Sb to St1 and also to St2.  You will probably have to build the link list manually or with a small program and then use the LINK command.   The corner points on Sb, St1, and St2 should be fixed.  Then you can use the PERIodic command and
solve.

[Xuannamdo-danang]

Dear Prof. Govindjee,

Thanks for your answer.

I enclose 3 pictures showing nodes needed to be linked and an input file in which I used commands: LINK and PERIodic CAUChy. Could you please check whether I exactly followed your instructions?

Thank you so much

Sincerely yours,
Nam Do

[Prof. R.L. Taylor]

A simple test is to fix all the nodes for which the symmetry conditions hold.  You do not need any links for this case and you will have a test to compare with using the linking with only the corner nodes fixed.

[Prof. S. Govindjee]

This will not quite work for a few reasons.

(1) The link commands need to come after the
END
TIE
commands for the MESH.

(2) You need to account for the fact that two slanted Y arms meet at a
vertical Y stem.  Thus if you have 6 nodes (evenly spaced) on the stem,
you should have 3 (evenly spaced) nodes on the top edge of each slanted Y arm.
I assume the bottom stem width is twice the top edge length (on each side)

Assume node numbers are

9 100 8                         6 57 5


           1 12 13 14 2


you will then link

13->9
14->100
2->8

1->6
12->57
13->5

I have not checked your other BC.  First get it to work as Prof. Taylor mentions, then move to linking as then next bit of sophistication.

[Xuannamdo-danang]

Thanks so much for your instruction in very detail, Prof. Govindjee. I understand now

Sincerely yours,
Nam Do

[Xuannamdo-danang]

Also, thanks a lot for your instructions, Prof. Taylor.

Sincerely yours,
Nam Do