PERIodic command for THERmal analysis

[TUDoR]

Hi everybody,

I try to use the PERIodic command for thermal analysis without any success.

Does anyone have ever tried this? Is it even possible in general?

Assuming it is possible:
In the future, I'd like to give periodic boundary conditions for the temperature
and the displacements in a coupled analysis. Would that be possible to realise?

[TUDoR]

I chose to use a combination of BOUN, DISP and LINK/ELIN which
seems to do actually what I intended to to.

[Prof. R.L. Taylor]

Your solution is good, and is what we expect for periodic behavior.

[TUDoR]

Thank you for your kind comment!

There is still one question remaining:
When I constrain the corner nodes of my body, these nodes are taken out of the system.
Due to that fact, these nodes are not taken into account by the ELINk command. So my
resulting boundaries are not periodically fitting. Could you please have a look on the
attached input file and tell me what should be changed?

[Prof. R.L. Taylor]

The implementation in the current release (8.3) does include the terms you need to include to get the full periodic behavior you want.   For the periodic case with superposed constant overall deformation the requirement is that:

   u+ = u- + eps*(x+ - x-)  where u+ is displ on positive side and u- on negative sign, etc for coords.

We plan to release also the ability to homogenize the solution to get effective properties from a serial run before using as an rve in an fe^2 problem.

Try the attached file to see if it works in your version.

[TUDoR]

Thank you a lot for your hint! Your input file works with my version of feap!

Since this is just working with pure mechanical problems I have to think
about another solution, how to deal with thermo-mechanical problems.

[Prof. R.L. Taylor]

Thermal should work the same way:

T+ = T- + Grad_T *(x+ - x-)

Just as eps is Grad_u (symmetric) - which does not matter.  In finite deformation we use the deformation gradient so that x+ = x- + F*(X+ - X-)

It is always the same for any periodic dof

[TUDoR]

Thank you for your kind comments!

I was able to use the PERIodic command to impose periodic boundary conditions on
a pure thermal problem as well without any trouble. Now, I'd like to do this for the coupled
case.

I attached a file which is nearly the same as you uploaded above. I just added one more
ndf for the temperature. Unfortunately, in this case I don't get any results for the temperature.

Could you please tell me how to handle this - is it possible at all?

[Prof. R.L. Taylor]

There is a framework to do coupled problems, however, the coding for the computation is not included in current releases.  The framework is there for the uncoupled thermal problam also.

The input is defined in 'pmesh.f' as PERIodic COUPled -- but no arrays are input for a coupled problem.

Similarly, you will find the call for the 'hill-mandel' projection in 'pmacr1.f' and some framework in 'hillmandel.f'.

You will need to develop the theory and implementation for the remainder of the computations.

[TUDoR]

Thank you very much for telling the names of the files which
have to be modified. I'll try to implement the modifications
for the coupled problem.

EDIT:
In my version of feap "PERIodic COUPled" is not defined in ''pmesh.f'.
Therein I just find an entry for the "PERIodic case". Furthermore I
don't have any 'hillmandel.f'-file (or "hill" "mandel" -string in any file).

Is there anything missing in my files?