Thermal Expansion

[Ehsan]

Hi,

I want to model a plate under mechanical and thermal loadings.
The plate is in steady state condition and the material is considered to be homogeneous isotropic elastic material.

The Thermal BCs are:
Left edge: prescribed temperature change.
Right edge: constant temperature (zero temperature change)
Top and bottom edges: adiabatic.

I modelled this problem with only mechanical loading and now I want to add thermal part. I want to solve the problem in monolithic way.

My question is:
Which steps I should I study?

Best regards.
Ehsan

[Andrew Mcbride]

The link below is to an MSc thesis that details all the steps to solve the thermoelastic problem in deal.II

https://copy.com/lGuC3Md4aiIRk9t8

Andrew

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[Ehsan]

Hi,

So many thanks for your reply.
I studied the thesis, but I could not find any useful information related to my question.

Best regards.
Ehsan

[Wolfgang Bangerth]

> I modelled this problem with only mechanical loading and now I want to add
> thermal part. I want to solve the problem in monolithic way.
>
> My question is:
> Which steps I should I study?

There aren't really any simple multi-physics examples in the tutorial right
now. The closest is probably step-46 but that addresses many other issues
(such as the fact that the equations are only posed on subdomains).

In the end, I would expect that you can do the same as for the many other
steps that solve systems of equations, e.g. step-20, step-22, etc.

Best
W.

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Wolfgang Bangerth email: bang...@math.tamu.edu
www: http://www.math.tamu.edu/~bangerth/

[deal.II-MailingList]

Hello Ehsan,

I composed a program which solves a thermoelastic problem and I found a helpful

2d-example to test my code in the thesis Andrew showed you. If you want to compute

this example later on and if you have difficulties to create the mesh for it let me know.

I solve the problem also in a monolithic way and I use a block diagonal preconditioner.

If you don't want to deal with parallelization you should take a look the steps Wolfgang

mentioned and at step 26.

Best regards,

Joerg

[Ehsan]

Hello Joerg,

Which kind of elements have you used?
I started to modify Step 20, but it is based on Raviart-Thomas elements.
I want to know if this kind of elements are proper or I should change it.

Best regards.
Ehsan

[deal.II-MailingList]

Hello Ehsan,

I use standard conforming finite elements of lowest order for the displacements
as well as for the temperature. To avoid possible locking effects which might occur depending
on your boundary conditions you can choose quadratic elements for the displacements.
There is no need for special elements like for the mixed Laplace problem.

Best,
Joerg

[Ehsan]

Hello Joerg

Which solver have you used?
I think cg can not solve this system of equations because the K matrix is not symmetric.

Best regards.
Ehsan

[Joerg Frohne]

Hello Ehsan,

I am using the GMRES solver of deal.ii. You can also try the Bicgstab solver but in my case it was slower.
For preconditioning of the system I am using a block-diagonal preconditioner with the Trilinos AMG for
the mechanical part and a SSOR preconditioner for the thermal part of the system. But you can also
try to replace the preconditioner by PreconditionIdentity() and see how long it takes.
Since the coupling is normal quite weak in thermoelastic problems due to a small thermal expansion
coefficient it could be acceptable for a small number of unknowns. But it will definitely be much faster with
a reasonable perconditioner.

Best,
Joerg

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[Muhammad Mashhood]

Hi Andrew! I am also working on the same problem and would be interested to have a look into Thesis but the link says it has been removed.

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