[glupieri]

Hello
The case analysed concerns the simulation of a cylinder with a heated hollow,
whose analytical solution has been provided by Timoshenko [1951].

The solvers used are both solidDisplacementFoam in of40 and fe40
and the native solution is obtained in Cartesian coordinates,
then it has been transformed in Cylindrical coordinates for a comparison
with the literature results.
The case analyses a full 2D cylinder instead of just a quarter
that is present as a test case in the tutorial of foam-extend.

The boundary conditions here adopted are: fixed value for temperature equal
to T = 100K at the inside cylinder (the hollow) and T = 0K in the outer cylinder;
traction displacement/pressure (equal to 0Pa) for the displacement.

For the computations I have used 3 grid with progressive refinement of the cell size.

Here I have attached the results:
Fig. 1 and Fig. 2 represent the stress components sigmaR and sigmaTheta
respectively (numerics vs theoretical)
Fig. 3 and Fig. 4 represent the same quantities at y=0, 0.3 < x < r = 1
as obtained with the three grids and with the two foam libraries.

I have seen that the solution of the same case has been provided to be
much closer to the analytical one in a previous post:
is there any comment on my work? Wrong pick of boundary conditions?

Thanks in advance for every contribute / comment
Guido Lupieri

[Tobi]

Dear Guido,

thanks for sharing. I am working on stress calculation using FVM (FOAM), too. I am not sure if your solution is 100% correct because my validation is a lot more accurate. However, I am not using a coordinate transformation and as you already said, foam-extend has a similar example that provides more accurate results.

However, I derived the equations myself and I am using another solver. One important thing that you might miss here is that OpenFOAM (solidDisplacementFoam) treats the thermal stresses based on the absolute temperature of 0 K. Therefore you should implement a reference temperature where you can say that the thermal stresses are zero (e.g. at starting temperature). Otherwise you will always have wrong results. It might be that this is your main problem. The temperature distribution should be more or less 100% accurate to the analytical one.

[glupieri]

Dear Tobias,
thank you for your replay (and also for your previous threads on this web pages:
I could read them with interest).
I need to continue with my investigation: the temperature field looks actually very close to
the analytical one ...
Best wishes
Guido Lupieri

[Tobi]

Hi, yes but in the solidDispFoam, there is no reference temperature. Did you take this into account?

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