Hi Mohamad.
In order for the results to be symmetric, the following need to be true:
- Geometry is symmetric. (true in your case)
- Loads are symmetric. (true in your case)
- Material is symmetric. (true in your case)
- Constraints are symmetric. (not true in your case. I will explain below.)
Can you provide more details about what you are seeing? For example,
- What is not symmetric in the results? Or what are you expecting to see different?
- The model did not include a nonlinear analysis with shrink fit. Where is that model?
For the symmetry of the results, your results look symmetric left to right and certainly have some symmetry top to bottom (Z direction). Since the cylindrical "shell" is only held in place by separation contact, and because the "shell" has a larger coefficient of thermal expansion than the solid, the "shell" contracts more than the solid. Are you expecting the "shell" to be floating in the middle so that the top-to-bottom displacement is 100% symmetric, like this?

Photoshopped image. Deformed shape exaggerated. The deformed shape is symmetric about the two centerlines shown. This is not going to happen in the analysis.
A more important question is this: why did the analysis give results when the model is statically unstable? It should have given an error because there is nothing holding the cylindrical "shell" in place! (At the very least, the "shell" is free to rotate about the Z axis.) Because of the shrinkage, the shell is also free to move in Z. The model is not statically stable.
The answer to this question is the analysis made an arbitrary decision about how to stabilize the model. In your analysis, the "shell" remained at the top of the solid. (I am assuming the Z axis is up in your image. The mini-axis is missing.) In my analysis, the shell remained attached at the bottom of the solid. The deformation or strain is symmetric; the displacement magnitude is not symmetric because the arbitrary constraint added by the solver is not symmetric. The results of your analysis and my analysis are both correct even though the displacements are completely different!

In my opinion, it is better to setup the analysis properly so that you get the results you want instead of letting the solver change the setup and give results that it wants to give! For example,
- bond the face on the top (or bottom) between the I.D. of the "shell" and solid so that the shell is statically stable. (This simulates that when the "shell" contracts more than the solid, the friction holds the "shell" in contact with the solid. This is an approximation but hopefully better than unexpected results.)
- split the outer face of the "shell" along the horizontal plane of symmetry. Apply a constraint so that the "shell" cannot move in the Z direction. Also apply constraints somewhere on the "shell" so that it cannot rotate about the Z. (This requires other splits so that nodes can be fixed in the appropriate direction while still leaving the "shell" free to contract.)
About shrink fit, I did not find a tutorial or video. Perhaps someone else knows of an example that I could not find. Otherwise, please attach the model with the shrink fit setup. Someone will look at the model and explain why it was taking longer than 20 minutes to start analyzing, and if the shrink fit setup is proper or not. Note that this article describes the basic steps to setup a shrink fit analysis. See How to perform a press-fit analysis in Inventor Nastran and Nastran In-CAD.
John
John Holtz, P.E. Global Product Support
Autodesk, Inc. If not provided already, be sure to indicate the version of Inventor Nastran you are using!"The knowledge you seek is at knowledge.autodesk.com" - Confucius 😉