what BC's should I apply?

[cspkumar]

I have a spherical thin film supported by a ring at film's
circumference. When I cool the system to an uniform temperature, intuitively it seems to me that both the ring & film should shrink together if CTE of film is same as that of the ring. In other words, it would be a sphere of smaller radius after cooling. My question is how do I model the boundary conditions for this problem without any rigid body motion?

I would really appreciate your thoughts on this.

Thank you.

 

[johnhors]

Use symmetry, so that you only model a quarter of the hemi-sphere. The model is restrained normal to each plane of symmetry and also at the ring's circumference. This prevents rigid body motion without affecting any results.

 

[Drej]

If you can't use John's suggestion of symmetry then appropriate placing of weak springs in the structure will also provide you with an unconstrained structure but without rigid body motion.


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[Denial]

If you do not apply any loads that would make the structure want to embark on a rigid body motion, then any statically determinate set of restraints will serve to remove the "mathematical possibility" of such a motion. These restraints can be weak springs if you want, but in theory they can be rigid.

It is only if your restaints are not statically determinate that you NEED to use weak springs. (There are circumstances under which it is not possible to use a statically determinate set of restraints.)

Either way, at the end of the analysis the very first thing you should check is that you have zero forces in all components of your restraining system.

 

[Drej]

> Either way, at the end of the analysis the very first thing you should check is that you have zero forces in all components of your restraining system.

Although any restraint with give you a reaction force, however small. The trick however is to reduce this reaction to as small a value as possible, and obviously one in which the response of the system becomes unaffected.


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[johnhors]

Drej, using a statically determinate set of restraints with a balanced load, the reactions should be only round off errors and thus effectively zero.

 

[Drej]

That's would I said in my post (ref. "however small").


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