Linear deformation with membranes problem help needed

[landersohn]

I have a problem of the following kind:
I have an approximately spherical soft material surrounded by a thin stong membrane. If I outward apply tension on a given circumference on the membrane, I expect the outer membrane to flatten my initial sphere and I end up with something looking like a discus.
Even though my initial shaphe is not quite a sphere, the problem is rotationally symmetric.
I made a model with two 2D bodies and tried to assign the appropriate properties.
Problem is: my solution does not converge and if I set the convergence criteria unrealistically wide, I get junk in the results. even if make Younds modulus of the inner material 0 and set the poisson ration to zero, i.e. basically create a vacuum inside my membrane, the membrane does not collapse as I would expect with the outward tension.
Does anybody have any ideas?