Axially symmetric analysis with contact: choosing the orientation of the rigid surface does not matter?

I have plate supported by contact condition around the circumference to simulate simple support. The simple support is a piece of a circular arc as a fixed rigid surface. The contact-pair formulation is chosen where the rigid surface is the master. Surprisingly choosing either face of the rigid surface for the contact leads to the "correct" response where the plate is supported. In three dimensions this does not work: choosing the wrong orientation of the surface means the plate is not supported. What is going on?

Additional details in this PDF file. Any hints will be appreciated.

 

Petr Krysl