I wonder whether 'theta' (when not interpreted as radians) is actually some sort of linear measurement... Also, does free R with enforced theta constitute a pin constraint? (I think it probably does, just with any loads reacted tangentially rather than radially, but it's not immediately intuitive.)
In the results without LDA, has each surface boundary around the bore translated tangentially?
How did you make the LDA run with a link? When I tried a model with a link and LDA, it told me that links were not permitted.
Is your model showing any shear stress around the bore with an enforced theta (it certainly appears to with free theta...)?