No-Penetration Model Without Initial Contact?

I don't know how to search for this topic, so I'm just going to ask it:

I have a model where gravity must "settle" one part against other parts (initially with very small gaps) that will support it in a precise position, orientation, and load distribution that are to be determined.  I'm getting mixed results -- either the solver runs happily but gives answers that don't see reasonable, or the solver doesn't run at all and says the model is insufficiently constrained.

I'm running SW Premium 2014 SP5.0 (thought 2015 SP2.1 is available).  The contacts are set up for zero gaps and surface-to-surface, and the (static) study properties are:

Gap/Contact: Improve accuracy for no-penetration contacting surfaces (slower)

Incompatible bonding options:  More accurate (slower)

Compute free body forces

Solver: Automatic

I'm beginning to wonder if this problem fundamentally requires a non-linear solution or if it can be done with a static simulation, perhaps with the large-displacement option.  A possibility is that I must figure out in advance the approximate contact points between the supports and the supported part so that the study can be started close to it's final solution.  (Obviously this would be inconvenient, since the problem must be solved in various orientations wrt gravity.)  Any suggestions would be greatly appreciated! -- John Willett

P.S. -- Here's some background that might help you understand what I need to do:  I have a sensitive instrument that must be supported on three bolts in an arbitrary orientation wrt gravity.  Conventional wisdom is that one bolt hole should be a close sliding fit, one a short slot pointed at the sliding bolt, and one a somewhat oversize hole.  (The gaps here are only 2.5 mil or less.)  That way strains in the supporting structure (small transverse relative motions of the bolts) will not be transmitted to the instrument.  The problem is that the instrument's weight is shared among the bolts.  For different orientations, different combinations of transverse loads will be applied to it through the asymmetric bolt holes.  I need to compute those forces and calculate the resulting strains in the instrument. -- J.W.

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