Hi Ataollah,

this type of problem is indeed called a 'contact problem'.  I don't
know how to solve them, neither in libmesh nor otherwise.  Anyways,
here a short recent discussion about it on libmesh-users:
http://comments.gmane.org/gmane.comp.mathematics.libmesh.user/3377

Mauro

At Sun, 3 Mar 2013 18:05:57 -0600,
Ataollah Mesgarnejad wrote:
> 
> Dear all,
> 
> I need some advice on how to implement an inhomogeneous Dirichlet BC for 
> elastic-rigid contact. This BC is a bit weird since it doesn't apply to all 
> of the faces of a boundary_id rather it applies to faces within the contact 
> range (changes with time) and all the other faces should have natural 
> (traction free) BCs. 
> 
> - can this be done using new Dirichlet API? and how?
> - if not can anyone suggest a smart way for implementing it ?
> 
> Thanks,
> Ata
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