Hamed, 

[...]
> I am going to do the same as Bastian, namely periodic boundary condition 
> for displacement  such that u( 0, y ) = u( 1, y ) + *lambda ,*
> * so I used the recommended above code by Bastian for applying 
> inhomogenity to predefined periodicity, in order to have reletive 
> dispacement between right and left faces,*
> *but my results shows that both left and right faces are moving equally to 
> the same direction, not relative to each other.*
>
What you are doing is
dof_left = dof_right
dof_right = c
resulting in
dof_left = dof_right = c.
The solution is to set inhomogeneities for the dofs on the left boundary 
instead of the right boundary and thus
dof_left = dof_right +c.
In particular, you don't want to constraint dofs that are not already in 
the ConstraintMatrix after you called make_periodicity_constraints.
Hence, the code should then work without calling constraints.add_line().

Best,
Daniel

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