Rajat,

The first equation is the usual equilibrium equation. It is solved to give 
> displacements. The stiffness matrix is then multiplied by this global 
> displacement vector to give the global traction vector which forms the rhs 
> for the second equation.
>
The easiest solution to deal with constraints to deal with them while 
assembling the matrix. Therefore, I would not compute the right-hand side 
for the second equation beforehand.
Instead just do it while assembling the second equation and use 
constraints.distribute_local_to_global().

Best,
Daniel

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