I am trying to solve the biharmonic equation in FEniCS, specifically the bending of a Kirchhoff-Love plate. My boundary conditions are those which lead to the Navier solution, namely w=0 and d2w/dn2 = 0. I found the following dolfin demo:
http://fenicsproject.org/documentation/dolfin/1.4.0/python/demo/documented/biharmonic/python/documentation.html
However, I get completely lost at the very first step: "a weak formulation of the biharmonic reads". There are no hints on how such an equation has been developed, could anyone point some references where this process can be followed?
Besides, what would be the different between this approach and simply solving the harmonic equation twice?