Hi,
I have thought about the problem again and now I have a solution proposal:
[[ u_i ]] = 0,
would I fulfill by adding entries in the constraint matrix.
E.g. u_i = u_j for each DoF pair on the boundary. I just have to figure out
the DoF indices i and j.
The average overall stress state, I want also archive with the constraint
matrix:
For the first DoF of the periodic boundary pair I would add a constrain
like
u_1 = A_1i u_i + A_1j u_j + ... + A_1N u_N + S_kl N_l
u_1 = sum_i^N ( A_1i u_i ) + S_k N_l
with i=2..N (all DoF indices on the periodic boundary), the prescribed
stress tensor S and a global normal vector of the boundary N.
And the coefficients are the the calculated by
A_ij = C_ijkl sym(u_k,l) n_j Jwxq
on the corresponding faces by iterating in standard fashion over all
cells/faces and evaluating the terms with via FEFaceValues.
[[ t_i n_i ]] = 0 should thereby be indirectly satisfied.
But I'm not sure if the evaluating the coefficients in such a manner, leads
in the end to the wanted behavior of the system (stress fluctuations on the
boundaries but an average prescribed stress tensor).
Is it a good idea to include coefficients in the constraint matrix that
depends on some shape function. I thought those belonged in the system
matrix.
Can this still work?
Another issue is how to make this concept work in a parallel context: Which
process must know about which DoF?
Regards,
Lukas Schöller
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