
From:  David Danan 
Subject:  Re: [Getfemusers] Computation of reaction forces associated to a dirichlet condition 
Date:  Fri, 30 Jul 2021 18:50:04 +0200 
Dear David,
I don't know if this explains the difference obtained because it is
really important, but the residual of the linear system and the
multiplier are not really comparable. The residual is not a force
density, its components represent some equivalent nodal forces whose
intensity depends on the mesh size, whereas the multiplier is taken from
a finite element field and represents a force density. To obtain a force
density from the nodal forces, a mass matrix must be inverted on the
contact boundary.
Best regards,
Yves
On 30/07/2021 12:41, David Danan wrote:
> Dear GetFem community,
>
> i am trying to compute the reaction forces associated to a dirichlet
> condition, in order to do so, i have followed the advices given in
> this thread
> https://www.mailarchive.com/getfemusers@gna.org/msg01136.html
> <https://www.mailarchive.com/getfemusers@gna.org/msg01136.html>
>
> You can also find enclosed my test case, using the python interface.
> The steps are the following:
> Solve a simple 2D elasticity problem on a rectangle (dirichlet on the
> left, neumann on the top)
> Compute the reaction forces arising from the residual without the
> dirichlet condition, by using the solution in displacement, the
> tangent matrix and the right hand side term
> Retrieve the value of the multiplier associated to the dirichlet
> condition
>
> In fact, i expected both quantity to be the same but they were not (2
> order of magnitude different, i didn't expect such large values for
> the multipliers) and i was wondering which one was correct.
> If it helps, you can find both quantities in Mult.png (Multipliers is
> the true multiplier and MultipliersResidual is the residual without
> the dirichlet condition).
>
> Next, i built a second model similar to the first one but without a
> dirichlet condition. I added an explicit rhs using the
> MultipliersResidual ( Multipliers gave strange results) and tried to
> solve the problem, you can see the original solution "Displacement"
> and newsolution "Displacement_test" result in Sol.png.
>
> It seems i am missing something there, i expected the solutions to be
> the same, not just close enough.
> Can you enlighten me?
>
> Best regards,
> David.
>

Yves Renard (Yves.Renard@insalyon.fr) tel : (33) 04.72.43.87.08
INSALyon
20, rue Albert Einstein
69621 Villeurbanne Cedex, FRANCE
http://math.univlyon1.fr/~renard

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