Re: [Getfem-users] Computation of reaction forces associated to a dirichlet condition

[Yves Renard]

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.mail-archive.com/getfem-users@gna.org/msg01136.html 
> <https://www.mail-archive.com/getfem-users@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@insa-lyon.fr)       tel : (33) 04.72.43.87.08
  INSA-Lyon
  20, rue Albert Einstein
  69621 Villeurbanne Cedex, FRANCE
  http://math.univ-lyon1.fr/~renard

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