Re: [Getfem-users] Computation of forces for prescribed displacements

[Igor Peterlik]

Hello,

the problem is that I still cannot figure out how the equivalent forces should
be computed if there is a Dirichlet condition imposed on some region.

In my task, a displacement for the top face of a cylinder is prescribed and
I want to compute the deformation of the cylinder and the reacting force 
F=(fx,fy,fz);

Therefore, besides mf_u object for displacements of nodes, I have another mesh_fem 
object mf_mult for Lagrange multipliers initialized with the mesh of the cylinder
(together with the correct  dimension and type of the FEM). Then I apply the 
Dirichlet
conditions using mf_mult:


         .......

         getfem::mesh_fem mf_mult(cylinder_mesh);

         ........

         getfem::mdbrick_Dirichlet<> final_model(volum_src_term, 
DIRICHLET_BNDRY_ID, mf_mult);

         .......


 Then I set the boundary conditions and compute the deformation using the standard_solve 
arriving to the solution stored in vector U which contains the displacement 
for each degree of freedom and the Lagrange multipliers for DOFs with prescribed displacements.
 And now I arrive to problem, as I do not know how
to combine the coefficients of Lagrange multipliers stored in the solution 
vector U
and the shape functions of mf_mult to get the reacting force  F (which is -- I 
suppose -- the integral
of force density over the top face of the cylinder for each direction x,y,z 
separately where
the density is computed using the shape function over the boundary elements multiplied by 
the Lagrange multipliers...)
I was trying to understand and employ the generic assembling procedures via 
getfem::generic_assembly
but the examples given in documentation were not enough for me to adapt them 
for my task.
Also in the examples included in getfem, the mf_mult object is defined several 
times, but it is never
used for some further computations.

Thank you in advance.


                                                        Igor

-------------------------------------------------------------------------------------------
> > Hello,
> >
> > I have a question about the boundary conditions.
> > I am using your test demo nonlinear_elastostatic.cc . Let's suppose
> > I neither consider the gravitation forces nor the torsion, but
> > I just prescribe some extension (ie. I displace the top face of the bar
> > using the Dirichlet boundary conditions).
> > What I want is to compute the deformation of the bar (that is OK)
> > but moreover, I want to calculate the force vector which is acting
> > in the top face which is displaced. I use the AUGMENTED_CONSTRAINTS
> > for the Dirichlet condition and so
> > for each prescribed displacement in the nodes of the top face I get
> > a coefficient in the solution vector. How can I use them in GetFem
> > to compute the overall force vector (f_x, f_y, f_z)?
> >
> > I tried simpler version of the deformation -- I just prescribed the
> > displacement one node of the mesh (in x,y,z). Then (using again the
> > AUGMENTED_CONSTRAINTS) I got three numbers in the tail of the solution
> > vector and I considered them being the forces f_x, f_y and f_z acting in
> > that displaced point of the mesh. Is this correct?
>
> Yes, the component of the multiplier corresponding to a certain node
> represents a so called "equivalent force" at this node. If you need the force
> density, you have to use the shape functions of the multiplier fem used.
>
> Yves.
>
> --
>
>  Yves Renard (address@hidden)       tel : (33) 04.72.43.87.08
>  Pole de Mathematiques,                       fax : (33) 04.72.43.85.29
>  Institut Camille Jordan - CNRS UMR 5208
>  INSA de Lyon, Universite de Lyon
>  20, rue Albert Einstein
>  69621 Villeurbanne Cedex, FRANCE
>  http://math.univ-lyon1.fr/~renard
>
> ---------