# [Getdp] LinearElasticity2D-how to apply a force field?

Paolo Guglielmi paolo.guglielmi at polito.it
Wed Oct 27 14:14:28 CEST 2004

```Dear Christophe,

Thanks for the prompt answer.

But things does not work as we expected, i.e. over a ring shaped disk
the displacement are not symmetrical.

Most probably the problem is in the formulation itself. I think that
the centrifugal force field should be proportional to the area of
each single triangle and applied in the direction:

f = Vector (x , y, 0)

in fact if I change the mesh the solution strongly changes.

I am supposing that the correct force vector to be applied to each
element should be given by an integration of the force

F[Slab] = Vector[k*X[], k*Y[], 0]

over the domain itself.

So I try to define a Integral Quantity in the formulation as :

{ Name A; Type Integral; NameOfSpace H_u_Mec2D;
[F[]]; In Domain_Force; Jacobian Vol; Integration GradGrad }

It does not work (error of memory reference); probably because I cannot
adopt an integral quantity this way:

Galerkin { [-{A},{u}];
In Domain_Force; Jacobian Vol; Intagration GradGrad;}

What can we try?

Notes:

- If I calculate the integral the same way described above in the post
processing (but not in the formulation) I can see the vector assigned
to each element be proportonal to the element area.

- Can we use the "A" as a result of a first solution, build a
space of forces, assign the "A" values as constraints to each
element, and than solve the problem again? ( use two different
problems?)

- Adopt "A" as Global Quantity? How?

At last I want to thak you for sharing this really nice program with all
of us.

Regards,

Paolo

On Tue, 26 Oct 2004 00:48:53 -0700
Christophe Geuzaine <geuzaine at acm.caltech.edu> wrote:

> Gianmario Pellegrino wrote:
> > Dear Christophe,
> > first of all congratulations for you very good job and many thanks
> > for sharing it.
> > We're trying to evaluate (my colleague is in copy) the centrifugal
> > stress and deformation of a rotating lamination, but we can't figure
> > out how to express the forcing term as a function of x and y.
> > Except for that, the LinearElasticity2d example fits very well.
> > The centrifugal force per volume is expressed by:
> >
> > f = Vector (k*x , k*y, 0)
> >
> > We tried to declare this term as a function, using both \$X,\$Y and
> > simply X,Y,
> >
> > F[Slab] = Vector[k*\$X, k*\$Y, 0 ]
> >
>
> Right... I almost forgot about this.
>
> Currently, you should use the "current values" \$X, \$Y and \$Z only in
> pre-processing constraints, and use the functions X[], Y[] and Z[] in
> the formulations, i.e.:
>
> F[Slab] = Vector[k*X[], k*Y[], 0]
>
> (We definitely need to clarify the documentation about current values;
> or actually fix the code ;-))
>
> Best,
>
> Christophe
>
> --
> Christophe Geuzaine
> Applied and Computational Mathematics, Caltech
> geuzaine at acm.caltech.edu - http://geuz.org
>

--
Paolo Guglielmi

Researcher
DIEI Politecnico di Torino
C.so Duca degli Abruzzi 24
10129 Torino (TO)
ITALY

ph.  +39 011 564 7150
fax. +39 011 564 7199
email paolo.guglielmi at polito.it

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