[Getdp] Question about force on magnets

[Ruth Vazquez Sabariego]

On 13 Apr 2017, at 09:38, Pablo Xavier Jara Palacios <pabloxjara at gmail.com<mailto:pabloxjara at gmail.com>> wrote:

Thanks Ruth, I really appreciate your help. Do you mean that un is used for the purpose of compute the normal direction of the force on each magnet?.
Not on each magnet but on each element that touches the boundary of the magnet.
On the other hand, in the weak formulation this part  "Galerkin { [ 0 * Dof{un~{i}} , {un~{i}} ]" is a separetely equation or is part of the same  equation of the weak formulation either scalar o vector potential?
You can see it as a dummy equation, as it has no influence on the system you are actually solving.
It is an additional equation with the only objective of generating the degrees of freedom (Dofs), they are set to zero unless indicated otherwise via a constraint.

The thing is that I do not undestand how un is computed if there is a 0 that is multipliying inside the integranl, so I would suppose that everything is canceled out in the integral.
As I said, it is not computed. All the coefficients associated with that basis function are set to zero except the ones fixed via the constraint => the boundary is set to one.

In this point is where I do not know how un is calculated at the end. Please maybe could you recommend me any book or paper where I could find a similar example?
I do not think there is an example of this as is. The 0 multiplying an equation, it is just a GetDP trick for getting the local normal.

The papers you can have a look at are those dealing with the Maxwell Stress Tensor, also called Arkkio method in the electrical-machine modelling community.

Have a look at:
A. Arkkio, Analysis of induction motors based on the numerical solution of the magnetic field and circuit equations , Acta Polytechnica Scandinavica, 1987, p. 56
Z. Ren, A. Razek, Local force computation in deformable bodies using edge elements , IEEE Trans. Magnetics, 28(2):1212–1215, 1992.
F. Henrotte, G. Deliége, K. Hameyer, The eggshell approach for the computations of electromagnetic forces in 2D and 3D , COMPEL, 23(4), 996–1005, 2004.

Regards,
Ruth




regards,




2017-04-12 7:43 GMT-07:00 Ruth Vazquez Sabariego <ruth.sabariego at kuleuven.be<mailto:ruth.sabariego at kuleuven.be>>:
Dear Pablo Xavier,

The force is calculated by means of the Maxwell Stress Tensor with the local normal computed with the help of an auxiliary basis function.
The dummy term added in the formulation is then only used in the post-processing stage for the force computation.

The unknowns linked to this basis function un are indeed fully fixed and linked to a layer of elements touching the magnet.
We impose 1 at the boundary of the magnet and the rest of the values are  0, as the function varies linearly per element, the gradient gives the normal modulus the size of the element.

HTH,
Ruth


—
Prof. Ruth V. Sabariego
KU Leuven
Dept. Electrical Engineering ESAT/Electa, EnergyVille
http://www.esat.kuleuven.be/electa
http://www.energyville.be

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On 12 Apr 2017, at 08:52, Pablo Xavier Jara Palacios <pabloxjara at gmail.com> wrote:

Hi,
I was reviewing the .pro file in example of magnet which is posted in onelab's page, but I do not understand how the force is calculated in this problem. There is a dummy term in the formulation that I do not know what it is. Please help me with this doubt.

Regards,


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