[Getfem-users] TR: RE: Sliding angle for Dirichlet condition

[SIMON AMEYE]

Dear all,

 

I finally found thanks to Yves.

In my case, the Dirichlet condition matrix

 matrix needs to validate the condition : H^2=k*H

If not, the sliding is blocked.

H = [x1 x2; x3 x4]

Moreover, [x1 x2] needs to be a vector orthogonal with the sliding direction of the boundary with the Dirichlet condition.

Here is a way I set my H matrix, with ‘Angle’ the angle between the sliding direction and [1 0].

 

x2 = -1;

x1 =tan(Angle);

x4 = (x2./sqrt(x1))^2;

x3 = x2;

 

Thank you again for your help,

 

Simon

 

 

 

De : SIMON AMEYE - U510180
Envoyé : mercredi 31 octobre 2018 10:58
À : 'address@hidden' <address@hidden>
Objet : RE: [Getfem-users] Sliding angle for Dirichlet condition

 

Dear Yves,

 

Thank you for your quick answer.

I tried H = [-2 1;0 0] but when the condition I found is not respected, the boundary is completely blocked.

It only slides when this condition is respected : A^2=k*A.

For example :

 

A =

   10.9899   -3.3151

   -3.3151    1.0000

 

If this property is not true, the boundary is blocked. I came to this conclusion trying a lot of combinations.

The problem is that I can't find the relation between the matrix definition and the sliding vector.

 

I want to precise that I use GetFem without having installed the full version (basic installation).

 

I attach my code below.

 

Simon

 

 

 

rot_mesh = gfMesh('from string', StringMesh);

 

 

%% Initialisation

gf_workspace('clear all')

% Numerical parameters

global E_rotor Nu_rotor

E = E_rotor; Nu = Nu_rotor;

lambda = E*Nu/((1+Nu)*(1-2*Nu));

mu = E/(2*(1+Nu));

 

%% Declaration of the mesh to GetFem

rot_mesh = gfMesh('from string', StringMesh);

 

 

%% Setting the var description

mim=gfMeshIm(rot_mesh);  set(mim, 'integ',gfInteg('IM_TRIANGLE(6)'));

mfu=gfMeshFem(rot_mesh,2); set(mfu, 'fem',gfFem('FEM_PK(2,1)'));

mfd=gfMeshFem(rot_mesh); set(mfd, 'fem',gfFem('FEM_PK(2,1)'));

mf0=gfMeshFem(rot_mesh); set(mf0, 'fem',gfFem('FEM_PK(2,0)'));

mfdu=gfMeshFem(rot_mesh); set(mfdu, 'fem',gfFem('FEM_PK_DISCONTINUOUS(2,1)'));

 

 

%% Boundary calculation

P=get(rot_mesh, 'pts');

pidlow=find(abs(P(2,:))<1e-6); %the bottom boundary can also be found using 'LowEdgeNodes' var

flow =get(rot_mesh,'faces from pid',pidlow);

ftop=get(rot_mesh,'faces from pid',(TopEdgeNodes'+1));

 

%% Assign boundary numbers

LOW_BOUND = 1; TOP_BOUND = 2;

rot_mesh.set_region(LOW_BOUND, flow);

rot_mesh.set_region(TOP_BOUND, ftop);

 

 

%% MODEL

md=gf_model('real');

gf_model_set(md, 'add fem variable', 'u', mfu);

gf_model_set(md, 'add initialized data', 'lambda', lambda);

gf_model_set(md, 'add initialized data', 'mu', mu);

gf_model_set(md, 'add isotropic linearized elasticity brick', mim, 'u', 'lambda', 'mu');

 

%% Centrifugal force source term

% 2D Centrifugal Force Model : F = Rho * W^2 * Distance_with_center .*[x or y].*Projection_On_[x or y]

FXX = get(mfd, 'eval', {[num2str(Rho_rotor),'.*',num2str(W),'.^2.*(x.^2+y.^2).^0.5   .*x./((x.^2+y.^2).^0.5)']});

FYY = get(mfd, 'eval', {[num2str(Rho_rotor),'.*',num2str(W),'.^2.*(x.^2+y.^2).^0.5   .*y./((x.^2+y.^2).^0.5)']});

gf_model_set(md, 'add initialized fem data', 'VolumicData', mfd, [FXX;FYY]);

gf_model_set(md, 'add source term brick', mim, 'u', 'VolumicData');

% Referencing cource terms to the right number

gf_model_set(md, 'add initialized data', ['VolumicData' num2str(Init_For_Mag_Term+i)], [Magn(i).PressureX,Magn(i).PressureY]);

       gf_model_set(md, 'add source term brick', mim, 'u', ['VolumicData' num2str(Init_For_Mag_Term+i)],Init_For_Mag_Term+i);

 

%% Sliding dirichlet conditions

% H matrix building : H_top is a projector (Hat) mathix : H^2=k*h and must be symetrical

% The H matrix rules the sliding angle of the boundary

x4 = 1;x1 =TopAngle;k = x4+x1;x2 = sqrt(x1)*(-sqrt(k-x1));x3 = x2;

gf_model_set(md, 'add initialized data', 'H_LOW', [0 0;0 1]);

gf_model_set(md, 'add initialized data', 'VECTOR_LOW', [0;0]);

gf_model_set(md, 'add initialized data', 'H_TOP', [x1 x2;x3 x4]);

gf_model_set(md, 'add initialized data', 'VECTOR_TOP', [0;0]);

gf_model_set(md, 'add generalized Dirichlet condition with multipliers', mim, 'u', mfu, LOW_BOUND,'VECTOR_LOW', 'H_LOW');

gf_model_set(md, 'add generalized Dirichlet condition with multipliers', mim, 'u', mfu, TOP_BOUND,'VECTOR_TOP', 'H_TOP');

 

 

%% Solver

gf_model_get(md, 'solve');

U = gf_model_get(md, 'variable', 'u');

VM = gf_model_get(md, 'compute isotropic linearized Von Mises or Tresca', 'u', 'lambda', 'mu', mfdu);

Max_VM = max(VM); %Pa

Max_Displacement = max(U); %m

 

 

 

 

-----Message d'origine-----

De : Yves Renard <address@hidden>

Envoyé : mercredi 31 octobre 2018 09:43

À : SIMON AMEYE - U510180 <address@hidden>

Cc : getfem-users <address@hidden>

Objet : Re: [Getfem-users] Sliding angle for Dirichlet condition

 

>>> Real sender address / Reelle adresse d expedition :

>>> address@hidden <<<

 

**********************************************************************

 

 

Dear Simon,

 

A priori, H is not necessarilly a hat matrix. In that case, you can juste take an orthognal vector, for instance [-2 1] and set H = [-2 1;0 0]], this should work, I think.

 

Best regards,

 

Yves

 

 

----- Original Message -----

From: "SIMON AMEYE" <address@hidden>

To: "getfem-users" <address@hidden>

Sent: Tuesday, October 30, 2018 1:52:54 PM

Subject: [Getfem-users] Sliding angle for Dirichlet condition

 

C1-Non sensitive

 

________________________________

Hi all,

 

It has been a long time I have tried to understand the H matrix for Dirichlet conditions.

I work with a 2D mesh, and I would like my boundary to slide freely according to a vector, let's say [1 2].

I think I understood that H needs to be a Hat matrix.

How to do so ?

 

I tried to construct a hat matrix this way, but the "Angle" is not respected :

 

x4 = 1;

x1 = x4/(pi/2/Angle);

k = x4+x1;

x2 = sqrt(x1)*(-sqrt(k-x1));

x3 = x2;

gf_model_set(md, 'add initialized data', 'H_TOP', [x1 x2;x3 x4]); gf_model_set(md, 'add initialized data', 'VECTOR_TOP', [0;0]); gf_model_set(md, 'add generalized Dirichlet condition with multipliers', mim, 'u', mfu, TOP_BOUND,'VECTOR_TOP', 'H_TOP');

 

Simon