MagnetostaticResults

Solve a 2-D electromagnetic problem on a geometry representing a plate with a hole in its center. Plot the resulting magnetic potential and field distribution.

Create an femodel object for magnetostatic analysis and include a geometry representing a plate with a hole.

model = femodel(AnalysisType="magnetostatic", ...
                Geometry="PlateHolePlanar.stl");

Plot the geometry.

pdegplot(model.Geometry,EdgeLabels="on")

Specify the vacuum permeability value in the SI system of units.

model.VacuumPermeability = 1.2566370614e-6;

Specify the relative permeability of the material.

model.MaterialProperties = ...
    materialProperties(RelativePermeability=5000);

Apply the magnetic potential boundary conditions on the edges framing the rectangle and the circle.

model.EdgeBC(1:4) = edgeBC(MagneticPotential=0); 
model.EdgeBC(5) = edgeBC(MagneticPotential=0.01);

Specify the current density for the entire geometry.

model.FaceLoad = faceLoad(CurrentDensity=0.5);

Generate the mesh.

model = generateMesh(model);

Solve the problem.

R = solve(model)

R = 
  MagnetostaticResults with properties:

      MagneticPotential: [1231x1 double]
          MagneticField: [1x1 FEStruct]
    MagneticFluxDensity: [1x1 FEStruct]
                   Mesh: [1x1 FEMesh]

Plot the magnetic potential and field.

pdeplot(R.Mesh,XYData=R.MagneticPotential, ...
               FlowData=[R.MagneticField.Hx ...
                         R.MagneticField.Hy])
axis equal

Solve a 3-D electromagnetic problem on a geometry representing a plate with a hole in its center. Plot the resulting magnetic potential and field distribution.

Create an femodel object for magnetostatic analysis and include a geometry representing a plate with a hole.

model = femodel(AnalysisType="magnetostatic", ...
                Geometry="PlateHoleSolid.stl");

Plot the geometry.

pdegplot(model.Geometry,FaceLabels="on",FaceAlpha=0.3)

Specify the vacuum permeability value in the SI system of units.

model.VacuumPermeability = 1.2566370614e-6;

Specify the relative permeability of the material.

model.MaterialProperties = ...
    materialProperties(RelativePermeability=5000);

Apply the magnetic potential boundary conditions on the side faces and the face bordering the hole.

model.FaceBC(3:6) = faceBC(MagneticPotential=[0;0;0]); 
model.FaceBC(7) = faceBC(MagneticPotential=[0;0;0.01]);

Specify the current density for the entire geometry.

model.CellLoad = cellLoad(CurrentDensity=[0;0;0.5]);

Generate the mesh.

model = generateMesh(model);

Solve the model.

R = solve(model)

R = 
  MagnetostaticResults with properties:

      MagneticPotential: [1x1 FEStruct]
          MagneticField: [1x1 FEStruct]
    MagneticFluxDensity: [1x1 FEStruct]
                   Mesh: [1x1 FEMesh]

Plot the z-component of the magnetic potential.

pdeplot3D(R.Mesh,ColormapData=R.MagneticPotential.Az)

Plot the magnetic field.

pdeplot3D(R.Mesh,FlowData=[R.MagneticField.Hx ...
                           R.MagneticField.Hy ...
                           R.MagneticField.Hz])

Use a solution obtained by performing a DC conduction analysis to specify current density for a magnetostatic problem.

Create an femodel object for DC conduction analysis and include a geometry representing a plate with a hole.

model = femodel(AnalysisType="dcConduction", ...
                Geometry="PlateHoleSolid.stl");

Plot the geometry.

pdegplot(model.Geometry,FaceLabels="on",FaceAlpha=0.3)

Specify the conductivity of the material.

model.MaterialProperties = ...
    materialProperties(ElectricalConductivity=6e4);

Apply the voltage boundary conditions on the left, right, top, and bottom faces of the plate.

model.FaceBC(3:6) = faceBC(Voltage=0);

Specify the surface current density on the face bordering the hole.

model.FaceLoad(7) = faceLoad(SurfaceCurrentDensity=100);

Generate the mesh.

model = generateMesh(model);

Solve the model.

R = solve(model);

Change the analysis type of the model to magnetostatic.

model.AnalysisType = "magnetostatic";

This model already has a quadratic mesh that you generated for the DC conduction analysis. For a 3-D magnetostatic model, the mesh must be linear. Generate a new linear mesh. The generateMesh function creates a linear mesh by default if the model is 3-D and magnetostatic.

model = generateMesh(model);

Specify the vacuum permeability value in the SI system of units.

model.VacuumPermeability = 1.2566370614e-6;

Specify the relative permeability of the material.

model.MaterialProperties = ...
    materialProperties(RelativePermeability=5000);

Apply the magnetic potential boundary conditions on the side faces and the face bordering the hole.

model.FaceBC(3:6) = faceBC(MagneticPotential=[0;0;0]);
model.FaceBC(7) = faceBC(MagneticPotential=[0;0;0.01]);

Specify the current density for the entire geometry using the DC conduction solution.

model.CellLoad = cellLoad(CurrentDensity=R);

Solve the problem.

Rmagnetostatic = solve(model);

Plot the x- and z-components of the magnetic potential.

pdeplot3D(Rmagnetostatic.Mesh, ...
          ColormapData=Rmagnetostatic.MagneticPotential.Ax)

pdeplot3D(Rmagnetostatic.Mesh, ...
          ColormapData=Rmagnetostatic.MagneticPotential.Az)

Solve a magnetostatic problem of a copper square with a permanent neodymium magnet in its center.

Create the unit square geometry with a circle in its center.

L = 0.8;
r = 0.25;
sq = [3 4 -L L L -L -L -L L L]';
circ = [1 0 0 r 0 0 0 0 0 0]';
gd = [sq,circ];
sf = "sq + circ";
ns = char('sq','circ');
ns = ns';
g = decsg(gd,sf,ns);

Plot the geometry with the face and edge labels.

pdegplot(g,FaceLabels="on",EdgeLabels="on")

Create an femodel object for magnetostatic analysis and include the geometry in the model.

model = femodel(AnalysisType="magnetostatic", ...
                Geometry=g);

Specify the vacuum permeability value in the SI system of units.

model.VacuumPermeability = 1.2566370614e-6;

Specify the relative permeability of the copper for the square.

model.MaterialProperties(1) = ...
    materialProperties(RelativePermeability=1);

Specify the relative permeability of the neodymium for the circle.

model.MaterialProperties(2) = ...
    materialProperties(RelativePermeability=1.05);

Specify the magnetization magnitude for the neodymium magnet.

M = 1e6;

Specify magnetization on the circular face in the positive x-direction. Magnetization for a 2-D model is a column vector of two elements.

dir = [1;0];
model.FaceLoad(2) = faceLoad(Magnetization=M*dir);

Apply the magnetic potential boundary conditions on the edges framing the square.

model.EdgeBC(1:4) = edgeBC(MagneticPotential=0);

Generate the mesh with finer meshing near the edges of the circle.

model = generateMesh(model,Hedge={5:8,0.007});
figure
pdemesh(model)

Solve the problem, and find the resulting magnetic fields B and H. Here, $\mathit{B}=\mu \mathit{H}+{\mu }_0\mathit{M}$, where $\mu$ is the absolute magnetic permeability of the material, ${\mu }_0$ is the vacuum permeability, and $\mathit{M}$ is the magnetization.

R = solve(model);
Bmag = sqrt(R.MagneticFluxDensity.Bx.^2 + R.MagneticFluxDensity.By.^2);
Hmag = sqrt(R.MagneticField.Hx.^2 + R.MagneticField.Hy.^2);

Plot the magnetic field B.

figure
pdeplot(R.Mesh,XYData=Bmag, ...
               FlowData=[R.MagneticFluxDensity.Bx ...
                         R.MagneticFluxDensity.By])

Plot the magnetic field H.

figure
pdeplot(R.Mesh,XYData=Hmag, ...
               FlowData=[R.MagneticField.Hx R.MagneticField.Hy])