MagnetostaticResults
Description
A MagnetostaticResults object contains the
magnetic potential, magnetic field, magnetic flux density, and mesh values in a form
convenient for plotting and postprocessing.
The magnetic potential, magnetic field, and magnetic flux density are calculated at the
nodes of the triangular or tetrahedral mesh generated by generateMesh. Magnetic potential values at the nodes appear in the
MagneticPotential property. Magnetic field values at the nodes appear in
the MagneticField property. Magnetic flux density values at the nodes
appear in the MagneticFluxDensity property.
To interpolate the magnetic potential, magnetic field, and magnetic flux density to a
custom grid, such as the one specified by meshgrid, use the interpolateMagneticPotential, interpolateMagneticField, and interpolateMagneticFlux functions.
Creation
Solve a magnetostatic problem using the solve function. This function returns a solution as a MagnetostaticResults object.
Properties
Object Functions
generateMaxwellStressTensor | Compute Maxwell stress tensor at nodal locations |
interpolateMagneticPotential | Interpolate magnetic potential in magnetostatic result at arbitrary spatial locations |
interpolateMagneticField | Interpolate magnetic field in magnetostatic result at arbitrary spatial locations |
interpolateMagneticFlux | Interpolate magnetic flux density in magnetostatic result at arbitrary spatial locations |
interpolateMaxwellStressTensor | Interpolate Maxwell stress tensor at arbitrary spatial locations |
Examples
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: [1231×1 double]
MagneticField: [1×1 FEStruct]
MagneticFluxDensity: [1×1 FEStruct]
Mesh: [1×1 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: [1×1 FEStruct]
MagneticField: [1×1 FEStruct]
MagneticFluxDensity: [1×1 FEStruct]
Mesh: [1×1 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, , where is the absolute magnetic permeability of the material, is the vacuum permeability, and 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]) axis equal
Plot the magnetic field H.
figure pdeplot(R.Mesh,XYData=Hmag, ... FlowData=[R.MagneticField.Hx R.MagneticField.Hy]) axis equal
Version History
Introduced in R2021a
