interpolateMaxwellStressTensor

Compute the Maxwell stress tensor at nodal locations, and then interpolate it to the specified grid.

Create a square geometry.

R1 = [3,4,-1,1,1,-1,1,1,-1,-1]';
g = decsg(R1,'R1',('R1')');

Create an femodel object for magnetostatic analysis. Include the square geometry.

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

Plot the geometry with edge labels.

pdegplot(model,EdgeLabels="on")
xlim([-1.1 1.1])
ylim([-1.1 1.1])

Specify the vacuum permeability 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 sides of the square.

model.EdgeBC([1 3]) = edgeBC(MagneticPotential=0);
model.EdgeBC([2 4]) = edgeBC(MagneticPotential=0.01);

Specify the current density for the entire geometry.

model.FaceLoad = faceLoad(CurrentDensity=0.5);

Generate the mesh. This assignment updates the mesh stored in the Geometry property of the model.

model = generateMesh(model);

Solve the model. The solution R is a MagnetostaticResults object. It does not include the Maxwell stress tensor by default.

R = solve(model)

R = 
  MagnetostaticResults with properties:

      MagneticPotential: [1529x1 double]
          MagneticField: [1x1 FEStruct]
    MagneticFluxDensity: [1x1 FEStruct]
                   Mesh: [1x1 FEMesh]

Generate the Maxwell stress tensor and store it as a property of the results object R.

R = generateMaxwellStressTensor(R)

R = 
  MagnetostaticResults with properties:

      MagneticPotential: [1529x1 double]
          MagneticField: [1x1 FEStruct]
    MagneticFluxDensity: [1x1 FEStruct]
                   Mesh: [1x1 FEMesh]
    MaxwellStressTensor: [2x2x1529 double]

Interpolate the resulting Maxwell stress tensor to a grid covering the central portion of the geometry, for x and y from -0.5 to 0.5.

v = linspace(-0.5,0.5,51);
[X,Y] = meshgrid(v);

MSTintrp = interpolateMaxwellStressTensor(R,X,Y);

Alternatively, you can specify the grid by using a matrix of query points.

querypoints = [X(:),Y(:)]';
MSTintrp = interpolateMaxwellStressTensor(R,querypoints);

Compute the Maxwell stress tensor at nodal locations, and then interpolate it to the specified grid.

Create an femodel object for electrostatic analysis. Include a geometry representing a plate with a hole.

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

Plot the geometry of the plate with face labels.

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

Specify the vacuum permittivity in the SI system of units.

model.VacuumPermittivity = 8.8541878128e-12;

Specify the relative permittivity of the material

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

Specify the charge density for the entire geometry.

model.CellLoad = cellLoad(ChargeDensity=5e-9);

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

model.FaceBC(3:6) = faceBC(Voltage=0);
model.FaceBC(7) = faceBC(Voltage=1000);

Generate the mesh. This assignment updates the mesh stored in the Geometry property of the model.

model = generateMesh(model);

Solve the model. The solution R is an ElectrostaticResults object. It does not include the Maxwell stress tensor by default.

R = solve(model)

R = 
  ElectrostaticResults with properties:

      ElectricPotential: [4919x1 double]
          ElectricField: [1x1 FEStruct]
    ElectricFluxDensity: [1x1 FEStruct]
                   Mesh: [1x1 FEMesh]

Generate the Maxwell stress tensor and store it as a property of the results object R.

R = generateMaxwellStressTensor(R)

R = 
  ElectrostaticResults with properties:

      ElectricPotential: [4919x1 double]
          ElectricField: [1x1 FEStruct]
    ElectricFluxDensity: [1x1 FEStruct]
                   Mesh: [1x1 FEMesh]
    MaxwellStressTensor: [3x3x4919 double]

Interpolate the resulting Maxwell stress tensor to a grid covering the entire geometry, for x, y, and z.

x = linspace(0,10,11);
y = linspace(0,1,5);
z = linspace(0,20,11);
[X,Y,Z] = meshgrid(x,y,z);

MSTintrp = interpolateMaxwellStressTensor(R,X,Y,Z);

Alternatively, you can specify the grid by using a matrix of query points.

querypoints = [X(:),Y(:),Z(:)]';
MSTintrp = interpolateMaxwellStressTensor(R,querypoints);