pdeplot3D

Plot solution or surface mesh for 3-D problem

Syntax

pdeplot3D(model,'ColorMapData',results.NodalSolution)

pdeplot3D(model,'ColorMapData',results.Temperature)

pdeplot3D(model,'ColorMapData',results.VonMisesStress,'Deformation',results.Displacement)

pdeplot3D(model,'ColorMapData',results.ElectricPotential)

pdeplot3D(model)

pdeplot3D(mesh)

pdeplot3D(nodes,elements)

pdeplot3D(___,Name,Value)

h = pdeplot3D(___)

Description

pdeplot3D(model,'ColorMapData',results.NodalSolution) plots the solution at nodal locations as colors on the surface of the 3-D geometry specified in model.

pdeplot3D(model,'ColorMapData',results.Temperature) plots the temperature at nodal locations for a 3-D thermal analysis model.

pdeplot3D(model,'ColorMapData',results.VonMisesStress,'Deformation',results.Displacement) plots the von Mises stress and shows the deformed shape for a 3-D structural analysis model.

pdeplot3D(model,'ColorMapData',results.ElectricPotential) plots the electric potential at nodal locations for a 3-D electrostatic analysis model.

pdeplot3D(model) plots the surface mesh specified in model.

pdeplot3D(mesh) plots the mesh defined as a Mesh property of a 3-D model object of type PDEModel.

pdeplot3D(nodes,elements) plots the mesh defined by nodes and elements.

pdeplot3D(___,Name,Value) plots the surface mesh, the data at nodal locations, or both the mesh and data, depending on the Name,Value pair arguments. Use any arguments from the previous syntaxes.

h = pdeplot3D(___) returns a handle to a plot, using any of the previous syntaxes.

Examples

Solution Plot on Surface

Plot a PDE solution on the geometry surface. First, create a PDE model and import a 3-D geometry file. Specify boundary conditions and coefficients. Mesh the geometry and solve the problem.

model = createpde;
importGeometry(model,'Block.stl');
applyBoundaryCondition(model,'dirichlet','Face',[1:4],'u',0);
specifyCoefficients(model,'m',0,'d',0,'c',1,'a',0,'f',2);
generateMesh(model);
results = solvepde(model)

results = 
  StationaryResults with properties:

    NodalSolution: [12691x1 double]
       XGradients: [12691x1 double]
       YGradients: [12691x1 double]
       ZGradients: [12691x1 double]
             Mesh: [1x1 FEMesh]

Access the solution at the nodal locations.

u = results.NodalSolution;

Plot the solution u on the geometry surface.

pdeplot3D(model,'ColorMapData',u)

Solution to Steady-State Thermal Model

Solve a 3-D steady-state thermal problem.

Create a thermal model for this problem.

thermalmodel = createpde('thermal');

Import and plot the block geometry.

importGeometry(thermalmodel,'Block.stl'); 
pdegplot(thermalmodel,'FaceLabel','on','FaceAlpha',0.5)
axis equal

Assign material properties.

thermalProperties(thermalmodel,'ThermalConductivity',80);

Apply a constant temperature of 100 °C to the left side of the block (face 1) and a constant temperature of 300 °C to the right side of the block (face 3). All other faces are insulated by default.

thermalBC(thermalmodel,'Face',1,'Temperature',100);
thermalBC(thermalmodel,'Face',3,'Temperature',300);

Mesh the geometry and solve the problem.

generateMesh(thermalmodel);
thermalresults = solve(thermalmodel)

thermalresults = 
  SteadyStateThermalResults with properties:

    Temperature: [12691x1 double]
     XGradients: [12691x1 double]
     YGradients: [12691x1 double]
     ZGradients: [12691x1 double]
           Mesh: [1x1 FEMesh]

The solver finds the temperatures and temperature gradients at the nodal locations. To access these values, use thermalresults.Temperature, thermalresults.XGradients, and so on. For example, plot temperatures at the nodal locations.

pdeplot3D(thermalmodel,'ColorMapData',thermalresults.Temperature)

Heat Flux for 3-D Steady-State Thermal Model

For a 3-D steady-state thermal model, evaluate heat flux at the nodal locations and at the points specified by x, y, and z coordinates.

Create a thermal model for steady-state analysis.

thermalmodel = createpde('thermal');

Create the following 3-D geometry and include it in the model.

importGeometry(thermalmodel,'Block.stl'); 
pdegplot(thermalmodel,'FaceLabels','on','FaceAlpha',0.5)
title('Copper block, cm')
axis equal

Assuming that this is a copper block, the thermal conductivity of the block is approximately $$4W/(cmK)$$.

thermalProperties(thermalmodel,'ThermalConductivity',4);

Apply a constant temperature of 373 K to the left side of the block (face 1) and a constant temperature of 573 K to the right side of the block (face 3).

thermalBC(thermalmodel,'Face',1,'Temperature',373);
thermalBC(thermalmodel,'Face',3,'Temperature',573);

Apply a heat flux boundary condition to the bottom of the block.

thermalBC(thermalmodel,'Face',4,'HeatFlux',-20);

Mesh the geometry and solve the problem.

generateMesh(thermalmodel);
thermalresults = solve(thermalmodel)

thermalresults = 
  SteadyStateThermalResults with properties:

    Temperature: [12691x1 double]
     XGradients: [12691x1 double]
     YGradients: [12691x1 double]
     ZGradients: [12691x1 double]
           Mesh: [1x1 FEMesh]

Evaluate heat flux at the nodal locations.

[qx,qy,qz] = evaluateHeatFlux(thermalresults);

figure
pdeplot3D(thermalmodel,'FlowData',[qx qy qz])

Create a grid specified by x, y, and z coordinates, and evaluate heat flux to the grid.

[X,Y,Z] = meshgrid(1:26:100,1:6:20,1:11:50);

[qx,qy,qz] = evaluateHeatFlux(thermalresults,X,Y,Z);

Reshape the qx, qy, and qz vectors, and plot the resulting heat flux.

qx = reshape(qx,size(X));
qy = reshape(qy,size(Y));
qz = reshape(qz,size(Z));
figure
quiver3(X,Y,Z,qx,qy,qz)

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

querypoints = [X(:) Y(:) Z(:)]';
[qx,qy,qz] = evaluateHeatFlux(thermalresults,querypoints);

qx = reshape(qx,size(X));
qy = reshape(qy,size(Y));
qz = reshape(qz,size(Z));
figure
quiver3(X,Y,Z,qx,qy,qz)

Deformed Shape for Cantilever Beam Problem

Create a structural analysis model for a 3-D problem.

structuralmodel = createpde('structural','static-solid');

Import the geometry and plot it.

importGeometry(structuralmodel,'SquareBeam.stl');
pdegplot(structuralmodel,'FaceLabels','on','FaceAlpha',0.5)

Specify the Young's modulus and Poisson's ratio.

structuralProperties(structuralmodel,'PoissonsRatio',0.3, ...
                                     'YoungsModulus',210E3);

Specify that face 6 is a fixed boundary.

structuralBC(structuralmodel,'Face',6,'Constraint','fixed');

Specify the surface traction for face 5.

structuralBoundaryLoad(structuralmodel,'Face',5, ...
                                       'SurfaceTraction', ...
                                       [0;0;-2]);

Generate a mesh and solve the problem.

generateMesh(structuralmodel);
structuralresults = solve(structuralmodel);

Plot the deformed shape with the von Mises stress using the default scale factor. By default, pdeplot3D internally determines the scale factor based on the dimensions of the geometry and the magnitude of deformation.

figure    
pdeplot3D(structuralmodel, ...
          'ColorMapData',structuralresults.VonMisesStress, ...
          'Deformation',structuralresults.Displacement)

Plot the same results with the scale factor 500.

figure
pdeplot3D(structuralmodel, ...
          'ColorMapData',structuralresults.VonMisesStress, ...
          'Deformation',structuralresults.Displacement, ...
          'DeformationScaleFactor',500)

Plot the same results without scaling.

figure
pdeplot3D(structuralmodel, ...
          'ColorMapData',structuralresults.VonMisesStress)

von Mises Stress for 3-D Structural Dynamic Problem

Evaluate the von Mises stress in a beam under a harmonic excitation.

Create a transient dynamic model for a 3-D problem.

structuralmodel = createpde('structural','transient-solid');

Create the geometry and include it in the model. Plot the geometry.

gm = multicuboid(0.06,0.005,0.01);
structuralmodel.Geometry = gm;
pdegplot(structuralmodel,'FaceLabels','on','FaceAlpha',0.5)
view(50,20)

Specify the Young's modulus, Poisson's ratio, and mass density of the material.

structuralProperties(structuralmodel,'YoungsModulus',210E9, ...
                                     'PoissonsRatio',0.3, ...
                                     'MassDensity',7800);

Fix one end of the beam.

structuralBC(structuralmodel,'Face',5,'Constraint','fixed');

Apply a sinusoidal displacement along the y-direction on the end opposite the fixed end of the beam.

structuralBC(structuralmodel,'Face',3, ...
                             'YDisplacement',1E-4, ...
                             'Frequency',50);

Generate a mesh.

generateMesh(structuralmodel,'Hmax',0.01);

Specify the zero initial displacement and velocity.

structuralIC(structuralmodel,'Displacement',[0;0;0],'Velocity',[0;0;0]);

Solve the model.

tlist = 0:0.002:0.2;
structuralresults = solve(structuralmodel,tlist);

Evaluate the von Mises stress in the beam.

vmStress = evaluateVonMisesStress(structuralresults);

Plot the von Mises stress for the last time-step.

figure
pdeplot3D(structuralmodel,'ColorMapData',vmStress(:,end))
title('von Mises Stress in the Beam for the Last Time-Step')

Solution to 3-D Electrostatic Analysis Model

Solve an electromagnetic problem and find the electric potential and field distribution for a 3-D geometry representing a plate with a hole.

Create an electromagnetic model for electrostatic analysis.

emagmodel = createpde('electromagnetic','electrostatic');

Import and plot the geometry representing a plate with a hole.

gm = importGeometry(emagmodel,'PlateHoleSolid.stl');
pdegplot(gm,'FaceLabels','on','FaceAlpha',0.3)

Specify the vacuum permittivity in the SI system of units.

emagmodel.VacuumPermittivity = 8.8541878128E-12;

Specify the relative permittivity of the material.

electromagneticProperties(emagmodel,'RelativePermittivity',1);

Specify the charge density for the entire geometry.

electromagneticSource(emagmodel,'ChargeDensity',5E-9);

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

electromagneticBC(emagmodel,'Voltage',0,'Face',3:6);
electromagneticBC(emagmodel,'Voltage',1000,'Face',7);

Generate the mesh.

generateMesh(emagmodel);

Solve the model.

R = solve(emagmodel)

R = 
  ElectrostaticResults with properties:

      ElectricPotential: [4359x1 double]
          ElectricField: [1x1 FEStruct]
    ElectricFluxDensity: [1x1 FEStruct]
                   Mesh: [1x1 FEMesh]

Plot the electric potential.

figure
pdeplot3D(emagmodel,'ColorMapData',R.ElectricPotential)

Plot the electric field.

pdeplot3D(emagmodel,'FlowData',[R.ElectricField.Ex ...
                                R.ElectricField.Ey ...
                                R.ElectricField.Ez])

3-D Mesh Plot

Create a PDE model, include the geometry, and generate a mesh.

model = createpde;
importGeometry(model,'Tetrahedron.stl');
mesh = generateMesh(model,'Hmax',20,'GeometricOrder','linear');

Plot the surface mesh.

pdeplot3D(model)

Alternatively, you can plot a mesh by using mesh as an input argument.

pdeplot3D(mesh)

Another approach is to use the nodes and elements of the mesh as input arguments for pdeplot3D.

pdeplot3D(mesh.Nodes,mesh.Elements)

Display the node labels on the surface of a simple mesh.

pdeplot3D(model,'NodeLabels','on')
view(101,12)

Display the element labels.

pdeplot3D(model,'ElementLabels','on')
view(101,12)

Input Arguments

model — Model object

PDEModel object | ThermalModel object | StructuralModel object | ElectromagneticModel object

Model object, specified as a PDEModel object, ThermalModel object, StructuralModel object, or ElectromagneticModel object.

Example: model = createpde(3)

Example: thermalmodel = createpde('thermal','steadystate')

Example: structuralmodel = createpde('structural','static-solid')

Example: emagmodel = createpde('electromagnetic','electrostatic')

mesh — Mesh object

Mesh property of a PDEModel object | output of generateMesh

Mesh object, specified as the Mesh property of a PDEModel object or as the output of generateMesh.

Example: model.Mesh

nodes — Nodal coordinates

3-by-NumNodes matrix

Nodal coordinates, specified as a 3-by-NumNodes matrix. NumNodes is the number of nodes.

elements — Element connectivity matrix in terms of node IDs

4-by-NumElements matrix | 10-by-NumElements matrix

Element connectivity matrix in terms of the node IDs, specified as a 4-by-NumElements or 10-by-NumElements matrix. Linear meshes contain only corner nodes. For linear meshes, the connectivity matrix has four nodes per 3-D element. Quadratic meshes contain corner nodes and nodes in the middle of each edge of an element. For quadratic meshes, the connectivity matrix has 10 nodes per 3-D element.

Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: pdeplot3D(model,'NodeLabels','on')

ColorMapData — Data to plot as colored surface

column vector

Data to plot as a colored surface, specified as the comma-separated pair consisting of 'ColorMapData' and a column vector with the number of elements that equals the number of points in the mesh. Typically, this data is the solution returned by solvepde for a scalar PDE problem and a component of the solution for a multicomponent PDE system.

Example: 'ColorMapData',results.NodalSolution

Example: 'ColorMapData',results.NodalSolution(:,1)

Data Types: double

FlowData — Data for quiver plot

matrix

Data for the quiver plot, specified as the comma-separated pair consisting of 'FlowData' and an M-by-3 matrix, where M is the number of mesh nodes. FlowData contains the x, y, and z values of the field at the mesh points. Set FlowData as follows:

results = solvepde(model);
[cgradx,cgrady,cgradz] = evaluateCGradient(results);
pdeplot3D(model,'FlowData',[cgradx cgrady cgradz])

pdeplot3D plots the real part of complex data.

Example: 'FlowData',[cgradx cgrady cgradz]

Data Types: double

Mesh — Indicator to show mesh

'off' (default) | 'on'

Indicator to show the mesh, specified as the comma-separated pair consisting of 'Mesh' and 'on' or 'off'. Specify 'on' to show the mesh in the plot.

Example: 'Mesh','on'

Data Types: char | string

NodeLabels — Node labels

'off' (default) | 'on'

Node labels, specified as the comma-separated pair consisting of 'NodeLabels' and 'off' or 'on'.

Example: 'NodeLabels','on'

Data Types: char | string

ElementLabels — Element labels

'off' (default) | 'on'

Element labels, specified as the comma-separated pair consisting of 'ElementLabels' and 'off' or 'on'.

Example: 'ElementLabels','on'

Data Types: char | string

FaceAlpha — Surface transparency for 3-D geometry

1 (default) | real number from 0 through 1

Surface transparency for 3-D geometry, specified as the comma-separated pair consisting of 'FaceAlpha' and a real number from 0 through 1. The default value 1 indicates no transparency. The value 0 indicates complete transparency.

Example: 'FaceAlpha',0.5

Data Types: double

Deformation — Deformed shape for structural analysis models

FEStruct object representing displacement values at nodes

Deformed shape for structural analysis models, specified as the comma-separated pair consisting of 'Deformation' and the FEStruct object representing displacement values at nodes. The displacement FEStruct object is a property of StaticStructuralResults, TransientStructuralResults, and FrequencyStructuralResults.

In an undeformed shape, center nodes in quadratic meshes are always added at half-distance between corners. When you plot a deformed shape, the center nodes might move away from the edge centers.

Example: 'Deformation',results.Displacement

DeformationScaleFactor — Scaling factor for plotting deformed shape

positive number

Scaling factor for plotting the deformed shape, specified as the comma-separated pair consisting of 'DeformationScaleFactor' and a positive number. Use this argument together with the Deformation name-value pair argument. The pdeplot3D function chooses the default value based on the geometry itself and on the magnitude of deformation.

Example: 'DeformationScaleFactor',1000

Data Types: double

Output Arguments

h — Handles to graphics objects

vector

Handles to graphics objects, returned as a vector.