pdeplot
Plot solution or mesh for 2-D problem
Syntax
Description
pdeplot(results.Mesh,XYData=results.Temperature,ColorMap="hot")
plots the temperature at nodal locations for a 2-D thermal analysis problem.
This syntax creates a colored surface plot using the "hot"
colormap.
pdeplot(results.Mesh,XYData=results.VonMisesStress,Deformation=results.Displacement)
plots the von Mises stress and shows the deformed shape for a 2-D structural
analysis problem.
pdeplot(results.Mesh,XYData=results.ModeShapes.ux)
plots
the x-component of the modal displacement for a 2-D
structural modal analysis problem.
pdeplot(results.Mesh,XYData=results.ElectricPotential)
plots the electric potential at nodal locations for a 2-D electrostatic analysis
problem.
pdeplot(results.Mesh,XYData=results.NodalSolution)
plots
the solution at nodal locations as a colored surface plot using the default
colormap.
pdeplot(
plots the mesh
specified in model
)model
. This syntax does not work with an
femodel
object.
pdeplot(___,
plots the mesh, the data at the nodal locations, or both the mesh and the data,
using the Name,Value
)Name,Value
pair arguments. Use any arguments from
the previous syntaxes.
Specify at least one of the FlowData
(vector field plot),
XYData
(colored surface plot), or
ZData
(3-D height plot) name-value pairs. You can
combine any number of plot types.
For a thermal analysis, you can plot temperature or gradient of temperature.
For a structural analysis, you can plot displacement, stress, strain, and von Mises stress. In addition, you can show the deformed shape and specify the scaling factor for the deformation plot.
For an electromagnetic analysis, you can plot electric or magnetic potentials, fields, and flux densities.
Examples
Solve Transient Thermal Problem
Solve a 2-D transient thermal problem.
Create a geometry representing a square plate with a diamond-shaped region in its center.
SQ1 = [3; 4; 0; 3; 3; 0; 0; 0; 3; 3]; D1 = [2; 4; 0.5; 1.5; 2.5; 1.5; 1.5; 0.5; 1.5; 2.5]; gd = [SQ1 D1]; sf = 'SQ1+D1'; ns = char('SQ1','D1'); ns = ns'; g = decsg(gd,sf,ns); pdegplot(g,EdgeLabels="on",FaceLabels="on") xlim([-1.5 4.5]) ylim([-0.5 3.5]) axis equal
Create an femodel
object for transient thermal analysis and include the geometry.
model = femodel(AnalysisType="thermalTransient", ... Geometry=g);
For the square region, assign these thermal properties:
Thermal conductivity is
Mass density is
Specific heat is
model.MaterialProperties(1) = ... materialProperties(ThermalConductivity=10, ... MassDensity=2, ... SpecificHeat=0.1);
For the diamond region, assign these thermal properties:
Thermal conductivity is
Mass density is
Specific heat is
model.MaterialProperties(2) = ... materialProperties(ThermalConductivity=2, ... MassDensity=1, ... SpecificHeat=0.1);
Assume that the diamond-shaped region is a heat source with a density of .
model.FaceLoad(2) = faceLoad(Heat=4);
Apply a constant temperature of 0 °C to the sides of the square plate.
model.EdgeBC([1 2 7 8]) = edgeBC(Temperature=0);
Set the initial temperature to 0 °C.
model.FaceIC = faceIC(Temperature=0);
Generate the mesh.
model = generateMesh(model);
The dynamics for this problem are very fast. The temperature reaches a steady state in about 0.1 second. To capture the most active part of the dynamics, set the solution time to logspace(-2,-1,10)
. This command returns 10 logarithmically spaced solution times between 0.01 and 0.1.
tlist = logspace(-2,-1,10);
Solve the equation.
thermalresults = solve(model,tlist);
Plot the solution with isothermal lines by using a contour plot.
T = thermalresults.Temperature; msh = thermalresults.Mesh; pdeplot(msh,XYData=T(:,10),Contour="on",ColorMap="hot")
Plot Deformed Shape for Static Plane-Strain Problem
Create an femodel
object for structural analysis and include the unit square geometry in the model.
model = femodel(AnalysisType="structuralStatic", ... Geometry=@squareg);
Plot the geometry.
pdegplot(model.Geometry,EdgeLabels="on")
xlim([-1.1 1.1])
ylim([-1.1 1.1])
Specify Young's modulus and Poisson's ratio.
model.MaterialProperties = ... materialProperties(PoissonsRatio=0.3, ... YoungsModulus=210E3);
Specify the x-component of the enforced displacement for edge 1.
model.EdgeBC(1) = edgeBC(XDisplacement=0.001);
Specify that edge 3 is a fixed boundary.
model.EdgeBC(3) = edgeBC(Constraint="fixed");
Generate a mesh and solve the problem.
model = generateMesh(model); R = solve(model);
Plot the deformed shape using the default scale factor. By default, pdeplot
internally determines the scale factor based on the dimensions of the geometry and the magnitude of deformation.
pdeplot(R.Mesh, ... XYData=R.VonMisesStress, ... Deformation=R.Displacement, ... ColorMap="jet")
Plot the deformed shape with the scale factor 500.
pdeplot(R.Mesh, ... XYData=R.VonMisesStress, ... Deformation=R.Displacement, ... DeformationScaleFactor=500,... ColorMap="jet")
Plot the deformed shape without scaling.
pdeplot(R.Mesh, ... XYData=R.VonMisesStress, ... ColorMap="jet")
Solve Modal Structural Analysis Problem
Find the fundamental (lowest) mode of a 2-D cantilevered beam, assuming prevalence of the plane-stress condition.
Specify geometric and structural properties of the beam, along with a unit plane-stress thickness.
length = 5; height = 0.1; E = 3E7; nu = 0.3; rho = 0.3/386;
Create a geometry.
gdm = [3;4;0;length;length;0;0;0;height;height]; g = decsg(gdm,'S1',('S1')');
Create an femodel
object for modal structural analysis and include the geometry.
model = femodel(Analysistype="structuralModal", ... Geometry=g);
Define a maximum element size (five elements through the beam thickness).
hmax = height/5;
Generate a mesh.
model=generateMesh(model,Hmax=hmax);
Specify the structural properties and boundary constraints.
model.MaterialProperties = ... materialProperties(YoungsModulus=E, ... MassDensity=rho, ... PoissonsRatio=nu); model.EdgeBC(4) = edgeBC(Constraint="fixed");
Compute the analytical fundamental frequency (Hz) using the beam theory.
I = height^3/12; analyticalOmega1 = 3.516*sqrt(E*I/(length^4*(rho*height)))/(2*pi)
analyticalOmega1 = 126.9498
Specify a frequency range that includes an analytically computed frequency and solve the model.
R = solve(model,FrequencyRange=[0,1e6])
R = ModalStructuralResults with properties: NaturalFrequencies: [32x1 double] ModeShapes: [1x1 FEStruct] Mesh: [1x1 FEMesh]
The solver finds natural frequencies and modal displacement values at nodal locations. To access these values, use R.NaturalFrequencies
and R.ModeShapes
.
R.NaturalFrequencies/(2*pi)
ans = 32×1
105 ×
0.0013
0.0079
0.0222
0.0433
0.0711
0.0983
0.1055
0.1462
0.1930
0.2455
⋮
R.ModeShapes
ans = FEStruct with properties: ux: [6511x32 double] uy: [6511x32 double] Magnitude: [6511x32 double]
Plot the y-component of the solution for the fundamental frequency.
pdeplot(R.Mesh,XYData=R.ModeShapes.uy(:,1)) title(['First Mode with Frequency ', ... num2str(R.NaturalFrequencies(1)/(2*pi)),' Hz']) axis equal
Solve 2-D Electrostatic Problem
Solve an electromagnetic problem and find the electric potential and field distribution for a 2-D geometry representing a plate with a hole.
Create an femodel
object for electrostatic analysis and include a geometry representing a plate with a hole.
model = femodel(AnalysisType="electrostatic",... Geometry="PlateHolePlanar.stl");
Plot the geometry with edge labels.
pdegplot(model.Geometry,EdgeLabels="on")
Specify the vacuum permittivity value in the SI system of units.
model.VacuumPermittivity = 8.8541878128E-12;
Specify the relative permittivity of the material.
model.MaterialProperties = ...
materialProperties(RelativePermittivity=1);
Apply the voltage boundary conditions on the edges framing the rectangle and the circle.
model.EdgeBC(1:4) = edgeBC(Voltage=0); model.EdgeBC(5) = edgeBC(Voltage=1000);
Specify the charge density for the entire geometry.
model.FaceLoad = faceLoad(ChargeDensity=5E-9);
Generate the mesh.
model = generateMesh(model);
Solve the model.
R = solve(model)
R = ElectrostaticResults with properties: ElectricPotential: [1231x1 double] ElectricField: [1x1 FEStruct] ElectricFluxDensity: [1x1 FEStruct] Mesh: [1x1 FEMesh]
Plot the electric potential and field.
pdeplot(R.Mesh,XYData=R.ElectricPotential, ... FlowData=[R.ElectricField.Ex ... R.ElectricField.Ey]) axis equal
Plot General PDE Solution
Create colored 2-D and 3-D plots of a solution to a PDE model.
Create a PDE model. Include the geometry of the built-in function lshapeg
. Mesh the geometry.
model = createpde; geometryFromEdges(model,@lshapeg); generateMesh(model);
Set the zero Dirichlet boundary conditions on all edges.
applyBoundaryCondition(model,"dirichlet", ... Edge=1:model.Geometry.NumEdges, ... u=0);
Specify the coefficients and solve the PDE.
specifyCoefficients(model,m=0, ... d=0, ... c=1, ... a=0, ... f=1); results = solvepde(model)
results = StationaryResults with properties: NodalSolution: [1141x1 double] XGradients: [1141x1 double] YGradients: [1141x1 double] ZGradients: [] Mesh: [1x1 FEMesh]
Plot the 2-D solution at the nodal locations.
u = results.NodalSolution; msh = results.Mesh; pdeplot(msh,XYData=u)
Plot the 3-D solution.
pdeplot(msh,XYData=u,ZData=u)
Plot Gradient of General PDE Solution
Plot the gradient of a PDE solution as a quiver plot.
Create a PDE model. Include the geometry of the built-in function lshapeg
. Mesh the geometry.
model = createpde; geometryFromEdges(model,@lshapeg); generateMesh(model);
Set the zero Dirichlet boundary conditions on all edges.
applyBoundaryCondition(model,"dirichlet", ... Edge=1:model.Geometry.NumEdges, ... u=0);
Specify coefficients and solve the PDE.
specifyCoefficients(model,m=0, ... d=0, ... c=1, ... a=0, ... f=1); results = solvepde(model)
results = StationaryResults with properties: NodalSolution: [1141x1 double] XGradients: [1141x1 double] YGradients: [1141x1 double] ZGradients: [] Mesh: [1x1 FEMesh]
Plot the gradient of the solution at the nodal locations as a quiver plot.
ux = results.XGradients; uy = results.YGradients; msh = results.Mesh; pdeplot(msh,FlowData=[ux,uy])
Plot General PDE Solution and Its Gradient
Plot the solution of a 2-D PDE in 3-D with the "jet"
coloring and a mesh, and include a quiver plot. Get handles to the axes objects.
Create a PDE model. Include the geometry of the built-in function lshapeg
. Mesh the geometry.
model = createpde; geometryFromEdges(model,@lshapeg); generateMesh(model);
Set zero Dirichlet boundary conditions on all edges.
applyBoundaryCondition(model,"dirichlet", ... Edge=1:model.Geometry.NumEdges, ... u=0);
Specify coefficients and solve the PDE.
specifyCoefficients(model,m=0, ... d=0, ... c=1, ... a=0, ... f=1); results = solvepde(model)
results = StationaryResults with properties: NodalSolution: [1141x1 double] XGradients: [1141x1 double] YGradients: [1141x1 double] ZGradients: [] Mesh: [1x1 FEMesh]
Plot the solution in 3-D with the "jet"
coloring and a mesh, and include the gradient as a quiver plot.
u = results.NodalSolution; ux = results.XGradients; uy = results.YGradients; msh = results.Mesh; h = pdeplot(msh,XYData=u,ZData=u, ... FaceAlpha=0.5, ... FlowData=[ux,uy], ... ColorMap="jet", ... Mesh="on");
Plot 2-D Mesh
Create an femodel
object and include the geometry of the built-in function lshapeg
.
model = femodel(Geometry=@lshapeg);
Generate and plot the mesh.
model = generateMesh(model); msh = model.Geometry.Mesh; pdeplot(msh)
Alternatively, you can use the nodes and elements of the mesh as input arguments for pdeplot
.
pdeplot(msh.Nodes,msh.Elements)
Display the node labels. Use xlim
and ylim
to zoom in on particular nodes.
pdeplot(msh,NodeLabels="on")
xlim([-0.2,0.2])
ylim([-0.2,0.2])
Display the element labels.
pdeplot(msh,ElementLabels="on")
xlim([-0.2,0.2])
ylim([-0.2,0.2])
Input Arguments
mesh
— Mesh description
FEMesh
object
Mesh description, specified as an FEMesh
object.
nodes
— Nodal coordinates
2-by-NumNodes matrix
Nodal coordinates, specified as a 2-by-NumNodes matrix. NumNodes is the number of nodes.
elements
— Element connectivity matrix in terms of node IDs
3-by-NumElements matrix | 6-by-NumElements matrix
Element connectivity matrix in terms of the node IDs, specified as a 3-by-NumElements or 6-by-NumElements matrix. Linear meshes contain only corner nodes. For linear meshes, the connectivity matrix has three nodes per 2-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 six nodes per 2-D element.
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.
p
— Mesh points
matrix
Mesh points, specified as a 2-by-Np
matrix of points, where
Np
is the number of points in the mesh. For a description of the
(p
,e
,t
) matrices, see Mesh Data as [p,e,t] Triples.
Typically, you use the p
, e
, and t
data exported from the PDE Modeler app, or generated by initmesh
or refinemesh
.
Example: [p,e,t] = initmesh(gd)
Data Types: double
e
— Mesh edges
matrix
Mesh edges, specified as a 7
-by-Ne
matrix of edges,
where Ne
is the number of edges in the mesh. For a description of the
(p
,e
,t
) matrices, see Mesh Data as [p,e,t] Triples.
Typically, you use the p
, e
, and t
data exported from the PDE Modeler app, or generated by initmesh
or refinemesh
.
Example: [p,e,t] = initmesh(gd)
Data Types: double
t
— Mesh triangles
matrix
Mesh triangles, specified as a 4
-by-Nt
matrix of
triangles, where Nt
is the number of triangles in the mesh. For a
description of the (p
,e
,t
)
matrices, see Mesh Data as [p,e,t] Triples.
Typically, you use the p
, e
, and t
data exported from the PDE Modeler app, or generated by initmesh
or refinemesh
.
Example: [p,e,t] = initmesh(gd)
Data Types: double
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: pdeplot(results.Mesh,XYData=u,ZData=u)
Tip
Specify at least one of the FlowData
(vector field plot),
XYData
(colored surface plot), or
ZData
(3-D height plot) name-value pairs. Otherwise,
pdeplot
plots the mesh with no data.
XYData
— Colored surface plot data
vector
Colored surface plot data, specified as a vector. If you use a
[p,e,t]
representation, specify data for points
in a vector of length size(p,2)
, or specify data for
triangles in a vector of length size(t,2)
.
Typically, you set
XYData
to the solutionu
. Thepdeplot
function usesXYData
for coloring both 2-D and 3-D plots.pdeplot
uses the colormap specified in theColorMap
name-value pair, using the style specified in theXYStyle
name-value pair.When the
Contour
name-value pair is"on"
,pdeplot
also plots level curves ofXYData
.pdeplot
plots the real part of complex data.
To plot the k
th component of a solution to a PDE
system, extract the relevant part of the solution, for example:
results = solvepde(model); u = results.NodalSolution; % each column of u has one component of u pdeplot(results.Mesh,XYData=u(:,k)) % data for column k
Example: XYData=u
Data Types: double
XYStyle
— Coloring choice
"interp"
(default) | "off"
| "flat"
Coloring choice, specified as one of the following values:
"off"
— No shading, only mesh is displayed."flat"
— Each triangle in the mesh has a uniform color."interp"
— Plot coloring is smoothly interpolated.
The coloring choice relates to the XYData
name-value pair.
Example: XYStyle="flat"
Data Types: char
| string
ZData
— Data for 3-D plot heights
matrix
Data for the 3-D plot heights, specified as a matrix. If you use a
[p,e,t]
representation, provide data for points
in a vector of length size(p,2)
or data for triangles
in a vector of length size(t,2)
.
Typically, you set
ZData
tou
, the solution. TheXYData
name-value pair sets the coloring of the 3-D plot.The
ZStyle
name-value pair specifies whether the plot is continuous or discontinuous.pdeplot
plots the real part of complex data.
To plot the k
th component of a solution to a PDE
system, extract the relevant part of the solution, for example:
results = solvepde(model); u = results.NodalSolution; % each column of u has one component of u pdeplot(results.Mesh,XYData=u(:,k),ZData=u(:,k)) % data for column k
Example: ZData=u
Data Types: double
ZStyle
— 3-D plot style
"continuous"
(default) | "off"
| "discontinuous"
3-D plot style, specified as one of these values:
"off"
— No 3-D plot."discontinuous"
— Each triangle in the mesh has a uniform height in a 3-D plot."continuous"
— 3-D surface plot is continuous.
If you use ZStyle
without specifying the
ZData
name-value pair, then
pdeplot
ignores
ZStyle
.
Example: ZStyle="discontinuous"
Data Types: char
| string
FlowData
— Data for quiver plot
matrix
Data for the quiver plot,
specified as an M
-by-2
matrix,
where M
is the number of mesh nodes.
FlowData
contains the x and
y values of the field at the mesh points.
When you use ZData
to represent a 2-D PDE solution
as a 3-D plot and you also include a quiver plot, the quiver plot
appears in the z = 0 plane.
pdeplot
plots the real part of complex data.
Example: FlowData=[ux uy]
Data Types: double
FlowStyle
— Indicator to show quiver plot
"arrow"
(default) | "off"
Indicator to show the quiver plot, specified as
"arrow"
or "off"
. Here,
"arrow"
displays the quiver plot specified by the FlowData
name-value pair.
Example: FlowStyle="off"
Data Types: char
| string
XYGrid
— Indicator to convert mesh data to x-y grid
"off"
(default) | "on"
Indicator to convert the mesh data to
x-y grid before plotting,
specified as "off"
or "on"
.
Note
This conversion can change the geometry and lessen the quality of the plot.
By default, the grid has about sqrt(size(t,2))
elements in each direction.
Example: XYGrid="on"
Data Types: char
| string
GridParam
— Customized x-y grid
[tn;a2;a3]
from an earlier call to
tri2grid
Customized x-y grid, specified
as a matrix [tn;a2;a3]
. For example:
[~,tn,a2,a3] = tri2grid(p,t,u,x,y);
pdeplot(p,e,t,XYGrid="on",GridParam=[tn;a2;a3],XYData=u)
For details on the grid data and its x
and
y
arguments, see tri2grid
. The
tri2grid
function does not work with
PDEModel
objects.
Example: GridParam=[tn;a2;a3]
Data Types: double
NodeLabels
— Node labels
"off"
(default) | "on"
Node labels, specified as "off"
or
"on"
.
pdeplot
ignores NodeLabels
when you use it with ZData
.
Example: NodeLabels="on"
Data Types: char
| string
ElementLabels
— Element labels
"off"
(default) | "on"
Element labels, specified as "off"
or
"on"
.
pdeplot
ignores ElementLabels
when you use it with ZData
.
Example: ElementLabels="on"
Data Types: char
| string
Deformation
— Data for plotting deformed shape
Displacement
property of
StaticStructuralResults
object
Data for plotting the deformed shape for a structural analysis model,
specified as the Displacement
property of the
StaticStructuralResults
object.
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 =
structuralresults.Displacement
DeformationScaleFactor
— Scaling factor for plotting deformed shape
real number
Scaling factor for plotting the deformed shape, specified as a real
number. Use this argument with the Deformation
name-value pair. The default value is defined internally, based on the
dimensions of the geometry and the magnitude of the deformation.
Example: DeformationScaleFactor=100
Data Types: double
ColorBar
— Indicator to include color bar
"on"
(default) | "off"
Indicator to include a color bar, specified as "on"
or "off"
. Specify "on"
to display
a bar giving the numeric values of colors in the plot. For details, see
colorbar
. The
pdeplot
function uses the colormap specified in
the ColorMap
name-value pair.
Example: ColorBar="off"
Data Types: char
| string
ColorMap
— Colormap
"cool"
(default) | ColorMap
value or matrix of such values
Colormap, specified as a value representing a built-in colormap, or a
colormap matrix. For details, see colormap
.
ColorMap
must be used with the
XYData
name-value pair.
Example: ColorMap="jet"
Data Types: double
| char
| string
Mesh
— Indicator to show mesh
"off"
(default) | "on"
Indicator to show the mesh, specified as "on"
or
"off"
. Specify "on"
to show
the mesh in the plot.
Example: Mesh="on"
Data Types: char
| string
Title
— Title of plot
string scalar | character vector
Title of plot, specified as a string scalar or character vector.
Example: Title="Solution Plot"
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 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
Contour
— Indicator to plot level curves
"off"
(default) | "on"
Indicator to plot level curves, specified as "off"
or "on"
. Specify "on"
to plot
level curves for the XYData
data. Specify the levels
with the Levels
name-value pair.
Example: Contour="on"
Data Types: char
| string
Levels
— Levels for contour plot
10
(default) | positive integer | vector of level values
Levels for contour plot, specified as a positive integer or a vector of level values.
Positive integer — Plot
Levels
as equally spaced contours.Vector — Plot contours at the values in
Levels
.
To obtain a contour plot, set the Contour
name-value pair to "on"
.
Example: Levels=16
Data Types: double
Output Arguments
h
— Handles to graphics objects
vector
Handles to graphics objects, returned as a vector.
More About
Quiver Plot
A quiver plot is a plot of a vector field. It is also called a flow plot.
Arrows show the direction of the field, with the lengths of
the arrows showing the relative sizes of the field strength. For details
on quiver plots, see quiver
.
Version History
Introduced before R2006aR2021a: Electromagnetic Analysis
You can now plot electromagnetic results, such as electric and magnetic potentials, fields, and fluxes.
R2020a: Improved performance for plots with many text labels
pdeplot
shows faster rendering and better responsiveness for
plots that display many text labels. Code containing
findobj(fig,'Type','Text')
no longer returns labels on
figures produced by pdeplot
.
R2018a: Highlighting particular nodes and elements on mesh plots
pdeplot
accepts node and element IDs as input arguments,
letting you highlight particular nodes and elements on mesh plots.
R2017b: Structural Analysis
You can now plot structural results, such as displacements, stresses, and strains.
R2017a: Thermal Analysis
You can now plot thermal results, such as temperatures and temperature gradients.
R2016b: Transparency, node and element labels
You can now set plot transparency by using FaceAlpha
, and
display node and element labels by using NodeLabels
and
ElementLabels
, respectively.
See Also
Functions
Live Editor Tasks
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