reduce
Reduce structural or thermal model
Syntax
Description
reduces a structural analysis model to the fixed interface modes in the frequency range
Rcb
= reduce(structuralmodel
,FrequencyRange=[omega1,omega2]
)[omega1,omega2]
and the boundary interface degrees of
freedom.
reduces a thermal analysis model to the modes specified in
Rtherm
= reduce(thermalmodel
,ModalResults=thermalModalR
)thermalModalR
. When reducing a thermal model, thermal properties of
materials, internal heat sources, and boundary conditions cannot depend on time or
temperature.
also truncates the number of modes to Rtherm
= reduce(thermalmodel
,ModalResults=thermalModalR
,NumModes=N
)N
. Using this syntax, you can
compute a larger number of modes and then use a subset of these modes to construct a
reduced-order model.
Examples
Reduce femodel
for Structural Analysis
Since R2024a
Reduce a model for transient structural analysis of a beam to the fixed interface modes in a specified frequency range and the boundary interface degrees of freedom.
Create an femodel
object for transient structural analysis of a 3-D problem, and assign the beam geometry to the model.
structuralmodel = femodel(AnalysisType="structuralTransient", ... Geometry=multicuboid(0.1,0.01,0.01));
Plot the geometry with edge labels.
pdegplot(structuralmodel,EdgeLabels="on",FaceAlpha=0.5)
view([50 25])
Specify Young's modulus, Poisson's ratio, and the mass density of the material.
structuralmodel.MaterialProperties = ... materialProperties(YoungsModulus=200e9, ... PoissonsRatio=0.3,MassDensity=7800);
Generate a mesh.
structuralmodel=generateMesh(structuralmodel);
Specify the ends of the beam as structural superelement interfaces by creating a romInterface
object for each superelement interface. The reduced-order model technique retains the degrees of freedom on the superelement interfaces while condensing all other degrees of freedom to a set of modal degrees of freedom. For better performance, use the set of edges that bound each side of the beam instead of using the entire face.
romObj1 = romInterface(Edge=[4,6,9,10]); romObj2 = romInterface(Edge=[2,8,11,12]);
Assign a vector of interface objects to the ROMInterfaces
property of the model.
structuralmodel.ROMInterfaces = [romObj1,romObj2];
Reduce the model to the fixed interface modes in the frequency range [-Inf,500000]
and the boundary interface degrees of freedom.
R = reduce(structuralmodel,FrequencyRange=[-Inf,500000])
R = ReducedStructuralModel with properties: K: [166x166 double] M: [166x166 double] NumModes: 22 RetainedDoF: [144x1 double] ReferenceLocations: [] Mesh: [1x1 FEMesh]
Reduce femodel
for Thermal Analysis
Since R2024a
Reduce a model for thermal analysis of a square using all modes or the specified number of modes from the modal solution.
Create an femodel
object for transient thermal analysis, and assign the unit square geometry to the model.
model = femodel(AnalysisType="thermalTransient",Geometry=@squareg);
Plot the geometry with the edge labels.
pdegplot(model,EdgeLabels="on")
xlim([-1.1 1.1])
ylim([-1.1 1.1])
Specify the thermal conductivity, mass density, and specific heat of the material.
model.MaterialProperties = ... materialProperties(ThermalConductivity=400, ... MassDensity=1300, ... SpecificHeat=600);
Set the temperature on the right edge to 100
.
model.EdgeBC(2) = edgeBC(Temperature=100);
Set an initial value of 0
for the temperature.
model.FaceIC = faceIC(Temperature=0);
Generate a mesh.
model = generateMesh(model);
Solve the model for three different values of heat source and collect snapshots.
tlist = 0:10:600; snapShotIDs = [1:10 59 60 61]; Tmatrix = []; heatVariation = [10000 15000 20000 -1000]; for q = heatVariation model.FaceLoad = faceLoad(Heat=q); results = solve(model,tlist); Tmatrix = [Tmatrix,results.Temperature(:,snapShotIDs)]; end
Switch the thermal model analysis type to modal.
model.AnalysisType="thermalModal";
Compute the POD modes.
RModal = solve(model,Snapshots=Tmatrix)
RModal = ModalThermalResults with properties: DecayRates: [6x1 double] ModeShapes: [1529x6 double] SnapshotsAverage: [1529x1 double] ModeType: "PODModes" Mesh: [1x1 FEMesh]
Reduce the thermal model using all modes in RModal
.
Rtherm = reduce(model,ModalResults=RModal)
Rtherm = ReducedThermalModel with properties: K: [7x7 double] M: [7x7 double] F: [7x1 double] InitialConditions: [7x1 double] Mesh: [1x1 FEMesh] ModeShapes: [1529x6 double] SnapshotsAverage: [1529x1 double]
Reduce the thermal model using only three modes.
Rtherm3 = reduce(model,ModalResults=RModal,NumModes=3)
Rtherm3 = ReducedThermalModel with properties: K: [4x4 double] M: [4x4 double] F: [4x1 double] InitialConditions: [4x1 double] Mesh: [1x1 FEMesh] ModeShapes: [1529x3 double] SnapshotsAverage: [1529x1 double]
Reduce Transient Structural Model
Reduce a transient structural model to the fixed interface modes in a specified frequency range and the boundary interface degrees of freedom.
Create a transient structural model for a 3-D problem.
structuralmodel = createpde("structural","transient-solid");
Create a geometry and include it in the model. Plot the geometry.
gm = multicuboid(0.1,0.01,0.01); structuralmodel.Geometry = gm; pdegplot(structuralmodel,"FaceLabels","on","FaceAlpha",0.5)
Specify Young's modulus, Poisson's ratio, and the mass density of the material.
structuralProperties(structuralmodel,"YoungsModulus",70E9, ... "PoissonsRatio",0.3, ... "MassDensity",2700);
Generate a mesh.
generateMesh(structuralmodel);
Specify the ends of the beam as structural superelement interfaces. The reduced-order model technique retains the degrees of freedom on the superelement interfaces while condensing the degrees of freedom on all other boundaries. For better performance, use the set of edges that bound each side of the beam instead of using the entire face.
structuralSEInterface(structuralmodel,"Edge",[4,6,9,10]); structuralSEInterface(structuralmodel,"Edge",[2,8,11,12]);
Reduce the model to the fixed interface modes in the frequency range [-Inf,500000]
and the boundary interface degrees of freedom.
R = reduce(structuralmodel,"FrequencyRange",[-Inf,500000])
R = ReducedStructuralModel with properties: K: [166x166 double] M: [166x166 double] NumModes: 22 RetainedDoF: [144x1 double] ReferenceLocations: [] Mesh: [1x1 FEMesh]
Reduce Thermal Model
Since R2022a
Reduce a thermal model using all modes or the specified number of modes from the modal solution.
Create a transient thermal model.
thermalmodel = createpde("thermal","transient");
Create a unit square geometry and include it in the model.
geometryFromEdges(thermalmodel,@squareg);
Plot the geometry, displaying edge labels.
pdegplot(thermalmodel,"EdgeLabels","on") xlim([-1.1 1.1]) ylim([-1.1 1.1])
Specify the thermal conductivity, mass density, and specific heat of the material.
thermalProperties(thermalmodel,"ThermalConductivity",400, ... "MassDensity",1300, ... "SpecificHeat",600);
Set the temperature on the right edge to 100
.
thermalBC(thermalmodel,"Edge",2,"Temperature",100);
Set an initial value of 0
for the temperature.
thermalIC(thermalmodel,0);
Generate a mesh.
generateMesh(thermalmodel);
Solve the model for three different values of heat source and collect snapshots.
tlist = 0:10:600; snapShotIDs = [1:10 59 60 61]; Tmatrix = []; heatVariation = [10000 15000 20000]; for q = heatVariation internalHeatSource(thermalmodel,q); results = solve(thermalmodel,tlist); Tmatrix = [Tmatrix,results.Temperature(:,snapShotIDs)]; end
Switch the thermal model analysis type to modal.
thermalmodel.AnalysisType = "modal";
Compute the POD modes.
RModal = solve(thermalmodel,"Snapshots",Tmatrix)
RModal = ModalThermalResults with properties: DecayRates: [6x1 double] ModeShapes: [1529x6 double] SnapshotsAverage: [1529x1 double] ModeType: "PODModes" Mesh: [1x1 FEMesh]
Reduce the thermal model using all modes in RModal
.
Rtherm = reduce(thermalmodel,"ModalResults",RModal)
Rtherm = ReducedThermalModel with properties: K: [7x7 double] M: [7x7 double] F: [7x1 double] InitialConditions: [7x1 double] Mesh: [1x1 FEMesh] ModeShapes: [1529x6 double] SnapshotsAverage: [1529x1 double]
Reduce the thermal model using only three modes.
Rtherm3 = reduce(thermalmodel,"ModalResults",RModal, ... "NumModes",3)
Rtherm3 = ReducedThermalModel with properties: K: [4x4 double] M: [4x4 double] F: [4x1 double] InitialConditions: [4x1 double] Mesh: [1x1 FEMesh] ModeShapes: [1529x3 double] SnapshotsAverage: [1529x1 double]
Input Arguments
structuralmodel
— Structural model
femodel
object for transient or modal structural
analysis | StructuralModel
object
Note
Domain-specific structural workflows is not recommended. New features might not be compatible with this workflow. For help migrating your existing code to the unified finite element workflow, see Migration from Domain-Specific to Unified Workflow.
Structural model, specified as an femodel
object for transient of
modal structural analysis or a StructuralModel
object.
[omega1,omega2]
— Frequency range
vector of two elements
Frequency range, specified as a vector of two elements. Define
omega1
as slightly lower than the lowest mode's frequency and
omega2
as slightly higher than the highest mode's frequency. For
example, if the lowest expected frequency is zero, then use a small negative value for
omega1
.
You can find natural frequencies and mode shapes for the specified frequency range by solving a modal analysis problem first. Then you can use a more precise frequency range to reduce the model. Note that a modal analysis problem still requires you to specify a frequency range. For example, see Modal Superposition Method for Structural Dynamics Problem.
Data Types: double
thermalmodel
— Modal thermal analysis model
femodel
object for transient or modal thermal analysis | ThermalModel
object
Note
Domain-specific heat transfer workflow is not recommended. New features might not be compatible with this workflow. For help migrating your existing code to the unified finite element workflow, see Migration from Domain-Specific to Unified Workflow.
Modal thermal analysis model, specified as an femodel
object for
transient or modal thermal analysis or a ThermalModel
object.
thermalModalR
— Modal analysis results for thermal model
ModalThermalResults
object
Modal analysis results for a thermal model, specified as a
ModalThermalResults
object.
N
— Number of modes
positive integer
Number of modes, specified as a positive integer.
Output Arguments
Rcb
— Reduced-order structural model obtained using the Craig-Bampton order reduction method
ReducedStructuralModel
object
Reduced-order structural model obtained using the Craig-Bampton order reduction
method, returned as a ReducedStructuralModel
object.
Rtherm
— Reduced-order thermal model
ReducedThermalModel
object
Reduced-order thermal model, returned as a ReducedThermalModel
object.
Version History
Introduced in R2019bR2024a: ROM support for femodel
objects
The reduce
function now also reduces structural and thermal analysis
models specified as femodel
objects. If
the AnalysisType
property of an femodel
object is
structuralTransient
or structuralModal
, then
reduce
returns a ReducedStructuralModel
object. If
the AnalysisType
property is thermalTransient
or
thermalModal
, then reduce
returns a
ReducedThermalModel
object.
R2022a: ROM support for thermal analysis
reduce
now also reduces thermal models.
See Also
Functions
Objects
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