reduce

Reduce structural or thermal model

Syntax

Rcb = reduce(structuralmodel,FrequencyRange=[omega1,omega2])

Rtherm = reduce(thermalmodel,ModalResults=thermalModalR)

Rtherm = reduce(thermalmodel,ModalResults=thermalModalR,NumModes=N)

Description

Rcb = reduce(structuralmodel,FrequencyRange=[omega1,omega2]) reduces a structural analysis model to the fixed interface modes in the frequency range [omega1,omega2] and the boundary interface degrees of freedom.

Rtherm = reduce(thermalmodel,ModalResults=thermalModalR) reduces a thermal analysis model to the modes specified in thermalModalR. When reducing a thermal model, thermal properties of materials, internal heat sources, and boundary conditions cannot depend on time or temperature.

Rtherm = reduce(thermalmodel,ModalResults=thermalModalR,NumModes=N) also truncates the number of modes to 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 R2019b

R2024a: 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.