reduce
Reduce structural or thermal model
Syntax
Description
Rcb = reduce(model,FrequencyRange=[omega1,omega2])model for structural analysis to the fixed interface modes
in the frequency range [omega1,omega2] and the boundary interface
degrees of freedom.
Rtherm = reduce(model,ModalResults=thermalModalR)model for thermal analysis to the modes specified in
thermalModalR. When reducing a model for thermal analysis, thermal
properties of materials, internal heat sources, and boundary conditions cannot depend on
time or temperature.
Rtherm = reduce(model,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
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: [166×166 double]
M: [166×166 double]
NumModes: 22
RetainedDoF: [144×1 double]
ReferenceLocations: []
Mesh: [1×1 FEMesh]
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: [6×1 double]
ModeShapes: [1529×6 double]
SnapshotsAverage: [1529×1 double]
ModeType: "PODModes"
Mesh: [1×1 FEMesh]
Reduce the thermal model using all modes in RModal.
Rtherm = reduce(model,ModalResults=RModal)
Rtherm =
ReducedThermalModel with properties:
K: [7×7 double]
M: [7×7 double]
F: [7×1 double]
InitialConditions: [7×1 double]
Mesh: [1×1 FEMesh]
ModeShapes: [1529×6 double]
SnapshotsAverage: [1529×1 double]
Reduce the thermal model using only three modes.
Rtherm3 = reduce(model,ModalResults=RModal,NumModes=3)
Rtherm3 =
ReducedThermalModel with properties:
K: [4×4 double]
M: [4×4 double]
F: [4×1 double]
InitialConditions: [4×1 double]
Mesh: [1×1 FEMesh]
ModeShapes: [1529×3 double]
SnapshotsAverage: [1529×1 double]
