ReducedStructuralModel

Reduced-order structural model results

Description

A ReducedStructuralModel object contains the stiffness matrix K, mass matrix M, mesh, multipoint constraint reference locations, and IDs of retained degrees of freedom.

To expand this data to a full solution that includes displacement, velocity, and acceleration, use reconstructSolution.

Creation

Reduce a structural model by using the reduce function. This function returns structural results obtained using the Craig-Bampton reduced order method as a ReducedStructuralModel object.

Properties

K — Reduced stiffness matrix

real matrix

Reduced stiffness matrix, specified as a real N-by-N matrix.

• For models without multipoint constraints, N is the sum of the number of retained degrees of freedom and the number of fixed interface modes.

• For models with Nmp multipoint constraints, N is the sum of 6*Nmp and the number of fixed interface modes.

Data Types: double

M — Reduced mass matrix

real matrix

Reduced mass matrix, specified as a real N-by-N matrix.

• For models without multipoint constraints, N is the sum of the number of retained degrees of freedom and the number of fixed interface modes.

• For models with Nmp multipoint constraints, N is the sum of 6*Nmp and the number of fixed interface modes.

Data Types: double

NumModes — Number of fixed interface modes

integer

Number of fixed interface modes, specified as an integer.

Data Types: double

RetainedDoF — IDs of retained degrees of freedom

real vector

IDs of retained degrees of freedom, specified as a real vector.

Data Types: double

ReferenceLocations — Multipoint constraint reference locations

real matrix

Multipoint constraint reference locations, specified as a real 2-by-Nmp or 3-by-Nmp matrix for a 2-D or 3-D geometry, respectively. Here, Nmp is the number of multipoint constraints. If there are no multipoint constraints, ReferenceLocations is an empty matrix.

Data Types: double

Mesh — Finite element mesh

FEMesh object

Finite element mesh, specified as a FEMesh object.

Object Functions

reconstructSolution

Recover full-model transient solution from reduced-order model (ROM)

Examples

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]

More About

Degrees of Freedom (DoFs)

In Partial Differential Equation Toolbox™, each node of a 2-D or 3-D geometry has two or three degrees of freedom (DoFs), respectively. DoFs correspond to translational displacements. If the number of mesh points in a model is NumNodes, then the toolbox assigns the IDs to the degrees of freedom as follows:

• Numbers from 1 to NumNodes correspond to an x-displacement at each node.

• Numbers from NumNodes+1 to 2*NumNodes correspond to a y-displacement at each node.

• Numbers from 2*NumNodes+1 to 3*NumNodes correspond to a z-displacement at each node of a 3-D geometry.

Version History

Introduced in R2019b