# ReducedStructuralModel

## 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. For details,
see FEMesh Properties.

## 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**

## See Also

`reduce`

| `reconstructSolution`

| `structuralSEInterface`

| `structuralBC`

| `StructuralModel`

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