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 of6*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 of6*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 anx
-displacement at each node.Numbers from
NumNodes+1
to2*NumNodes
correspond to ay
-displacement at each node.Numbers from
2*NumNodes+1
to3*NumNodes
correspond to az
-displacement at each node of a 3-D geometry.
Version History
Introduced in R2019b
See Also
reduce
| reconstructSolution
| structuralSEInterface
| structuralBC
| StructuralModel
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)