# Reduced Order Flexible Solid

**Libraries:**

Simscape /
Multibody /
Body Elements /
Flexible Bodies

## Description

The Reduced Order Flexible Solid block creates a flexible body by using reduced-order model (ROM) data.

A reduced-order model is a computationally efficient model that characterizes the properties of a flexible body that can have linear elastic deformations. The ROM data must include:

Coordinates and unit quaternions that specify the positions and orientations of all interface frames relative to a common reference frame. See Interface Frames.

A symmetric stiffness matrix that describes the elastic properties of the flexible body. See Stiffness Matrix.

A symmetric mass matrix that describes the inertial properties of the flexible body. See Mass Matrix.

To generate ROM data, you can use the Flexible Body Model Builder app or finite-element analysis tools, such as the Partial Differential Equation Toolbox™. By using the toolbox, you can start with the CAD geometry of the body, generate a finite-element mesh, apply the Craig-Bampton method, and generate the corresponding ROM data. For more information, see Model an Excavator Dipper Arm as a Flexible Body.

### Common Reference Frame

The data provided to the Reduced Order Flexible
Solid block must refer to a consistent common reference frame.
This reference frame defines the *x*, *y*, and
*z* directions that specify the relative position of all points
in the body. The frame also defines the directions of the elastic degrees of freedom
associated with each interface frame.

### Requirements for the ROM Data

The ROM data for the Reduced Order Flexible Solid block must satisfy these requirements:

The ROM data must have at least one boundary node. Each boundary node determines the location of an interface frame.

Each boundary node must contribute six degrees of freedom to the reduced-order model. The degrees of freedom for node

*i*must be retained in the order*U*= [_{i}*T*,_{x}_{i}*T*,_{y}_{i}*T*,_{z}_{i}*R*,_{x}_{i}*R*,_{y}_{i}*R*],_{z}_{i}where:

*T*,_{x}_{i}*T*, and_{y}_{i}*T*are translational degrees of freedom along the_{z}_{i}*x*,*y*, and*z*directions of the common reference frame.*R*,_{x}_{i}*R*, and_{y}_{i}*R*are rotational degrees of freedom about the_{z}_{i}*x*,*y*, and*z*axes of the common reference frame.

The reduced-order model can also include additional degrees of freedom,
*D _{1}*,

*D*, ⋯,

_{2}*D*, that correspond to retained normal vibration modes. For a reduced-order model that has

_{m}*n*boundary nodes and

*m*modal degrees of freedom, the degrees of the freedom of the model is:

*U _{reduced}*
= [

*U*,

_{1}*U*, ⋯,

_{2}*U*,

_{n}*D*,

_{1}*D*, ⋯,

_{2}*D*].

_{m}

The number of the degrees of freedom
*N _{reduced}*
equals 6

*n*+

*m*, which includes six rigid-body degrees of freedom. The number of elastic degrees of freedom equals

*N*- 6. The number of the degrees of freedom determines the size of the stiffness and mass matrices. For the matrices, the order of the rows and columns must correspond to the order of the

_{reduced}*U*.

_{reduced}### Reduce the Degrees of Freedom for a Flexible Body

You can use the block to further reduce the degrees of freedom for a flexible body. The fewer the degrees of freedom for flexible bodies, the faster the simulation.

For example, a ROM data set generated by the Craig-Bampton method with two
boundary nodes and 10 fixed-interface normal modes has a total of 22 degrees of
freedom. If you use the ROM data, the block generates an internal representation of
the flexible body that has six rigid-body and 16 elastic degrees of freedom. To
further reduce the number of the elastic degrees of freedom, you can set
**Reduction** to `Modally Reduced`

. If
you specify **Number of Retained Modes** to `8`

,
the flexible body retains the eight lowest-frequency modal degrees of freedom in
addition to the six rigid-body degrees of freedom.

### Damping

To specify the damping characteristics of the flexible bodies, the block has three damping methods: proportional damping, uniform modal damping, and damping matrix methods. For more informations, see Damping.

### Simulation Performance

Flexible bodies can increase the numerical stiffness of a multibody model. To
avoid simulation issues, use a stiff solver such as `ode15s`

or
`ode23t`

.

Damping can significantly influence simulation performance. For example, when modeling a body with little or no damping, undesirable high-frequency modes in the response can slow the simulation. In that case, adding a small amount of damping can improve the speed of the simulation without significantly affecting the accuracy of the model.

## Examples

## Ports

### Frame

## Parameters

## References

[1] Shabana, Ahmed A. *Dynamics of Multibody Systems*. Fourth edition. New York: Cambridge University Press, 2014.

[2] Agrawal, Om P., and Ahmed A. Shabana. “Dynamic Analysis of Multibody Systems Using Component Modes.” *Computers & Structures* 21, no. 6 (January 1985): 1303–12. https://doi.org/10.1016/0045-7949(85)90184-1.

## Extended Capabilities

## Version History

**Introduced in R2019b**