Flexible body based on a reduced-order model

**Library:**Simscape / Multibody / Body Elements / Flexible Bodies

The Reduced Order Flexible Solid block models a deformable body of arbitrary geometry based on a reduced-order model.

A *reduced-order model* is a computationally efficient model that
characterizes the mechanical properties of a flexible body under small deformations. The
basic data imported from the reduced-order model includes:

A list of coordinate triples that specify the position of all interface frame origins 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.

If you already have a detailed CAD model of a component in a Simscape™ Multibody™ model, you can use finite-element analysis (FEA) tools to generate the reduced-order data required by this block. For example, with the Partial Differential Equation Toolbox™, you can start with the CAD geometry of your component, generate a finite-element mesh, apply the Craig-Bampton FEA substructuring method, and generate a reduced-order model. For more information, see Model an Excavator Dipper Arm as a Flexible Body.

The block, the reduced-order model, and the CAD geometry must use a consistent
common reference frame. This local reference frame defines the *x*,
*y*, and *z* directions used to specify the
relative position of all points in the body. The reference frame also defines the
directions of the small-deformation degrees of freedom (the translations and
rotations) associated with each interface frame.

Your reduced-order model must contain at least one boundary node. Each boundary node determines the location of an interface frame where the flexible body connects to other Simscape Multibody elements, such as joints, constraints, forces, and sensors. You specify the boundary nodes in the reduced-order model in the same order as the corresponding interface frames on the block.

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}* =
[

where:

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

Your model can also include additional degrees of freedom,
*D _{1}*,

The number of degrees of freedom determines the size of the stiffness and mass
matrices. In a flexible body with *n* boundary nodes and
*m* modal degrees of freedom, these matrices have *r* = 6*n* +
*m* rows and columns. The order of the rows and columns must
correspond to the order of the degrees of freedom:

*U _{reduced}*
= [

The more degrees of freedom in the model, the larger the matrices that describe the flexible body and the slower the simulation.

To specify the damping characteristics of the flexible body, you can:

Assume a proportional damping model where the damping matrix is equal to the product of the stiffness matrix and a damping constant. For this damping model, the damping ratios associated with vibration modes increase with frequency.

Provide an explicit damping matrix that you computed with the stiffness and mass matrices. For example, you can use this option to specify a modal damping model for the flexible body.

Model an undamped flexible body.

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 down 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.