# /RBE2

Block Format Keyword Defines a rigid body whose independent degrees of freedom are specified at a single independent node and whose dependent degrees of freedom are specified at an arbitrary number of dependent nodes.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/RBE2/rbe2_ID
rbe2_title
node_ID Trarotref Skew_ID grnd_ID Iflag

## Definition

Field Contents SI Unit Example
rbe2_ID Rigid element identifier.

(Integer, maximum 10 digits)

rbe2_title Rigid element title.

(Character, maximum 100 characters)

node_ID Independent node identifier.

(Integer)

Trarotref Code of DOF used for the dependent components.
=0
free DOF
=1
fixed DOF

(6 Booleans)

Default (blank or 6 zeros) set on all DOF

Skew_ID Local skew identifier of element.

(Integer)

grnd_ID Dependent nodes group identifier.

(Integer)

Iflag Dependent relation formulation flag. 1
= 0 (Default)
Rigid body formulation (OptiStruct)
= 1

(Integer)

## Codes for Translation and Rotation: Trarot

(1)-1 (1)-2 (1)-3 (1)-4 (1)-5 (1)-6 (1)-7 (1)-8 (1)-9 (1)-10
TX TY TZ   ${\omega }_{X}$ ${\omega }_{Y}$ ${\omega }_{Z}$

## Definition

Field Contents SI Unit Example
TX Code for translation TX.
=0
free DOF
=1
fixed DOF

(Boolean)

TY Code for translation TY.
=0
free DOF
=1
fixed DOF

(Boolean)

TZ Code for translation TZ.
=0
free DOF
=1
fixed DOF

(Boolean)

${\omega }_{X}$ Code for rotation ${\omega }_{X}$ .
=0
free DOF
=1
fixed DOF

(Boolean)

${\omega }_{Y}$ Code for rotation ${\omega }_{Y}$ .
=0
free DOF
=1
fixed DOF

(Boolean)

${\omega }_{Z}$ Code for rotation ${\omega }_{Z}$ .
=0
free DOF
=1
fixed DOF

(Boolean)

1. Two formulations of dependent motion are available in Iflag:
If Iflag=0(1)
(2)
${\stackrel{˙}{\theta }}_{s}\left(rotation\right)=\left[Rot\right]{\stackrel{˙}{\theta }}_{m}$
If Iflag=1(3)
${\stackrel{˙}{u}}_{s}\left(translation\right)=\left[Tra\right]{\stackrel{˙}{u}}_{m}+{\stackrel{˙}{D}}_{sm}\otimes \left[Rot\right]{\stackrel{˙}{\theta }}_{m}$
(4)
${\overline{\theta }}_{s}\left(rotation\right)=\left[Rot\right]{\overline{\theta }}_{m}$
(5)
$\left[Tra\right],\left[Rot\right]=\left[\begin{array}{ccc}i& 0& 0\\ 0& j& 0\\ 0& 0& k\end{array}\right]$

With $i$ , $j$ , $k$ =0,1

The default formulation Iflag =0 corresponds to OptiStruct's RBE2, in which the motion of a group of dependent nodes depends on the motion of one independent node which always has 6 DOF. The input Trarotref is applied on the dependent nodes and the element behaves like a rigid body.

The second formulation is similar to /RLINK; but takes into account the equilibrium between translations and rotations. The input Trarotref is applied on independent node, this formulation is used prior to version 10.0.5.

2. A independent node can be attached to a finite element. The independent node can also be defined in a different RBE2 as independent node and/or dependent node, but the dependent node cannot have the incompatible kinematic conditions.
3. It is not recommended for dependent or independent nodes of an /RBE2 to also be dependent or independent nodes in another constraint equation (kinematic conditions). However, this is permitted if the hierarchy rule has been respected: RBE2 should have a higher level than Interface TYPE2 (independent nodes of Interface TYPE2 can be dependent node of RBE2); but a lower level than RBE3 and RBODY. The hierarchy between different RBE2s is allowed, re-ordering will be done automatically to determine the hierarchy by Radioss Starter, if hierarchy levels between RBE2 are too high, error will be printed out.
4. Hierarchy rule involving /INTER/TYPE2, /RBE2, /RBE3 and /RBODY is:

RBODY > RBE3 > RBE2 > INTERFACE TYPE2

5. More output messages could be obtained using Ipri of /IOFLAG: Ipri > 3 will printout new mass and inertia of the independent nodes; Ipri > 5 will printout the new RBE2 identifier and hierarchy level after re-ordering.
6. The RBE2 uses a scalar inertia calculation similar to using /RBODY with Ispher=1.