3.1.4.3. Rigid Link¶
This command is used to construct a single MP_Constraint object.
 rigidLink $type $retainedNodeTag $constrainedNodeTag
Argument 
Type 
Description 

$type 
string 
stringbased argument for rigidlink type:
bar only the translational degreeoffreedom will be constrained to be exactly the same as those at the master node
beam both the translational and rotational degrees of freedom are constrained.

$retainedNodeTag 
integer 
integer tag identifying the retained node 
$constrainedNodeTag 
integer 
integer tag identifying the constrained node 
Note
By retained node, we mean the node who’s degreesoffreedom are retained in the system of equations. The constrained nodes degreesoffreedom need not appear in the system (depending on the constraint handler).
For 2d and 3d problems with a beam type link, the constraint matrix (that matrix relating the responses at constrained node, \(U_c\), to responses at retained node, \(U_r\), i.e. \(U_c = C_{cr} U_r\), is constructed assuming small rotations. For 3d problems this results in the following constraint matrix:
(3.1.4.5)¶\[\begin{split}\begin{bmatrix} 1 & 0 & 0 & 0 & \Delta Z & \Delta Y \\ 0 & 1 & 0 & \Delta Z & 0 & \Delta X \\ 0 & 0 & 1 & \Delta Y & \Delta X & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{bmatrix}\end{split}\]For 2d problems, the constraint matrix is the following:
(3.1.4.5)¶\[\begin{split}\begin{bmatrix} 1 & 0 & \Delta Y \\ 0 & 1 & \Delta X \\ 0 & 0 & 1 \end{bmatrix}\end{split}\]where \(\Delta X\) is x coordinate of constrained node minus the x coordinate of the retained node. \(\Delta Y\) and \(\Delta Z\) being similarily defined for y and z coordinates of the nodes.
For 2d and 3d problems with a rod type link the constraint matrix, that which matrix relates the responses at translational degreesoffreedom at the constrained node to corresponding responses at retained node, is the identity matrix. For 3d problems this results in the following constraint matrix:
For 2d problems, the constraint matrix is the following:
(3.1.4.5)¶\[\begin{split}\begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix}\end{split}\]
The rod constraint can also be generated using the equalDOF command.
Example:
The following command will constrain node 3 to move rigidly following rules for small rotations to displacements and rotations at node 2 is
Tcl Code
rigidLink beam 2 3
Python Code
rigidLink('beam',2,3)