3.1.5.3. Rigid Link

This command is used to construct a single MP_Constraint object.

rigidLink $type $retainedNodeTag $constrainedNodeTag

Argument	Type	Description
$type	string	string-based argument for rigid-link type: bar only the translational degree-of-freedom 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

1. By retained node, we mean the node who’s degrees-of-freedom are retained in the system of equations. The constrained nodes degrees-of-freedom need not appear in the system (depending on the constraint handler).

2. 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:

   (3.1.5.5)\[\begin{split}\begin{bmatrix} 1 & 0 & 0 & 0 & \Delta Z & -\Delta Y \\ 0 & 1 & 0 & -\Delta Z & 0 & \Delta X \\ 0 & 0 & 1 & \Delta Y & -\Delta X & 0 \\ 0 & 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \end{bmatrix}\end{split}\]

   For 2d problems, the constraint matrix is the following:

   (3.1.5.5)\[\begin{split}\begin{bmatrix} 1 & 0 & -\Delta Y \\ 0 & 1 & \Delta X \\ 0 & 0 & 1 \end{bmatrix}\end{split}\]

   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.

3. For 2d and 3d problems with a rod type link the constraint matrix, that which matrix relates the responses at translational degrees-of-freedom at the constrained node to corresponding responses at retained node, is the identity matrix. For 3d problems this results in the following constraint matrix:

(3.1.5.5)\[\begin{split}\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\end{split}\]

For 2d problems, the constraint matrix is the following:

(3.1.5.5)\[\begin{split}\begin{bmatrix} 1 & 0 \\ 0 & 1 \\ \end{bmatrix}\end{split}\]

4. 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

1. Tcl Code

rigidLink beam 2 3

2. Python Code

rigidLink('beam',2,3)