Rigid Link

This command is used to construct a single MP_Constraint object.

rigidLink $type $retainedNodeTag $constrainedNodeTag

Argument	Type	Description
$type	[s tring]{.t itle-ref}	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.
$retain edNodeTag	[in teger]{.t itle-ref}	integer tag identifying the retained node
$ constrain edNodeTag	[in teger]{.t itle-ref}	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:

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}

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

begin{bmatrix}

1 & 0 & -Delta Y \ 0 & 1 & Delta X \ 0 & 0 & 1

end{bmatrix}

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:

\[\begin{aligned} \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \end{aligned}\]

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

begin{bmatrix}

1 & 0 \ 0 & 1 \

end{bmatrix}

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)