3.1.4.2. Rigid Diaphragm

This command is used to construct a number of Multi-Point Constraint (MP_Constraint) objects. These objects will constraint certain degrees-of-freedom at the listed constrained nodes to move as if in a rigid plane with the retained node.

rigidDiaphragm $perpDirn $retainedNodeTag $constrainedNodeTag1 $constrainedNodeTag2 ...

Argument	Type	Description
$perpDirn	integer	direction perpendicular to the rigid plane (i.e. direction 3 (Z) corresponds to the 1-2 (X-Y) plane) – for 2D models direction of rigid motion (1 (X) or 2 (Y))
$retainedNodeTag	integer	integer tag identifying the primary (retained) node
$constrainedNodeTag1 $constrainedNodeTag2 …	list integer	integer tags identifying the secondary (constrained) nodes

Note

1. The constraint object is constructed assuming small rotations in 3D.

2. The rigidDiaphragm command works for problems in three dimensions with six-degrees-of-freedom at the nodes (ndf=6) and in two dimensions with ndf=3.

Example:

The following command will constrain nodes 4,5,6 to move as if in the same 1-2 plane as node 22. The constraint matrix added for each of the constrained nodes, which defines the motion of degrees-of-freedom (x, y, rZ) or (1, 2, and 6) at node 4,5,6 relative to those same degrees-of-freedom at the retained node 22 is as follows:

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

where \(\Delta X\) is x (or 1) coordinate of constrained node minus the x coordinate of the retained node and \(\Delta Y\) is y (or 2) coordinate of constrained node minus the y coordinate of the retained node and \(\Delta Y\)

1. Tcl Code

rigidDiaphragm 3 22 4 5 6

2. Python Code

rigidDiaphragm(3,22,4,5,6)