3.1.10.4. CoupledZeroLength Element

This command is used to construct a CoupledZeroLength element object. The element is defined by two nodes at the same location and couples two degrees of freedom (dirn1 and dirn2) through a single UniaxialMaterial. Unlike a ZeroLength element, which provides a rectangular force interaction surface in a 2D plane, this element provides a circular force interaction surface in the plane of the two directions.

element coupledZeroLength $eleTag $iNode $jNode $dirn1 $dirn2 $matTag <-doRayleigh $rFlag>

Argument	Type	Description
$eleTag	integer	unique element object tag
$iNode $jNode	integer	end node tags
$dirn1 $dirn2	integer	the two coupled directions (1 through ndf)
$matTag	integer	tag associated with previously-defined UniaxialMaterial
$rFlag	integer	optional, default = 0 0 = NO RAYLEIGH DAMPING (default) 1 = include Rayleigh damping

Theory

If the change in element end displacements for the two DOFs of interest are $\delta_1$ and $\delta_2$, the deformation (strain) of the uniaxial material is:

\[\epsilon = \sqrt{\delta_1^2 + \delta_2^2}\]

If the resulting force (stress from the uniaxial material) is $\Sigma$, the forces in the two directions are:

\[F_1 = \frac{\Sigma \cdot \delta_1}{\epsilon}, \quad F_2 = \frac{\Sigma \cdot \delta_2}{\epsilon}\]

When $\epsilon = 0$, the forces are computed using $\Sigma$ and the last committed set of displacements that were not zero.

Note

The valid queries to this element when creating an ElementRecorder object are ‘force’ and ‘material matArg1 matArg2 …’.