BeamEndContact3D

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This command is used to construct a BeamEndContact3D element object.

element BeamEndContact3D $eleTag $iNode $jNode $cNode $lNode $radius $gTol $fTol <$cFlag$>

$eleTag	unique integer tag identifying element object
$iNode	retained node from the beam (-ndm 3 -ndf 6)
$jNode	the remaining node on the beam element with $iNode (-ndm 3 -ndf 6)
$cNode	constrained node (-ndm 3 -ndf 3)
$lNode	Lagrange multiplier node (-ndm 3 -ndf 3)
$radius	radius of circular beam associated with beam element
$gTol	gap tolerance
$fTol	force tolerance
$cFlag	optional initial contact flag
	$cFlag = 0 >> contact between bodies is initially assumed (DEFAULT)
	$cFlag = 1 >> no contact between bodies is initially assumed

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The BeamEndContact3D element is a node-to-surface contact element which defines a normal contact interface between the end of a beam element and a separate body. The first retained node ($iNode) is the beam node which is at the end of the beam (i.e. only connected to a single beam element), the second node ($jNode) is the remaining node on the beam element in question. The constrained node ($cNode) is a node from a second body. The Lagrange multiplier node ($lNode) is required to enforce the contact condition. This node should not be shared with any other element in the domain, and should be created with the same number of DOF as the constrained node.

The BeamEndContact3D element enforces a contact condition between a fictitious circular plane associated with a beam element and a node from a second body. The normal direction of the contact plane coincides with the endpoint tangent of the beam element at the retained beam node ($iNode). The extents of this circular plane are defined by the radius input parameter. The retained beam node can only come into contact with a constrained node which is within the extents of the contact plane. There is a lag step associated with changing between the 'in contact' and 'not in contact' conditions.

This element was developed for use in establishing a contact condition for the tip of a pile modeled as using beam elements and the underlying soil elements in three-dimensional analysis.

NOTE:

1. The BeamEndContact3D element does not use a material object.
2. The valid recorder queries for this element are:
   1. force - returns the contact force acting on the constrained node in vector form.
   2. masterforce - returns the reactions (forces and moments) acting on the retained node.
3. The BeamEndContact3D element works well in static and pseudo-static analysis situations.
4. In transient analysis, the presence of the contact constraints can effect the stability of commonly-used time integration methods in the HHT or Newmark family (e.g., Laursen, 2002). For this reason, use of alternative time-integration methods which numerically damp spurious high frequency behavior may be required. The TRBDF2 integrator is an effective method for this purpose. The Newmark integrator can also be effective with proper selection of the gamma and beta coefficients. The trapezoidal rule, i.e., Newmark with gamma = 0.5 and beta = 0.25, is particularly prone to instability related to the contact constraints and is not recommended.

EXAMPLE: BeamEndContact3D element with tag 1, and connectivity with nodes 1, 2, 3, and 4, beam radius of 0.25, gap and force tolerances of 1.0e-10, and a contact flag set to initially assume contact.

element BeamEndContact3D 1  1 2 3 4  0.25 1.0e-10 1.0e-10 0

REFERENCES:

Laursen, T. A. (2002). Computational Contact and Impact Mechanics. Springer-Verlag, Berlin.

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Code Developed by: Chris McGann, Pedro Arduino, & Peter Mackenzie-Helnwein, at the University of Washington

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