ObjectContactCircleCable2D

A very specialized penalty-based contact condition between a 2D circle (=marker0, any Position-marker) on a body and an ANCFCable2DShape (=marker1, Marker: BodyCable2DShape), in xy-plane. A node NodeGenericData is required with the number of cordinates according to the number of contact segments; the contact gap \(g\) is integrated (piecewise linear) along the cable and circle; the contact force \(f_c\) is zero for \(gap>0\) and otherwise computed from \(f_c = g*contactStiffness\), without damping; during Newton iterations, the contact force is actived only, if \(dataCoordinate[0] <= 0\); dataCoordinate is set equal to gap in nonlinear iterations, but not modified in Newton iterations.

Interface

Nodes it takes: NodeGenericData

Parameters

The parameters of the item; in a dictionary, its type is ‘ContactCircleCable2D’:

name	type	default	description
name	String	‘’	connector’s unique name
markerNumbers	ArrayMarkerIndex	[ invalid (-1), invalid (-1) ]	markers define contact gap
nodeNumber	NodeIndex	invalid (-1)	node number of a NodeGenericData for nSegments dataCoordinates (used for active set strategy ==> hold the gap of the last discontinuous iteration and the friction state)
numberOfContactSegments	Index	3	number of linear contact segments to determine contact; each segment is a line and is associated to a data (history) variable; must be same as in according marker
contactStiffness	UReal	0.	contact (penalty) stiffness [SI:N/m/(contact segment)]; the stiffness is per contact segment; specific contact forces (per length) \(f_N\) act in contact normal direction only upon penetration
circleRadius	UReal	0.	radius [SI:m] of contact circle
offset	Real	0.	offset [SI:m] of contact, e.g. to include thickness of cable element
activeConnector	Bool	True	flag, which determines, if the connector is active; used to deactivate (temporarily) a connector or constraint
visualization	VObjectContactCircleCable2D		parameters for visualization of item

Visualization parameters

The parameters of VObjectContactCircleCable2D, given as visualization:

name	type	size	default	description
show	Bool		True	set true, if item is shown in visualization and false if it is not shown
showContactCircle	Bool		True	if True and show=True, the underlying contact circle is shown; uses circleTiling*4 for tiling (from VisualizationSettings.general)
drawSize	float		-1.	drawing size = diameter of spring; size == -1.f means that default connector size is used
color	Float4	4	[-1.,-1.,-1.,-1.]	RGBA connector color; if R==-1, use default color

Drawing

Drawn as all connectors; with connectors.showContact, the circle (showContactCircle, 4 times general.circleTiling segments), the contact points of the cable, and lines where it penetrates.

Settings beyond those of all connectors: connectors.showContact, contact.contactPointsDefaultSize, general.circleTiling.

Detailed description

Markers

Marker 0 is the center of the circle, any marker with a position; marker 1 is a MarkerBodyCable2DShape on an ANCF cable element, with the same numberOfContactSegments as the connector.

Geometric relations

The cable is divided into numberOfContactSegments straight segments between the points of the shape marker; for each segment the gap is the distance of the circle center from the segment minus circleRadius and offset, and the penetration is integrated, piecewise linear, along the segment.

Connector forces

Per segment in contact, a force per length \(f_N = k_c\, g\) in the normal direction of the contact, with contactStiffness per segment and without damping; the forces act on the cable through the shape functions of the marker and on the circle center. There is no friction and no torque on the circle: otherwise geometry and equations are those of ObjectContactFrictionCircleCable2D, see ObjectContactFrictionCircleCable2D. The data coordinates, one per segment, hold the gap of the last post Newton step and decide on contact (active set).

Mini example

from exudyn.beams import GenerateBeamElementsAlongLine
#the shape of an ANCF cable element as line segments, for contact: a cantilever falls onto a circle
cable = ObjectANCFCable2D(massPerLength=1, bendingStiffness=10, axialStiffness=1e4,
                          bendingDamping=0.1)
beamInfo = GenerateBeamElementsAlongLine(mbs, positionStart=[0,0,0], positionEnd=[1,0,0],
                        numberOfElements=4, beamTemplate=cable, gravity=[0,-9.81,0],
                        groundConstraintsStart=[1,1,0,1])
nodes, elements = beamInfo['nodes'], beamInfo['elements']
mCircle = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oGround, localPosition=[0.8,-0.2,0]))
nSegments = 4
for e in elements:
    mShape = mbs.AddMarker(MarkerBodyCable2DShape(bodyNumber=e, numberOfSegments=nSegments))
    nData = mbs.AddNode(NodeGenericData(numberOfDataCoordinates=nSegments, initialCoordinates=[0.1]*nSegments))
    mbs.AddObject(ObjectContactCircleCable2D(markerNumbers=[mCircle, mShape], nodeNumber=nData,
                                             numberOfContactSegments=nSegments, circleRadius=0.1,
                                             contactStiffness=1e4))

mbs.Assemble()
mbs.SolveDynamic()

#the tip rests beyond the circle, whose top is at y=-0.1
exu.sys['testResult'] = mbs.GetNodeOutput(nodes[-1], exu.OutputVariableType.Position)[1]

Relevant Examples (Ex) and TestModels (TM) with weblink to github: ANCFcontactCircle.py (Ex), ANCFcontactCircle2.py (Ex), ANCFmovingRigidbody.py (Ex), ANCFslidingJoint2D.py (Ex), ANCFcontactCircleTest.py (TM), ANCFmovingRigidBodyTest.py (TM), ANCFslidingAndALEjointTest.py (TM), connectorOutputVariablesTest.py (TM)