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(testmodels-ancfslidingandalejointtest)=
# ANCFslidingAndALEjointTest.py

You can view and download this file on Github: [ANCFslidingAndALEjointTest.py](https://github.com/jgerstmayr/EXUDYN/tree/master/python/TestModels/ANCFslidingAndALEjointTest.py)

```{code-block} python
:linenos:

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  Test model for rigid bodies sliding on cables
#
# Author:   Andreas Zwölfer, Johannes Gerstmayr
# Date:     2019-12-18
#
# Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details.
#
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

import exudyn as exu
from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities
from exudyn.beams import GenerateAleSlidingJoint, GenerateSlidingJoint, GenerateBeamElementsAlongLine
import exudyn.graphics as graphics

testIsActive = exu.sys.get('testIsActive', False)

SC = exu.SystemContainer()
mbs = SC.AddSystem()


##################################################################################################################################################################
def AddBodyWithSlidingJoints(mbs,xPositionOfFirstNodes=0,referencePositionOfBodyAlongCable=0,gravityFieldConstant=0):

    a = 0.8*2     #y-dim/2 of Body
    b = 0.02    #x-dim/2 of Body
    massRigid = 5000 #moving mass
    inertiaRigid = massRigid/12*(2*a)**2
    #rigid body which slides:
    graphicsRigid1 = graphics.Lines([[-b,-a,0], [b,-a,0], [b,a,0], [-b,a,0], [-b,-a,0]]) #drawing of rigid body
    yCOM = a    #COM distance to attachment point on suspension rope; in vertical direction      
    
    nRigid = mbs.AddNode(Rigid2D(referenceCoordinates=[xPositionOfFirstNodes+referencePositionOfBodyAlongCable,-yCOM,0]));
    oRigid = mbs.AddObject(RigidBody2D(mass=massRigid, inertia=inertiaRigid,nodeNumber=nRigid,visualization=VObjectRigidBody2D(graphicsData= [graphicsRigid1])))  
    markerRigidTop=mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid, localPosition=[0.,yCOM,0.])) #support point
    markerRigidTopAle = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid, localPosition=[0.,yCOM-offset,0.])) #support point
    
    if gravityFieldConstant:
        mR2 = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oRigid, localPosition=[ 0.,0.,0.])) #center of mass (for load)
        mbs.AddLoad(Force(markerNumber=mR2, loadVector=[0,-massRigid*gravityFieldConstant,0]))
    
    
    #find index of cable element associated with "referencePositionOfBodyAlongCable"
    cummulativeLength=0
    count=0
    while referencePositionOfBodyAlongCable >= cummulativeLength:
        cummulativeLength+=mbs.GetObjectParameter(cable2ObjectList[count],'length')
        count+=1
    count+=-1
    
    #AleSlidingJoint:
    oAleSlidingJoint=GenerateAleSlidingJoint(mbs,cable1ObjectList,markerRigidTopAle,AleNode=nALE,localMarkerIndexOfStartCable=count,AleSlidingOffset=referencePositionOfBodyAlongCable)[0]
      
    
    #slidingJoint:
    oSlidingJoint=GenerateSlidingJoint(mbs,cable2ObjectList,markerRigidTop,localMarkerIndexOfStartCable=count,slidingCoordinateStartPosition=referencePositionOfBodyAlongCable)[0] 
        
    return [oRigid,nRigid, oAleSlidingJoint, oSlidingJoint] 


#Background:
rect = [-2,-2,4,2] #xmin,ymin,xmax,ymax
background0 = {'type':'Line', 'color':[0.1,0.1,0.8,1], 'data':[rect[0],rect[1],0, rect[2],rect[1],0, rect[2],rect[3],0, rect[0],rect[3],0, rect[0],rect[1],0]} #background
background1 = {'type':'Line', 'color':[0.1,0.1,0.8,1], 'data':[0,-1,0, 2,-1,0]} #background
oGround=mbs.AddObject(ObjectGround(referencePosition= [0,0,0]))

L=100  #length of ropes
gravityFieldConstant=9.81   
complianceFactBend = 1
complianceFactAxial = 1
nEl=6 #must be even number
vALE=0 
offset=0.35 #distance between the two ropes
offsetCarrier=-0.515 #distance between suspension rope and slack carrier wheel

nGlobalGround = mbs.AddNode(NodePointGround(referenceCoordinates=[0,0,0])) 
mGlobalGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nGlobalGround, coordinate=0))

fixANCFRotation = 0

#######################ROPE2 (Carrier rope)########################################################################################################################
cable2Template=Cable2D(massPerLength=10, bendingStiffness=50000*complianceFactBend, axialStiffness=2e8*complianceFactAxial)

beamInfo=GenerateBeamElementsAlongLine(mbs=mbs, 
                positionStart=[0,0,0], positionEnd=[L,0,0], numberOfElements=nEl, 
                beamTemplate=cable2Template, gravity=[0,-gravityFieldConstant,0], 
                groundConstraintsStart=[1,1,0,fixANCFRotation], groundConstraintsEnd=[1,1,0,fixANCFRotation])
cable2NodeList, cable2ObjectList, suspensionLoadList, cable2NodePositionList, dummy = beamInfo['nodes'], beamInfo['elements'], beamInfo['loads'], beamInfo['nodePositions'], beamInfo['constraintObjects']
##################################################################################################################################################################

 
######################ROPE1#######################################################################################################################################
nALE = mbs.AddNode(NodeGenericODE2(numberOfODE2Coordinates=1, referenceCoordinates=[0], initialCoordinates=[0], initialCoordinates_t=[vALE]))
mALE = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nALE, coordinate=0)) #ALE velocity  marker

cable1Template=ALECable2D(massPerLength=3, bendingStiffness=4000*complianceFactBend, 
                          axialStiffness=5e7*complianceFactAxial,useCouplingTerms=False,
                          addALEvariation=False) #for compatibility with test suite results
cable1Template.nodeNumbers[2]=nALE

beamInfo=GenerateBeamElementsAlongLine(mbs=mbs, 
            positionStart=[0,-offset,0], positionEnd=[L,-offset,0], numberOfElements=nEl, 
            beamTemplate=cable1Template, gravity=[0,-gravityFieldConstant,0], 
            groundConstraintsStart=[1,1,0,fixANCFRotation], groundConstraintsEnd=[1,1,0,fixANCFRotation])
cable1NodeList, cable1ObjectList, haulageLoadList, cable1NodePositionList, dummy = beamInfo['nodes'], beamInfo['elements'], beamInfo['loads'], beamInfo['nodePositions'], beamInfo['constraintObjects']

cAleConstraint=mbs.AddObject(CoordinateConstraint(markerNumbers=[mGlobalGround,mALE]))
###################################################################################################################################################################


#Slack carrier:
carrierWheelRadius=0.42/2  
mSuspensionRopeAttachmentNodeX=mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = cable2NodeList[int(nEl/2)], coordinate=0))
mSuspensionRopeAttachmentNodeY=mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = cable2NodeList[int(nEl/2)], coordinate=1))

graphicsCarrier={'type':'Circle', 'color':[.1,0.1,0.8,1], 'position':[0,0,0], 'radius': carrierWheelRadius}
nCarrierRigidBody = mbs.AddNode(Rigid2D(referenceCoordinates=[L/2,offsetCarrier-carrierWheelRadius,0]))
oCarrierRigidBody = mbs.AddObject(RigidBody2D(mass=200, inertia=1, 
                                nodeNumber=nCarrierRigidBody,visualization=VObjectRigidBody2D(graphicsData= [graphicsCarrier])))  

mCarrierX = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nCarrierRigidBody,coordinate=0))
mCarrierY = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nCarrierRigidBody,coordinate=1))
mCarrierRot = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nCarrierRigidBody,coordinate=2))

mbs.AddObject(CoordinateConstraint(markerNumbers=[mSuspensionRopeAttachmentNodeX,mCarrierX])) 
mbs.AddObject(CoordinateConstraint(markerNumbers=[mSuspensionRopeAttachmentNodeY,mCarrierY])) 
mbs.AddObject(CoordinateConstraint(markerNumbers=[mGlobalGround,mCarrierRot]))

#mCarrierWheelLoad = mbs.AddMarker(MarkerBodyPosition(bodyNumber=oCarrierRigidBody, localPosition=[ 0.,0.,0.])) #center of mass (for load)
#mbs.AddLoad(Force(markerNumber=mConnectionWheelLoad, loadVector=[0,-CarrierMass*gravityFieldConstant,0]))
               
nSegments = 4 #number of contact segments; must be consistent between nodedata and contact element
useFriction = True
nFactFriction = 1
if useFriction: nFactFriction = 3

initialGapList = [0.1]*(nSegments*nFactFriction) #initial gap of 0.1
cStiffness = 1e7
mContactCarrier=mbs.AddMarker(MarkerBodyRigid(bodyNumber = oCarrierRigidBody))  


for i in cable1ObjectList:
    mContactCable = mbs.AddMarker(MarkerBodyCable2DShape(bodyNumber=i, numberOfSegments = nSegments))  
    nodeDataContactCable = mbs.AddNode(NodeGenericData(initialCoordinates=initialGapList,numberOfDataCoordinates=nSegments*nFactFriction)) 
    if useFriction: 
        mbs.AddObject(ObjectContactFrictionCircleCable2D(markerNumbers=[mContactCarrier, mContactCable], 
                        nodeNumber = nodeDataContactCable, numberOfContactSegments=nSegments, 
                        contactStiffness = cStiffness, circleRadius = carrierWheelRadius))  
    else:
        mbs.AddObject(ObjectContactCircleCable2D(markerNumbers=[mContactCarrier, mContactCable], 
                    nodeNumber = nodeDataContactCable, numberOfContactSegments=nSegments, 
                    contactStiffness = cStiffness, circleRadius = carrierWheelRadius, offset = 0))  
      

#Add Bodys
cRigidBodyRotList=[]
cRigidBodyTranslationXlist=[]
cRigidBodyTranslationYlist=[]
distanceBetweenBodys=32
numberOfBodys=2
positionOfBody=0
for i in range(numberOfBodys):

    #Add Body
    [oRigid,nRigid,oAleSlidingJoint,oSlidingJoint]=AddBodyWithSlidingJoints(mbs,xPositionOfFirstNodes=0,referencePositionOfBodyAlongCable=positionOfBody,gravityFieldConstant=gravityFieldConstant)
    mbs.SetObjectParameter(oSlidingJoint, 'useClassicalFormulation', False) #test model computed with new sliding joint formulation

    #fix rotation of rigid body
    mRigidBodyRot = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nRigid, coordinate=2)) #add rigid body marker
    cRigidBodyRot = mbs.AddObject(CoordinateConstraint(markerNumbers=[mGlobalGround,mRigidBodyRot])) 
    cRigidBodyRotList+=[cRigidBodyRot]
    
    #add damper for rotation of rigid body
    mbs.AddObject(CoordinateSpringDamper(markerNumbers=[mGlobalGround,mRigidBodyRot],damping = 1e6, visualization=VObjectConnectorCoordinateSpringDamper(show=False)))  

    positionOfBody+=distanceBetweenBodys
    

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++#
# Assemble multibody system
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++#
mbs.Assemble()
#exu.Print(mbs)

#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++#
# Simualtion settings:
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++#
simulationSettings = exu.SimulationSettings()
simulationSettings.timeIntegration.newton.useModifiedNewton = False #Just for the test; modified Newton is usually faster
#simulationSettings.staticSolver.loadStepGeometric = True
#simulationSettings.staticSolver.adaptiveStep = False
simulationSettings.staticSolver.numberOfLoadSteps=10
#simulationSettings.staticSolver.loadStepGeometricRange = 100
simulationSettings.staticSolver.newton.relativeTolerance = 1e-7 #with this error tolerance, the adaptive step selection needs 4 steps

#simulationSettings.staticSolver.verboseMode=1
#simulationSettings.staticSolver.verboseModeFile=2
simulationSettings.staticSolver.stabilizerODE2term = 2


SC.visualizationSettings.general.circleTiling = 64
SC.visualizationSettings.nodes.defaultSize=0.125
SC.visualizationSettings.contour.outputVariable = exu.OutputVariableType.Displacement
SC.visualizationSettings.contour.outputVariableComponent = 1 # plot y-component
SC.visualizationSettings.contact.contactPointsDefaultSize = .005
SC.visualizationSettings.connectors.showContact = True


if not testIsActive: 
    SC.renderer.Start()

#get initial velocities
vInit = mbs.systemData.GetODE2Coordinates_t(configuration = exu.ConfigurationType.Initial)

#start static calculation
mbs.SolveStatic(simulationSettings) 

#++++++++++++++++++++++++++++++++++++++++
#compute error for test suite:
ltgCable = mbs.systemData.GetObjectLTGODE2(cable1ObjectList[int(len(cable1ObjectList)/2)])
nc = ltgCable[1] #vertical displacement
exu.Print("select cable coordinate", nc)
sol = mbs.systemData.GetODE2Coordinates(); 
uStatic = sol[nc]; #y-displacement of first node of four bar mechanism
exu.Print('static solution of cable1 =',uStatic)
exu.sys['testResult'] = uStatic 

#++++++++++++++++++++++++++++++++++++++++
#store solution for next computation
u = mbs.systemData.GetODE2Coordinates()
data = mbs.systemData.GetDataCoordinates()

#Add drive via ALE:
def userLoadDriveAle(mbs, t, load):
    #if t < 1:
    return t*50000*5
    #else: return 0

mbs.AddLoad(LoadCoordinate(markerNumber = mALE, loadUserFunction=userLoadDriveAle))
mbs.Assemble() #because of new load

#++++++++++++++++++++++++++++++++++++++++
#resuse old solution
mbs.systemData.SetODE2Coordinates(u,configuration = exu.ConfigurationType.Initial)
mbs.systemData.SetODE2Coordinates_t(vInit,configuration = exu.ConfigurationType.Initial)
mbs.systemData.SetDataCoordinates(data,configuration = exu.ConfigurationType.Initial)


# remove rigid body motion constraints for dynamic analysis
for item in cRigidBodyRotList:
    mbs.SetObjectParameter(item, 'activeConnector', False)
mbs.SetObjectParameter(cAleConstraint, 'activeConnector', False)


solveDynamic = True
if solveDynamic:
    # time related settings:
    steps=400
    tend=0.8
    h=tend/steps
    SC.visualizationSettings.openGL.lineWidth = 2
    simulationSettings.timeIntegration.numberOfSteps = steps 
    simulationSettings.timeIntegration.endTime = tend 
    simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = True
    simulationSettings.timeIntegration.generalizedAlpha.useNewmark = simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints
    simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.3
    simulationSettings.timeIntegration.verboseMode = 1
    simulationSettings.show.statistics = True
    
    mbs.SolveDynamic(simulationSettings)
    
if not testIsActive: 
    #SC.renderer.DoIdleTasks()
    SC.renderer.Stop() #safely close rendering window!


sol = mbs.systemData.GetODE2Coordinates(); 
uDynamic = sol[nc]; #y-displacement of first node of four bar mechanism
exu.Print('dynamic solution of cable1 =',uDynamic)

exu.sys['testResult'] += uDynamic

exu.Print('result of ANCFslidingAndALEjointTest=',exu.sys['testResult'])
```