You can view and download this file on Github: ANCFcontactCircle.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: ANCF Cable2D contact test
#
# Author: Johannes Gerstmayr
# Date: 2019-10-01
#
# 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.itemInterface import *
SC = exu.SystemContainer()
mbs = SC.AddSystem()
#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], visualization=VObjectGround(graphicsData= [background0, background1])))
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#cable:
mypi = 3.141592653589793
L=2 # length of ANCF element in m
#L=mypi # length of ANCF element in m
E=2.07e11 # Young's modulus of ANCF element in N/m^2
rho=7800 # density of ANCF element in kg/m^3
b=0.001 # width of rectangular ANCF element in m
h=0.001 # height of rectangular ANCF element in m
A=b*h # cross sectional area of ANCF element in m^2
I=b*h**3/12 # second moment of area of ANCF element in m^4
f=3*E*I/L**2 # tip load applied to ANCF element in N
print("load f="+str(f))
print("EI="+str(E*I))
nGround = mbs.AddNode(NodePointGround(referenceCoordinates=[0,0,0])) #ground node for coordinate constraint
mGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nGround, coordinate=0)) #Ground node ==> no action
cableList=[] #for cable elements
nodeList=[] #for nodes of cable
markerList=[] #for nodes
nc0 = mbs.AddNode(Point2DS1(referenceCoordinates=[0,0,1,0]))
nodeList+=[nc0]
nElements = 8
lElem = L / nElements
for i in range(nElements):
nLast = mbs.AddNode(Point2DS1(referenceCoordinates=[lElem*(i+1),0,1,0]))
nodeList+=[nLast]
elem=mbs.AddObject(Cable2D(physicsLength=lElem, physicsMassPerLength=rho*A,
physicsBendingStiffness=E*I, physicsAxialStiffness=E*A, nodeNumbers=[int(nc0)+i,int(nc0)+i+1]))
cableList+=[elem]
mANCF0 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nc0, coordinate=0))
mANCF1 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nc0, coordinate=1))
mANCF2 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nc0, coordinate=3))
mbs.AddObject(CoordinateConstraint(markerNumbers=[mGround,mANCF0]))
mbs.AddObject(CoordinateConstraint(markerNumbers=[mGround,mANCF1]))
mbs.AddObject(CoordinateConstraint(markerNumbers=[mGround,mANCF2]))
#add gravity:
markerList=[]
for i in range(len(nodeList)):
m = mbs.AddMarker(MarkerNodePosition(nodeNumber=nodeList[i]))
markerList+=[m]
fact = 1 #add (half) weight of two elements to node
if (i==0) | (i==len(nodeList)-1): fact = 0.5 # first and last node only weighted half
mbs.AddLoad(Force(markerNumber = m, loadVector = [0, -40*2*rho*A*fact*lElem, 0])) #will be changed in load steps
#mANCFend = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nodeList[-1], coordinate=1)) #last marker
#mbs.AddObject(CoordinateConstraint(markerNumbers=[mGround,mANCFend]))
#mGroundTip = mbs.AddMarker(MarkerBodyPosition(bodyNumber = oGround, localPosition=[L,0,0]))
#mbs.AddObject(CartesianSpringDamper(markerNumbers=[mGroundTip,markerList[-1]], stiffness=[10,10,10], damping=[0.1,0.1,0.1]))
#mGroundTip2 = mbs.AddMarker(MarkerBodyPosition(bodyNumber = oGround, localPosition=[L,0.2,0]))
#mbs.AddObject(SpringDamper(markerNumbers=[mGroundTip2,markerList[-1]], stiffness=0.1, referenceLength=0.2))
#mANCFLast = mbs.AddMarker(MarkerNodePosition(nodeNumber=nLast)) #force
#mbs.AddLoad(Force(markerNumber = mANCFLast, loadVector = [0, -1e8, 0])) #will be changed in load steps
#mANCFrigid = mbs.AddMarker(MarkerBodyRigid(bodyNumber=elem, localPosition=[lElem,0,0])) #local position L = beam tip
#mbs.AddLoad(Torque(markerNumber = mANCFrigid, loadVector = [0, 0, E*I*1*mypi]))
#mANCFnode = mbs.AddMarker(MarkerNodeRigid(nodeNumber=nLast)) #local position L = beam tip
#mbs.AddLoad(Torque(markerNumber = mANCFnode, loadVector = [0, 0, 3*E*I*1*mypi]))
cStiffness = 1e3
cDamping = 0.02*cStiffness
useContact = False
if useContact:
tipContact = False
if tipContact:
nodeData = mbs.AddNode(NodeGenericData(initialCoordinates=[0],numberOfDataCoordinates=1))
mbs.AddObject(ObjectContactCoordinate(markerNumbers=[mGround, mANCFend],nodeNumber = nodeData, contactStiffness = cStiffness, contactDamping=0*cDamping, offset = -0.8))
else:
for i in range(len(nodeList)):
mNC = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber = nodeList[i], coordinate=1))
nodeData = mbs.AddNode(NodeGenericData(initialCoordinates=[1],numberOfDataCoordinates=1)) #start with gap!
mbs.AddObject(ObjectContactCoordinate(markerNumbers=[mGround, mNC], nodeNumber = nodeData, contactStiffness = cStiffness, contactDamping=0*cDamping, offset = -1))
useCircleContact = True
if useCircleContact:
nSegments = 4 #number of contact segments; must be consistent between nodedata and contact element
initialGapList = [0.1]*nSegments #initial gap of 0.1
mGroundCircle = mbs.AddMarker(MarkerBodyPosition(bodyNumber = oGround, localPosition=[0.75*L,-0.5,0]))
mGroundCircle2 = mbs.AddMarker(MarkerBodyPosition(bodyNumber = oGround, localPosition=[0.25*L,-0.15,0]))
#mCable = mbs.AddMarker(MarkerBodyCable2DShape(bodyNumber=elem, numberOfSegments = nSegments))
#nodeDataContactCable = mbs.AddNode(NodeGenericData(initialCoordinates=initialGapList,numberOfDataCoordinates=nSegments))
#mbs.AddObject(ObjectContactCircleCable2D(markerNumbers=[mGroundCircle, mCable], nodeNumber = nodeDataContactCable,
# numberOfContactSegments=nSegments, contactStiffness = cStiffness, contactDamping=cDamping,
# circleRadius = 0.4, offset = 0))
for i in range(len(cableList)):
mCable = mbs.AddMarker(MarkerBodyCable2DShape(bodyNumber=cableList[i], numberOfSegments = nSegments))
nodeDataContactCable = mbs.AddNode(NodeGenericData(initialCoordinates=initialGapList,numberOfDataCoordinates=nSegments))
mbs.AddObject(ObjectContactCircleCable2D(markerNumbers=[mGroundCircle, mCable], nodeNumber = nodeDataContactCable,
numberOfContactSegments=nSegments, contactStiffness = cStiffness, contactDamping=0*cDamping,
circleRadius = 0.2, offset = 0))
nodeDataContactCable = mbs.AddNode(NodeGenericData(initialCoordinates=initialGapList,numberOfDataCoordinates=nSegments))
mbs.AddObject(ObjectContactCircleCable2D(markerNumbers=[mGroundCircle2, mCable], nodeNumber = nodeDataContactCable,
numberOfContactSegments=nSegments, contactStiffness = cStiffness, contactDamping=0*cDamping,
circleRadius = 0.1, offset = 0))
#mbs.systemData.Info()
mbs.Assemble()
print(mbs)
simulationSettings = exu.SimulationSettings() #takes currently set values or default values
#simulationSettings.solutionSettings.coordinatesSolutionFileName = 'ANCFCable2Dbending' + str(nElements) + '.txt'
fact = 10000
simulationSettings.timeIntegration.numberOfSteps = 1*fact
simulationSettings.timeIntegration.endTime = 0.001*fact
simulationSettings.solutionSettings.writeSolutionToFile = True
simulationSettings.solutionSettings.solutionWritePeriod = simulationSettings.timeIntegration.endTime/fact
#simulationSettings.solutionSettings.outputPrecision = 4
simulationSettings.displayComputationTime = True
simulationSettings.timeIntegration.verboseMode = 1
simulationSettings.timeIntegration.newton.relativeTolerance = 1e-8*10 #10000
simulationSettings.timeIntegration.newton.absoluteTolerance = 1e-10*100
simulationSettings.timeIntegration.newton.useModifiedNewton = False
simulationSettings.timeIntegration.newton.maxModifiedNewtonIterations = 5
simulationSettings.timeIntegration.newton.numericalDifferentiation.minimumCoordinateSize = 1
simulationSettings.timeIntegration.newton.numericalDifferentiation.relativeEpsilon = 6.055454452393343e-06*0.1 #eps^(1/3)
simulationSettings.timeIntegration.newton.modifiedNewtonContractivity = 1e8
simulationSettings.timeIntegration.generalizedAlpha.useIndex2Constraints = False
simulationSettings.timeIntegration.generalizedAlpha.useNewmark = False
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.6 #0.6 works well
simulationSettings.displayStatistics = True
#SC.visualizationSettings.nodes.showNumbers = True
SC.visualizationSettings.bodies.showNumbers = False
#SC.visualizationSettings.connectors.showNumbers = True
SC.visualizationSettings.nodes.defaultSize = 0.01
SC.visualizationSettings.markers.defaultSize = 0.01
SC.visualizationSettings.connectors.defaultSize = 0.01
SC.visualizationSettings.contact.contactPointsDefaultSize = 0.005
SC.visualizationSettings.connectors.showContact = 1
simulationSettings.solutionSettings.solutionInformation = "ANCF cable with imposed curvature or applied tip force/torque"
solveDynamic = False
if solveDynamic:
exu.StartRenderer()
mbs.SolveDynamic(simulationSettings)
SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!
else:
simulationSettings.staticSolver.newton.numericalDifferentiation.relativeEpsilon = 1e-10 #can be quite small; WHY?
simulationSettings.staticSolver.verboseMode = 2
simulationSettings.staticSolver.numberOfLoadSteps = 40
simulationSettings.staticSolver.newton.relativeTolerance = 1e-7 #10000
simulationSettings.staticSolver.newton.absoluteTolerance = 1e-10
simulationSettings.staticSolver.newton.maxIterations = 20 #50 for bending into circle
simulationSettings.staticSolver.discontinuous.iterationTolerance = 1e-3
simulationSettings.staticSolver.stabilizerODE2term = 2 #may only act on position degrees of freedom
exu.StartRenderer()
#mbs.WaitForUserToContinue()
mbs.SolveStatic(simulationSettings)
sol = mbs.systemData.GetODE2Coordinates()
n = len(sol)
print('tip displacement: x='+str(sol[n-4])+', y='+str(sol[n-3]))
SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!
# exu.InfoStat();