You can view and download this file on Github: flexiblePendulumANCF.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: simple flexible pendulum using 2D ANCF elements
#
# Author: Johannes Gerstmayr
# Date: 2022-06-28
#
# 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 sys
sys.exudynFast = True
import exudyn as exu
from exudyn.utilities import *
import numpy as np
#from math import sqrt, sin, cos
#%%++++++++++++++++++++++++++++++++++++++++
useGraphics = True
plotResults=False
tEnd = 3
h= 1e-4
SC = exu.SystemContainer()
mbs = SC.AddSystem()
gravity = 9.81
L=1. #length of ANCF element in m
rhoA=10 #beam + discrete masses
hBeam = 0.05
wBeam = 0.05
Abeam = hBeam*wBeam
Ibeam = wBeam*hBeam**3/12
Ebeam = 2.1e10
nu = 0.3
EA=Abeam*Ebeam
EI=Ibeam*Ebeam
nElements = 25
lElem = L/nElements
# #additional bending and axial damping
bendingDamping=0*0.1*EI # for ALE Element
axialDamping=0 # for ALE Element
#generate coordinate marker
#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
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#create one beam template
cable = Cable2D(#physicsLength=L,
physicsMassPerLength=rhoA,
physicsBendingStiffness=EI,
physicsAxialStiffness=EA,
physicsBendingDamping=bendingDamping,
physicsAxialDamping=axialDamping,
# physicsUseCouplingTerms = True,
useReducedOrderIntegration = 0, #faster
visualization=VCable2D(drawHeight=hBeam)
)
#alternative to mbs.AddObject(ALECable2D(...)) with nodes:
yOff = 0*0.5*hBeam
ancf=GenerateStraightLineANCFCable2D(mbs=mbs,
positionOfNode0=[0,yOff,0], positionOfNode1=[L,yOff,0],
numberOfElements=nElements,
cableTemplate=cable, #this defines the beam element properties
massProportionalLoad = [0,-gravity,0], #add larger gravity for larger deformation
fixedConstraintsNode0 = [1,1,0,0], #hinged
#fixedConstraintsNode1 = [0,0,0,0]) #free
)
ancfNodes = ancf[0]
ancfObjects = ancf[1]
oGround=mbs.AddObject(ObjectGround(referencePosition= [0,0,0],
visualization=VObjectGround(graphicsData=[GraphicsDataCheckerBoard(size=2)])))
#++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#sensorFileName = 'solution/beamTip.txt'
sTipNode = mbs.AddSensor(SensorNode(nodeNumber=ancfNodes[-1], storeInternal=True,
outputVariableType=exu.OutputVariableType.Position))
sPos = mbs.AddSensor(SensorBody(bodyNumber=ancfObjects[-1], storeInternal=True, localPosition=[lElem,0,0.],
outputVariableType=exu.OutputVariableType.Position))
sVel = mbs.AddSensor(SensorBody(bodyNumber=ancfObjects[-1], storeInternal=True, localPosition=[lElem,0,0.],
outputVariableType=exu.OutputVariableType.Velocity))
mbs.Assemble()
simulationSettings = exu.SimulationSettings() #takes currently set values or default values
simulationSettings.parallel.numberOfThreads = 4 #4 is optimal for 25 elements
simulationSettings.solutionSettings.writeSolutionToFile = False
simulationSettings.solutionSettings.sensorsWritePeriod = h*100
simulationSettings.timeIntegration.verboseMode = 1
simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
simulationSettings.timeIntegration.endTime = tEnd
simulationSettings.timeIntegration.newton.useModifiedNewton = True
simulationSettings.timeIntegration.newton.relativeTolerance = 1e-6
simulationSettings.timeIntegration.newton.absoluteTolerance = 1e-6
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.8
simulationSettings.timeIntegration.adaptiveStep = True #disable adaptive step reduction
simulationSettings.linearSolverType = exu.LinearSolverType.EigenSparse
simulationSettings.displayStatistics = True
SC.visualizationSettings.loads.show = False
SC.visualizationSettings.contour.outputVariable = exu.OutputVariableType.StrainLocal
#SC.visualizationSettings.contour.outputVariable = exu.OutputVariableType.CurvatureLocal
#SC.visualizationSettings.bodies.beams.axialTiling = 500
#SC.visualizationSettings.bodies.beams.crossSectionTiling = 8
if useGraphics:
exu.StartRenderer()
mbs.WaitForUserToContinue()
success = mbs.SolveDynamic(simulationSettings,
exudyn.DynamicSolverType.TrapezoidalIndex2)
if useGraphics:
SC.WaitForRenderEngineStopFlag()
#SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!
#%%++++++++++++++++++
if True:
import matplotlib.pyplot as plt
from exudyn.signalProcessing import FilterSensorOutput
mbs.PlotSensor(sensorNumbers=[sPos,sPos], components=[0,1],
title='ang vel', closeAll=True,
markerStyles=['','x ','o '], lineStyles=['-','',''])