You can view and download this file on Github: manualExplicitIntegrator.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: ANCF Cable2D cantilever bent with manual explicit integrator
#
# Author: Johannes Gerstmayr
# Date: 2020-01-08
#
# 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 *
useGraphics = True #without test
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel:
try: #only if called from test suite
from modelUnitTests import exudynTestGlobals #for globally storing test results
useGraphics = exudynTestGlobals.useGraphics
except:
class ExudynTestGlobals:
pass
exudynTestGlobals = ExudynTestGlobals()
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
SC = exu.SystemContainer()
mbs = SC.AddSystem()
exu.Print("\n\n++++++++++++++++++++++++++\nStart EXUDYN version "+exu.GetVersionString()+"\n")
#background
rect = [-2,-2,2,2] #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':'Circle', 'radius': 0.1, 'position': [-1.5,0,0]}
background2 = {'type':'Text', 'position': [-1,-1,0], 'text':'Example with text\nin two lines:.=!'} #background
oGround=mbs.AddObject(ObjectGround(referencePosition= [0,0,0], visualization=VObjectGround(graphicsData= [background0, background1, background2])))
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#cable:
mypi = 3.141592653589793
L=2. # length of ANCF element in m
#L=mypi # length of ANCF element in m
E=2.07e11*1e-5 # Young's modulus of ANCF element in N/m^2
rho=7800 # density of ANCF element in kg/m^3
b=0.1 # width of rectangular ANCF element in m
h=0.1 # 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
exu.Print("load f="+str(f))
exu.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=[]
nc0 = mbs.AddNode(Point2DS1(referenceCoordinates=[0,0,1,0]))
nElements = 4 #for tests use nElements = 4
lElem = L / nElements
nLast = 0
for i in range(nElements):
nLast = mbs.AddNode(Point2DS1(referenceCoordinates=[lElem*(i+1),0,1,0]))
elem=mbs.AddObject(Cable2D(physicsLength=lElem, physicsMassPerLength=rho*A,
physicsBendingStiffness=E*I, physicsAxialStiffness=E*A*0.1,
nodeNumbers=[int(nc0)+i,int(nc0)+i+1], useReducedOrderIntegration=True))
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]))
mANCFLast = mbs.AddMarker(MarkerNodePosition(nodeNumber=nLast)) #force
mbs.AddLoad(Force(markerNumber = mANCFLast, loadVector = [0, -1000, 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*0.25*mypi]))
#mANCFnode = mbs.AddMarker(MarkerNodeRigid(nodeNumber=nLast)) #local position L = beam tip
#mbs.AddLoad(Torque(markerNumber = mANCFnode, loadVector = [0, 0, 0.4*E*I*0.25*mypi]))
#mbs.AddLoad(Force(markerNumber = mANCFnode, loadVector = [0, 0.4*E*I*0.25*mypi,0]))
mbs.Assemble()
#exu.Print(mbs)
simulationSettings = exu.SimulationSettings() #takes currently set values or default values
#SC.visualizationSettings.bodies.showNumbers = False
SC.visualizationSettings.nodes.defaultSize = 0.025
dSize=0.01
SC.visualizationSettings.bodies.defaultSize = [dSize, dSize, dSize]
#simulationSettings.staticSolver.newton.numericalDifferentiation.relativeEpsilon = 1e-9
simulationSettings.staticSolver.verboseMode = 1
simulationSettings.staticSolver.verboseModeFile = 2
simulationSettings.solutionSettings.solverInformationFileName = 'solution/solverInformation.txt'
#simulationSettings.staticSolver.newton.absoluteTolerance = 1e-8
simulationSettings.staticSolver.newton.relativeTolerance = 1e-6 #1e-5 works for 64 elements
simulationSettings.staticSolver.newton.maxIterations = 20 #50 for bending into circle
if useGraphics: #only start graphics once, but after background is set
exu.StartRenderer()
simulationSettings.staticSolver.numberOfLoadSteps = 10
simulationSettings.staticSolver.adaptiveStep = True
import numpy as np
testRefVal = 0
#compute eigenvalues manually:
calcEig = True
if calcEig:
from scipy.linalg import solve, eigh, eig #eigh for symmetric matrices, positive definite
staticSolver = exu.MainSolverStatic()
#staticSolver.SolveSystem(mbs, simulationSettings)
staticSolver.InitializeSolver(mbs, simulationSettings)
staticSolver.ComputeMassMatrix(mbs)
m = staticSolver.GetSystemMassMatrix()
#exu.Print("m =",m)
staticSolver.ComputeJacobianODE2RHS(mbs, scalarFactor_ODE2=-1, scalarFactor_ODE2_t=0)
staticSolver.ComputeJacobianAE(mbs)
K = staticSolver.GetSystemJacobian()
#exu.Print("K =",K)
nODE2 = staticSolver.GetODE2size()
K2 = K[0:nODE2,0:nODE2]
[eigvals, eigvecs] = eigh(K2, m) #this gives omega^2 ... squared eigen frequencies (rad/s)
ev = np.sort(a=abs(eigvals))
#exu.Print("ev =",ev)
if (len(ev) >= 7):
f6 = np.sqrt(abs(ev[6]))/(2*np.pi)
exu.Print("ev=", f6)
testRefVal += f6 #first bending eigenmode
staticSolver.FinalizeSolver(mbs, simulationSettings)
#++++++++++++++++++++++++++++++++++++++++++++++++++
#TEST
def UserFunctionInitializeStep(mainSolver, mainSys, sims):
#exu.Print("t=", mainSolver.it.currentTime)
mainSolver.UpdateCurrentTime(mainSys, sims)
mainSys.systemData.SetTime(mainSolver.it.currentTime);
return True
#test for explicit integrator:
def UserFunctionNewton(mainSolver, mainSys, sims):
nODE2 = mainSolver.GetODE2size()
nAE = mainSolver.GetAEsize()
#nSys = nODE2+nAE
#print("u=", mainSys.systemData.GetODE2Coordinates())
dynamicSolver.ComputeODE2RHS(mbs)
res = dynamicSolver.GetSystemResidual()
Fode2 = res[0:nODE2]
#print("res=", Fode2)
dynamicSolver.ComputeMassMatrix(mbs)
M = dynamicSolver.GetSystemMassMatrix()
a = np.linalg.solve(M,Fode2) #acceleration
h = dynamicSolver.it.currentStepSize
u0 = mainSys.systemData.GetODE2Coordinates()
v0 = mainSys.systemData.GetODE2Coordinates_t()
mainSys.systemData.SetODE2Coordinates(u0+h*v0)
mainSys.systemData.SetODE2Coordinates_t(v0+h*a)
return True
dynamicSolver = exu.MainSolverImplicitSecondOrder()
simulationSettings.timeIntegration.numberOfSteps = 5000 #1000 steps for test suite/error
simulationSettings.timeIntegration.endTime = 0.05 #1s for test suite / error
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.5
#simulationSettings.displayComputationTime = True
simulationSettings.timeIntegration.verboseMode = 1
#dynamicSolver.SetUserFunctionInitializeStep(mbs, UserFunctionInitializeStep)
dynamicSolver.SetUserFunctionNewton(mbs, UserFunctionNewton)
dynamicSolver.SolveSystem(mbs, simulationSettings)
#mbs.SolveDynamic(simulationSettings)
uy=mbs.GetNodeOutput(nLast,exu.OutputVariableType.Position)[1] #y-coordinate of tip
exu.Print("uy=", uy)
exu.Print("testResult=", testRefVal + uy)
exudynTestGlobals.testError = testRefVal + uy - (2.280183538481952-0.2204849087896498) #2020-01-16: 2.280183538481952-0.2204849087896498
exudynTestGlobals.testResult = testRefVal + uy
if useGraphics: #only start graphics once, but after background is set
SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!