You can view and download this file on Github: NGsolveCMStutorial.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: Test for Hurty-Craig-Bampton modes using a simple flexible pendulum meshed with Netgen
#
# Author: Johannes Gerstmayr
# Date: 2021-04-20
#
# 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 *
from exudyn.utilities import *
from exudyn.FEM import *
from exudyn.graphicsDataUtilities import *
SC = exu.SystemContainer()
mbs = SC.AddSystem()
import numpy as np
import time
#import timeit
import exudyn.basicUtilities as eb
import exudyn.rigidBodyUtilities as rb
import exudyn.utilities as eu
useGraphics = True
fileName = 'testData/netgenHinge' #for load/save of FEM data
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
#netgen/meshing part:
fem = FEMinterface()
#geometrical parameters:
L = 0.4 #Length of plate (X)
w = 0.04 #width of plate (Y)
h = 0.02 #height of plate (Z)
d = 0.03 #diameter of bolt
D = d*2 #diameter of bushing
b = 0.05 #length of bolt
nModes = 8
meshH = 0.01 #0.01 is default, 0.002 gives 100000 nodes and is fairly converged;
#meshH = 0.0014 #203443 nodes, takes 1540 seconds for eigenmode computation (free-free) and 753 seconds for postprocessing on i9
#steel:
rho = 7850
Emodulus=2.1e11
nu=0.3
#test high flexibility
Emodulus=2e8
# nModes = 32
#helper function for cylinder with netgen
def CSGcylinder(p0,p1,r):
v = VSub(p1,p0)
v = Normalize(v)
cyl = Cylinder(Pnt(p0[0],p0[1],p0[2]), Pnt(p1[0],p1[1],p1[2]),
r) * Plane(Pnt(p0[0],p0[1],p0[2]), Vec(-v[0],-v[1],-v[2])) * Plane(Pnt(p1[0],p1[1],p1[2]), Vec(v[0],v[1],v[2]))
return cyl
meshCreated = False
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
if True: #needs netgen/ngsolve to be installed to compute mesh, see e.g.: https://github.com/NGSolve/ngsolve/releases
import ngsolve as ngs
import netgen
from netgen.meshing import *
from netgen.geom2d import unit_square
#import netgen.libngpy as libng
from netgen.csg import *
geo = CSGeometry()
#plate
block = OrthoBrick(Pnt(0, 0, -0.5*h),Pnt(L, w, 0.5*h))
#bolt
bolt0 = CSGcylinder(p0=[0,w,0], p1=[0,0,0], r=1.6*h)
bolt = CSGcylinder(p0=[0,0.5*w,0], p1=[0,-b,0], r=0.5*d)
#bushing
bushing = (CSGcylinder(p0=[L,w,0], p1=[L,-b,0], r=0.5*D) -
CSGcylinder(p0=[L,0,0], p1=[L,-b*1.1,0], r=0.5*d))
geo.Add(block+bolt0+bolt+bushing)
curvaturesafety = 5
if meshH==0.04:
curvaturesafety = 1.2#this case is for creating very small files ...
mesh = ngs.Mesh( geo.GenerateMesh(maxh=meshH, curvaturesafety=curvaturesafety))
mesh.Curve(1)
if False: #set this to true, if you want to visualize the mesh inside netgen/ngsolve
# import netgen
import netgen.gui
ngs.Draw(mesh)
for i in range(10000000):
netgen.Redraw() #this makes the netgen window interactive
time.sleep(0.05)
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
#Use fem to import FEM model and create FFRFreducedOrder object
[bfM, bfK, fes] = fem.ImportMeshFromNGsolve(mesh, density=rho, youngsModulus=Emodulus, poissonsRatio=nu)
meshCreated = True
if (meshH==0.04):
print('save file')
fem.SaveToFile(fileName)
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
#compute Hurty-Craig-Bampton modes
if True: #now import mesh as mechanical model to EXUDYN
if not meshCreated: fem.LoadFromFile(fileName)
boltP1=[0,0,0]
boltP2=[0,-b,0]
nodesOnBolt = fem.GetNodesOnCylinder(boltP1, boltP2, radius=0.5*d)
#print("boundary nodes bolt=", nodesOnBolt)
nodesOnBoltLen = len(nodesOnBolt)
nodesOnBoltWeights = np.array((1./nodesOnBoltLen)*np.ones(nodesOnBoltLen))
bushingP1=[L,0,0]
bushingP2=[L,-b,0]
nodesOnBushing = fem.GetNodesOnCylinder(bushingP1, bushingP2, radius=0.5*d)
#print("boundary nodes bushing=", nodesOnBushing)
nodesOnBushingLen = len(nodesOnBushing)
nodesOnBushingWeights = np.array((1./nodesOnBushingLen)*np.ones(nodesOnBushingLen))
print("nNodes=",fem.NumberOfNodes())
strMode = ''
if True: #pure eigenmodes
print("compute eigen modes... ")
start_time = time.time()
if False: #faster but not so accurate
fem.ComputeEigenmodesNGsolve(bfM, bfK, nModes, excludeRigidBodyModes = 6)
else:
fem.ComputeEigenmodes(nModes, excludeRigidBodyModes = 6, useSparseSolver = True)
print("eigen modes computation needed %.3f seconds" % (time.time() - start_time))
print("eigen freq.=", fem.GetEigenFrequenciesHz())
else:
strMode = 'HCB'
#boundaryList = [nodesOnBolt, nodesOnBolt, nodesOnBushing] #for visualization, use first interface twice
boundaryList = [nodesOnBolt, nodesOnBushing]
print("compute HCB modes... ")
start_time = time.time()
fem.ComputeHurtyCraigBamptonModes(boundaryNodesList=boundaryList,
nEigenModes=nModes,
useSparseSolver=True,
computationMode = HCBstaticModeSelection.RBE2)
print("eigen freq.=", fem.GetEigenFrequenciesHz())
print("HCB modes needed %.3f seconds" % (time.time() - start_time))
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
#compute stress modes for postprocessing (inaccurate for coarse meshes, just for visualization):
if True:
mat = KirchhoffMaterial(Emodulus, nu, rho)
varType = exu.OutputVariableType.StressLocal
#varType = exu.OutputVariableType.StrainLocal
print("ComputePostProcessingModes ... (may take a while)")
start_time = time.time()
#without NGsolve:
if True: #faster with ngsolve
fem.ComputePostProcessingModesNGsolve(fes, material=mat,
outputVariableType=varType)
else:
fem.ComputePostProcessingModes(material=mat,
outputVariableType=varType)
print(" ... needed %.3f seconds" % (time.time() - start_time))
SC.visualizationSettings.contour.reduceRange=True
SC.visualizationSettings.contour.outputVariable = varType
SC.visualizationSettings.contour.outputVariableComponent = 0 #x-component
else:
varType = exu.OutputVariableType.DisplacementLocal
SC.visualizationSettings.contour.outputVariable = exu.OutputVariableType.DisplacementLocal
SC.visualizationSettings.contour.outputVariableComponent = 0
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
print("create CMS element ...")
cms = ObjectFFRFreducedOrderInterface(fem)
objFFRF = cms.AddObjectFFRFreducedOrder(mbs, positionRef=[0,0,0],
initialVelocity=[0,0,0],
initialAngularVelocity=[0,0,0],
color=[0.9,0.9,0.9,1.],
)
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
#add markers and joints
nodeDrawSize = 0.0025 #for joint drawing
#mRB = mbs.AddMarker(MarkerNodeRigid(nodeNumber=objFFRF['nRigidBody']))
if True:
boltMidPoint = 0.5*(np.array(boltP1)+boltP2)
oGround = mbs.AddObject(ObjectGround(referencePosition= [0,0,0]))
altApproach = True
mBolt = mbs.AddMarker(MarkerSuperElementRigid(bodyNumber=objFFRF['oFFRFreducedOrder'],
meshNodeNumbers=np.array(nodesOnBolt), #these are the meshNodeNumbers
#referencePosition=boltMidPoint,
useAlternativeApproach=altApproach,
weightingFactors=nodesOnBoltWeights))
bushingMidPoint = 0.5*(np.array(bushingP1)+bushingP2)
#add marker for visualization of boundary nodes
mBushing = mbs.AddMarker(MarkerSuperElementRigid(bodyNumber=objFFRF['oFFRFreducedOrder'],
meshNodeNumbers=np.array(nodesOnBushing), #these are the meshNodeNumbers
#referencePosition=bushingMidPoint,
useAlternativeApproach=altApproach,
weightingFactors=nodesOnBushingWeights))
lockedAxes=[1,1,1,1,1*0,1]
if True:
mGroundBolt = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround,
localPosition=boltMidPoint,
visualization=VMarkerBodyRigid(show=True)))
mbs.AddObject(GenericJoint(markerNumbers=[mGroundBolt, mBolt],
constrainedAxes = lockedAxes,
visualization=VGenericJoint(show=False, axesRadius=0.1*b, axesLength=0.1*b)))
else:
mGroundBushing = mbs.AddMarker(MarkerBodyRigid(bodyNumber=oGround, localPosition=bushingMidPoint))
mbs.AddObject(GenericJoint(markerNumbers=[mGroundBushing, mBushing],
constrainedAxes = lockedAxes,
visualization=VGenericJoint(axesRadius=0.1*b, axesLength=0.1*b)))
if False:
cms = ObjectFFRFreducedOrderInterface(fem)
objFFRF = cms.AddObjectFFRFreducedOrder(mbs, positionRef=[0,0,0],
initialVelocity=[0,0,0],
initialAngularVelocity=[0,0,0],
color=[0.9,0.9,0.9,1.],
)
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
#animate modes
SC.visualizationSettings.markers.show = True
SC.visualizationSettings.markers.defaultSize=0.0075
SC.visualizationSettings.markers.drawSimplified = False
SC.visualizationSettings.loads.show = False
SC.visualizationSettings.loads.drawSimplified = False
SC.visualizationSettings.loads.defaultSize=0.1
SC.visualizationSettings.loads.defaultRadius = 0.002
SC.visualizationSettings.openGL.multiSampling=4
SC.visualizationSettings.openGL.lineWidth=2
if False: #activate to animate modes
from exudyn.interactive import AnimateModes
mbs.Assemble()
SC.visualizationSettings.nodes.show = False
SC.visualizationSettings.openGL.showFaceEdges = True
SC.visualizationSettings.openGL.multiSampling=4
SC.visualizationSettings.openGL.lineWidth=2
SC.visualizationSettings.window.renderWindowSize = [1600,1080]
SC.visualizationSettings.contour.showColorBar = False
SC.visualizationSettings.general.textSize = 16
#%%+++++++++++++++++++++++++++++++++++++++
#animate modes of ObjectFFRFreducedOrder (only needs generic node containing modal coordinates)
SC.visualizationSettings.general.autoFitScene = False #otherwise, model may be difficult to be moved
nodeNumber = objFFRF['nGenericODE2'] #this is the node with the generalized coordinates
AnimateModes(SC, mbs, nodeNumber, period=0.1, showTime=False, renderWindowText='Hurty-Craig-Bampton: 2 x 6 static modes and 8 eigenmodes\n',
runOnStart=True)
# import sys
# sys.exit()
#add gravity (not necessary if user functions used)
oFFRF = objFFRF['oFFRFreducedOrder']
mBody = mbs.AddMarker(MarkerBodyMass(bodyNumber=oFFRF))
mbs.AddLoad(LoadMassProportional(markerNumber=mBody, loadVector= [0,0,-9.81]))
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++
fileDir = 'solution/'
# sensBolt = mbs.AddSensor(SensorMarker(markerNumber=mBolt,
# fileName=fileDir+'hingePartBoltPos'+str(nModes)+strMode+'.txt',
# outputVariableType = exu.OutputVariableType.Position))
# sensBushing= mbs.AddSensor(SensorMarker(markerNumber=mBushing,
# fileName=fileDir+'hingePartBushingPos'+str(nModes)+strMode+'.txt',
# outputVariableType = exu.OutputVariableType.Position))
sensBushingVel= mbs.AddSensor(SensorMarker(markerNumber=mBushing,
fileName=fileDir+'hingePartBushingVel'+str(nModes)+strMode+'.txt',
outputVariableType = exu.OutputVariableType.Velocity))
sensBushing= mbs.AddSensor(SensorMarker(markerNumber=mBushing,
fileName=fileDir+'hingePartBushing'+str(nModes)+strMode+'.txt',
outputVariableType = exu.OutputVariableType.Position))
mbs.Assemble()
simulationSettings = exu.SimulationSettings()
SC.visualizationSettings.nodes.defaultSize = nodeDrawSize
SC.visualizationSettings.nodes.drawNodesAsPoint = False
SC.visualizationSettings.connectors.defaultSize = 2*nodeDrawSize
SC.visualizationSettings.nodes.show = False
SC.visualizationSettings.nodes.showBasis = True #of rigid body node of reference frame
SC.visualizationSettings.nodes.basisSize = 0.12
SC.visualizationSettings.bodies.deformationScaleFactor = 1 #use this factor to scale the deformation of modes
SC.visualizationSettings.openGL.showFaceEdges = True
SC.visualizationSettings.openGL.showFaces = True
SC.visualizationSettings.sensors.show = True
SC.visualizationSettings.sensors.drawSimplified = False
SC.visualizationSettings.sensors.defaultSize = 0.01
simulationSettings.solutionSettings.solutionInformation = "CMStutorial "+str(nModes)+" "+strMode+"modes"
h=0.25e-3*4
tEnd = 0.25*8
simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
simulationSettings.timeIntegration.endTime = tEnd
simulationSettings.solutionSettings.writeSolutionToFile = True
simulationSettings.timeIntegration.verboseMode = 1
#simulationSettings.timeIntegration.verboseModeFile = 3
simulationSettings.timeIntegration.newton.useModifiedNewton = True
simulationSettings.solutionSettings.sensorsWritePeriod = h
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.8
#simulationSettings.displayStatistics = True
simulationSettings.displayComputationTime = True
#create animation:
# simulationSettings.solutionSettings.recordImagesInterval = 0.005
# SC.visualizationSettings.exportImages.saveImageFileName = "animation/frame"
SC.visualizationSettings.window.renderWindowSize=[1920,1080]
SC.visualizationSettings.openGL.multiSampling = 4
useGraphics=True
if True:
if useGraphics:
SC.visualizationSettings.general.autoFitScene=False
exu.StartRenderer()
if 'renderState' in exu.sys: SC.SetRenderState(exu.sys['renderState']) #load last model view
mbs.WaitForUserToContinue() #press space to continue
#SC.RedrawAndSaveImage()
if True:
# mbs.SolveDynamic(solverType=exu.DynamicSolverType.TrapezoidalIndex2,
# simulationSettings=simulationSettings)
mbs.SolveDynamic(simulationSettings=simulationSettings)
else:
mbs.SolveStatic(simulationSettings=simulationSettings)
# uTip = mbs.GetSensorValues(sensTipDispl)[1]
# print("nModes=", nModes, ", tip displacement=", uTip)
if varType == exu.OutputVariableType.StressLocal:
mises = CMSObjectComputeNorm(mbs, 0, exu.OutputVariableType.StressLocal, 'Mises')
print('max von-Mises stress=',mises)
if useGraphics:
SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!
if False:
mbs.PlotSensor(sensorNumbers=[sensBushingVel], components=[1])
#%%
if False:
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
import exudyn as exu
from exudyn.utilities import *
CC = PlotLineCode
comp = 1 #1=x, 2=y, ...
var = ''
# data = np.loadtxt('solution/hingePartBushing'+var+'2.txt', comments='#', delimiter=',')
# plt.plot(data[:,0], data[:,comp], CC(7), label='2 eigenmodes')
# data = np.loadtxt('solution/hingePartBushing'+var+'4.txt', comments='#', delimiter=',')
# plt.plot(data[:,0], data[:,comp], CC(8), label='4 eigenmodes')
data = np.loadtxt('solution/hingePartBushing'+var+'8.txt', comments='#', delimiter=',')
plt.plot(data[:,0], data[:,comp], CC(9), label='8 eigenmodes')
data = np.loadtxt('solution/hingePartBushing'+var+'16.txt', comments='#', delimiter=',')
plt.plot(data[:,0], data[:,comp], CC(10), label='16 eigenmodes')
data = np.loadtxt('solution/hingePartBushing'+var+'32.txt', comments='#', delimiter=',')
plt.plot(data[:,0], data[:,comp], CC(11), label='32 eigenmodes')
data = np.loadtxt('solution/hingePartBushing'+var+'2HCB.txt', comments='#', delimiter=',')
plt.plot(data[:,0], data[:,comp], CC(1), label='HCB + 2 eigenmodes')
data = np.loadtxt('solution/hingePartBushing'+var+'4HCB.txt', comments='#', delimiter=',')
plt.plot(data[:,0], data[:,comp], CC(2), label='HCB + 4 eigenmodes')
data = np.loadtxt('solution/hingePartBushing'+var+'8HCB.txt', comments='#', delimiter=',')
plt.plot(data[:,0], data[:,comp], CC(3), label='HCB + 8 eigenmodes')
data = np.loadtxt('solution/hingePartBushing'+var+'16HCB.txt', comments='#', delimiter=',')
plt.plot(data[:,0], data[:,comp], CC(4), label='HCB + 16 eigenmodes')
data = np.loadtxt('solution/hingePartBushing'+var+'32HCB.txt', comments='#', delimiter=',')
plt.plot(data[:,0], data[:,comp], CC(5), label='HCB + 32 eigenmodes')
data = np.loadtxt('solution/hingePartBushing'+var+'64HCB.txt', comments='#', delimiter=',')
plt.plot(data[:,0], data[:,comp], CC(6), label='HCB + 64 eigenmodes')
data = np.loadtxt('solution/hingePartBushing'+var+'128HCB.txt', comments='#', delimiter=',')
plt.plot(data[:,0], data[:,comp], CC(7), label='HCB + 128 eigenmodes')
ax=plt.gca() # get current axes
ax.grid(True, 'major', 'both')
ax.xaxis.set_major_locator(ticker.MaxNLocator(10))
ax.yaxis.set_major_locator(ticker.MaxNLocator(10))
#
plt.xlabel("time (s)")
plt.ylabel("y-component of tip velocity of hinge (m)")
plt.legend() #show labels as legend
plt.tight_layout()
plt.show()