.. _examples-ngsolvecmstutorial: ********************* NGsolveCMStutorial.py ********************* You can view and download this file on Github: `NGsolveCMStutorial.py `_ .. code-block:: python :linenos: #+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ # 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 # Update: 2024-05-14: add node weighting and add some fixes # # 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 import exudyn.graphics as graphics #only import if it does not conflict from exudyn.FEM import * SC = exu.SystemContainer() mbs = SC.AddSystem() import numpy as np import time 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 = 2 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) nodesOnBoltWeights = fem.GetNodeWeightsFromSurfaceAreas(nodesOnBolt) bushingP1=[L,0,0] bushingP2=[L,-b,0] nodesOnBushing = fem.GetNodesOnCylinder(bushingP1, bushingP2, radius=0.5*d) #print("boundary nodes bushing=", nodesOnBushing) nodesOnBushingWeights = fem.GetNodeWeightsFromSurfaceAreas(nodesOnBushing) 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 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 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 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))) #%%+++++++++++++++++++++++++++++++++++++++++++++++++++++ #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=1e-3 tEnd = 2 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) 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 * #includes itemInterface and rigidBodyUtilities import exudyn.graphics as graphics #only import if it does not conflict 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()