ANCFcantileverTest.py

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  1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  2# This is an EXUDYN example
  3#
  4# Details:  ANCF Cable2D cantilever test
  5#
  6# Model:    Cantilever beam with cable elements
  7#
  8# Author:   Johannes Gerstmayr
  9# Date:     2019-11-15
 10# Update:   2022-03-16: get to run static example again, compared to paper!
 11#
 12# 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.
 13#
 14# *clean example*
 15#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 16
 17## import exudyn and utilities
 18import exudyn as exu
 19from exudyn.utilities import *
 20
 21## create container and main system to work with
 22SC = exu.SystemContainer()
 23mbs = SC.AddSystem()
 24
 25
 26## create graphics background
 27rect = [-0.5,-2,2.5,0.5] #xmin,ymin,xmax,ymax
 28background = {'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
 29oGround=mbs.AddObject(ObjectGround(referencePosition= [0,0,0], visualization=VObjectGround(graphicsData= [background])))
 30
 31#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 32## define beam dimensions and tip load
 33L=2                    # length of ANCF element in m
 34E=2.07e11             # Young's modulus of ANCF element in N/m^2
 35rho=7800               # density of ANCF element in kg/m^3
 36b=0.1                  # width of rectangular ANCF element in m
 37h=0.1                  # height of rectangular ANCF element in m
 38A=b*h                  # cross sectional area of ANCF element in m^2
 39I=b*h**3/12            # second moment of area of ANCF element in m^4
 40f=3*E*I/L**2           # tip load applied to ANCF element in N
 41
 42print("load f="+str(f))
 43
 44#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 45## generate ANCFCable2D template containing beam parameters
 46cableTemplate = Cable2D(#physicsLength = L / nElements, #set in GenerateStraightLineANCFCable2D(...)
 47                        physicsMassPerLength = rho*A,
 48                        physicsBendingStiffness = E*I,
 49                        physicsAxialStiffness = E*A,
 50                        useReducedOrderIntegration = 0,
 51                        #nodeNumbers = [0, 0], #will be filled in GenerateStraightLineANCFCable2D(...)
 52                        )
 53
 54## define nodal positions of beam (3D vectors, while cable element is only 2D)
 55positionOfNode0 = [0, 0, 0] # starting point of line
 56positionOfNode1 = [L, 0, 0] # end point of line
 57
 58## number of cable elements for discretization
 59numberOfElements = 64
 60
 61## use utility function to create set of straight cable elements between two positions with options for constraints at supports
 62#alternative to mbs.AddObject(Cable2D(...)) with nodes:
 63ancf=GenerateStraightLineANCFCable2D(mbs,
 64                positionOfNode0, positionOfNode1,
 65                numberOfElements,
 66                cableTemplate, #this defines the beam element properties
 67                massProportionalLoad = [0,-9.81*0,0], #optionally add gravity
 68                fixedConstraintsNode0 = [1,1,0,1], #add constraints for pos and rot (r'_y)
 69                fixedConstraintsNode1 = [0,0,0,0])
 70
 71## add load vector on last node in y-direction
 72mANCFLast = mbs.AddMarker(MarkerNodePosition(nodeNumber=ancf[0][-1])) #ancf[0][-1] = last node
 73mbs.AddLoad(Force(markerNumber = mANCFLast, loadVector = [0, -f, 0])) #will be changed in load steps
 74
 75
 76#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 77## assemble system and create simulation settings
 78mbs.Assemble()
 79
 80simulationSettings = exu.SimulationSettings() #takes currently set values or default values
 81
 82tEnd = 0.1
 83h = 1e-4
 84simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
 85simulationSettings.timeIntegration.endTime = tEnd
 86simulationSettings.solutionSettings.writeSolutionToFile = True
 87simulationSettings.solutionSettings.solutionWritePeriod = simulationSettings.timeIntegration.endTime/1000
 88simulationSettings.displayComputationTime = False
 89simulationSettings.timeIntegration.verboseMode = 1
 90
 91simulationSettings.timeIntegration.newton.useModifiedNewton = True
 92
 93simulationSettings.displayStatistics = True
 94simulationSettings.displayComputationTime = True
 95
 96SC.visualizationSettings.nodes.defaultSize = 0.01
 97simulationSettings.solutionSettings.solutionInformation = "ANCF cantilever beam"
 98simulationSettings.linearSolverType = exu.LinearSolverType.EigenSparse
 99
100doDynamicSimulation = True #switch between static and dynamic simulation
101
102
103if doDynamicSimulation:
104    ## do dynamic simulation
105    exu.StartRenderer()
106    mbs.SolveDynamic(simulationSettings)
107    SC.WaitForRenderEngineStopFlag()
108    exu.StopRenderer() #safely close rendering window!
109    ##
110else:
111    ## perform static simulation with manual load stepping
112    simulationSettings.staticSolver.verboseMode = 0
113
114    simulationSettings.staticSolver.newton.relativeTolerance = 1e-8
115    simulationSettings.staticSolver.newton.absoluteTolerance = 1e-3 #1 for 256 elements; needs to be larger for larger number of load steps
116    #simulationSettings.staticSolver.numberOfLoadSteps = 1
117
118    nLoadSteps = 1;
119    for loadSteps in range(nLoadSteps):
120        nLoad = 0
121        loadValue = f**((loadSteps+1)/nLoadSteps) #geometric increment of loads
122        print('load='+str(loadValue))
123
124        mbs.SetLoadParameter(nLoad, 'loadVector', [0, -loadValue,0])
125        print('load vector=' + str(mbs.GetLoadParameter(nLoad, 'loadVector')) )
126
127        mbs.SolveStatic(simulationSettings, updateInitialValues=True)
128
129        sol = mbs.systemData.GetODE2Coordinates()
130
131        n = len(sol)
132        print('nEL=',numberOfElements, ', tip displacement: x='+str(sol[n-4])+', y='+str(sol[n-3]))
133        #MATLAB 1 element: x=0.3622447298905063, y=0.9941447587249748 = paper "on the correct ..."
134        #2022-03-16:
135        # nEL= 1 ,  tip displacement: x=-0.36224472989050654,y=-0.9941447587249747
136        # nEL= 2 ,  tip displacement: x=-0.4889263085609102, y=-1.1752228652637502
137        # nEL= 4 ,  tip displacement: x=-0.5074287154557922, y=-1.2055337025602493
138        # nEL= 8 ,  tip displacement: x=-0.5085092365729895, y=-1.207197756093103
139        # nEL= 16 , tip displacement: x=-0.5085365799149556, y=-1.207238895003594
140        # nEL= 32 , tip displacement: x=-0.508537277761696,  y=-1.2072398264650905
141        # nEL= 64 , tip displacement: x=-0.5085373030408489, y=-1.207239853404364
142        # nEL= 128, tip displacement: x=-0.5085373043168473, y=-1.2072398545511795
143        # nEL= 256, tip displacement: x=-0.5085373043916903, y=-1.207239854614031
144
145        #with second SolveStatic:
146        #nEL= 256 , tip displacement: x=-0.5085373043209366, y=-1.2072398545457574
147        #converged:                   x=-0.508537304326,     y=-1.207239854550
148
149        #here (OLD):
150        #1:  x=-0.36224472989050543, y=-0.994144758724973
151        #2:  x=-0.4889263083414858, y=-1.1752228650551666
152        #4:  x=-0.5074287151188892, y=-1.2055337022335404
153        #8:  x=-0.5085092364970802, y=-1.2071977560198281
154        #64: x=-0.5085373029700947, y=-1.2072398533360738
155        #256:x=-0.5085373043209689, y=-1.2072398545457785
156
157
158
159
160        #sol = mbs.systemData.GetODE2Coordinates(exu.ConfigurationType.Initial)
161        #print('initial values='+str(sol))