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 * #includes itemInterface and rigidBodyUtilities
20import exudyn.graphics as graphics #only import if it does not conflict
21
22## create container and main system to work with
23SC = exu.SystemContainer()
24mbs = SC.AddSystem()
25
26
27## create graphics background
28rect = [-0.5,-2,2.5,0.5] #xmin,ymin,xmax,ymax
29background = {'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
30oGround=mbs.AddObject(ObjectGround(referencePosition= [0,0,0], visualization=VObjectGround(graphicsData= [background])))
31
32#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
33## define beam dimensions and tip load
34L=2 # length of ANCF element in m
35E=2.07e11 # Young's modulus of ANCF element in N/m^2
36rho=7800 # density of ANCF element in kg/m^3
37b=0.1 # width of rectangular ANCF element in m
38h=0.1 # height of rectangular ANCF element in m
39A=b*h # cross sectional area of ANCF element in m^2
40I=b*h**3/12 # second moment of area of ANCF element in m^4
41f=3*E*I/L**2 # tip load applied to ANCF element in N
42
43print("load f="+str(f))
44
45#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
46## generate ANCFCable2D template containing beam parameters
47cableTemplate = Cable2D(#physicsLength = L / nElements, #set in GenerateStraightLineANCFCable2D(...)
48 physicsMassPerLength = rho*A,
49 physicsBendingStiffness = E*I,
50 physicsAxialStiffness = E*A,
51 useReducedOrderIntegration = 0,
52 #nodeNumbers = [0, 0], #will be filled in GenerateStraightLineANCFCable2D(...)
53 )
54
55## define nodal positions of beam (3D vectors, while cable element is only 2D)
56positionOfNode0 = [0, 0, 0] # starting point of line
57positionOfNode1 = [L, 0, 0] # end point of line
58
59## number of cable elements for discretization
60numberOfElements = 64
61
62## use utility function to create set of straight cable elements between two positions with options for constraints at supports
63#alternative to mbs.AddObject(Cable2D(...)) with nodes:
64ancf=GenerateStraightLineANCFCable2D(mbs,
65 positionOfNode0, positionOfNode1,
66 numberOfElements,
67 cableTemplate, #this defines the beam element properties
68 massProportionalLoad = [0,-9.81*0,0], #optionally add gravity
69 fixedConstraintsNode0 = [1,1,0,1], #add constraints for pos and rot (r'_y)
70 fixedConstraintsNode1 = [0,0,0,0])
71
72## add load vector on last node in y-direction
73mANCFLast = mbs.AddMarker(MarkerNodePosition(nodeNumber=ancf[0][-1])) #ancf[0][-1] = last node
74mbs.AddLoad(Force(markerNumber = mANCFLast, loadVector = [0, -f, 0])) #will be changed in load steps
75
76
77#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
78## assemble system and create simulation settings
79mbs.Assemble()
80
81simulationSettings = exu.SimulationSettings() #takes currently set values or default values
82
83tEnd = 0.1
84h = 1e-4
85simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
86simulationSettings.timeIntegration.endTime = tEnd
87simulationSettings.solutionSettings.writeSolutionToFile = True
88simulationSettings.solutionSettings.solutionWritePeriod = simulationSettings.timeIntegration.endTime/1000
89simulationSettings.displayComputationTime = False
90simulationSettings.timeIntegration.verboseMode = 1
91
92simulationSettings.timeIntegration.newton.useModifiedNewton = True
93
94simulationSettings.displayStatistics = True
95simulationSettings.displayComputationTime = True
96
97SC.visualizationSettings.nodes.defaultSize = 0.01
98simulationSettings.solutionSettings.solutionInformation = "ANCF cantilever beam"
99simulationSettings.linearSolverType = exu.LinearSolverType.EigenSparse
100
101doDynamicSimulation = True #switch between static and dynamic simulation
102
103
104if doDynamicSimulation:
105 ## do dynamic simulation
106 exu.StartRenderer()
107 mbs.SolveDynamic(simulationSettings)
108 SC.WaitForRenderEngineStopFlag()
109 exu.StopRenderer() #safely close rendering window!
110 ##
111else:
112 ## perform static simulation with manual load stepping
113 simulationSettings.staticSolver.verboseMode = 0
114
115 simulationSettings.staticSolver.newton.relativeTolerance = 1e-8
116 simulationSettings.staticSolver.newton.absoluteTolerance = 1e-3 #1 for 256 elements; needs to be larger for larger number of load steps
117 #simulationSettings.staticSolver.numberOfLoadSteps = 1
118
119 nLoadSteps = 1;
120 for loadSteps in range(nLoadSteps):
121 nLoad = 0
122 loadValue = f**((loadSteps+1)/nLoadSteps) #geometric increment of loads
123 print('load='+str(loadValue))
124
125 mbs.SetLoadParameter(nLoad, 'loadVector', [0, -loadValue,0])
126 print('load vector=' + str(mbs.GetLoadParameter(nLoad, 'loadVector')) )
127
128 mbs.SolveStatic(simulationSettings, updateInitialValues=True)
129
130 sol = mbs.systemData.GetODE2Coordinates()
131
132 n = len(sol)
133 print('nEL=',numberOfElements, ', tip displacement: x='+str(sol[n-4])+', y='+str(sol[n-3]))
134 #MATLAB 1 element: x=0.3622447298905063, y=0.9941447587249748 = paper "on the correct ..."
135 #2022-03-16:
136 # nEL= 1 , tip displacement: x=-0.36224472989050654,y=-0.9941447587249747
137 # nEL= 2 , tip displacement: x=-0.4889263085609102, y=-1.1752228652637502
138 # nEL= 4 , tip displacement: x=-0.5074287154557922, y=-1.2055337025602493
139 # nEL= 8 , tip displacement: x=-0.5085092365729895, y=-1.207197756093103
140 # nEL= 16 , tip displacement: x=-0.5085365799149556, y=-1.207238895003594
141 # nEL= 32 , tip displacement: x=-0.508537277761696, y=-1.2072398264650905
142 # nEL= 64 , tip displacement: x=-0.5085373030408489, y=-1.207239853404364
143 # nEL= 128, tip displacement: x=-0.5085373043168473, y=-1.2072398545511795
144 # nEL= 256, tip displacement: x=-0.5085373043916903, y=-1.207239854614031
145
146 #with second SolveStatic:
147 #nEL= 256 , tip displacement: x=-0.5085373043209366, y=-1.2072398545457574
148 #converged: x=-0.508537304326, y=-1.207239854550
149
150 #here (OLD):
151 #1: x=-0.36224472989050543, y=-0.994144758724973
152 #2: x=-0.4889263083414858, y=-1.1752228650551666
153 #4: x=-0.5074287151188892, y=-1.2055337022335404
154 #8: x=-0.5085092364970802, y=-1.2071977560198281
155 #64: x=-0.5085373029700947, y=-1.2072398533360738
156 #256:x=-0.5085373043209689, y=-1.2072398545457785
157
158
159
160
161 #sol = mbs.systemData.GetODE2Coordinates(exu.ConfigurationType.Initial)
162 #print('initial values='+str(sol))