You can view and download this file on Github: ANCFcantileverTest.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: ANCF Cable2D cantilever test
#
# Model: Cantilever beam with cable elements
#
# Author: Johannes Gerstmayr
# Date: 2019-11-15
# Update: 2022-03-16: get to run static example again, compared to paper!
#
# 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.
#
# *clean example*
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
## import exudyn and utilities
import exudyn as exu
from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities
import exudyn.graphics as graphics #only import if it does not conflict
## create container and main system to work with
SC = exu.SystemContainer()
mbs = SC.AddSystem()
## create graphics background
rect = [-0.5,-2,2.5,0.5] #xmin,ymin,xmax,ymax
background = {'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
oGround=mbs.AddObject(ObjectGround(referencePosition= [0,0,0], visualization=VObjectGround(graphicsData= [background])))
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
## define beam dimensions and tip load
L=2 # length of ANCF element in m
E=2.07e11 # 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
print("load f="+str(f))
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
## generate ANCFCable2D template containing beam parameters
cableTemplate = Cable2D(#physicsLength = L / nElements, #set in GenerateStraightLineANCFCable2D(...)
physicsMassPerLength = rho*A,
physicsBendingStiffness = E*I,
physicsAxialStiffness = E*A,
useReducedOrderIntegration = 0,
#nodeNumbers = [0, 0], #will be filled in GenerateStraightLineANCFCable2D(...)
)
## define nodal positions of beam (3D vectors, while cable element is only 2D)
positionOfNode0 = [0, 0, 0] # starting point of line
positionOfNode1 = [L, 0, 0] # end point of line
## number of cable elements for discretization
numberOfElements = 64
## use utility function to create set of straight cable elements between two positions with options for constraints at supports
#alternative to mbs.AddObject(Cable2D(...)) with nodes:
ancf=GenerateStraightLineANCFCable2D(mbs,
positionOfNode0, positionOfNode1,
numberOfElements,
cableTemplate, #this defines the beam element properties
massProportionalLoad = [0,-9.81*0,0], #optionally add gravity
fixedConstraintsNode0 = [1,1,0,1], #add constraints for pos and rot (r'_y)
fixedConstraintsNode1 = [0,0,0,0])
## add load vector on last node in y-direction
mANCFLast = mbs.AddMarker(MarkerNodePosition(nodeNumber=ancf[0][-1])) #ancf[0][-1] = last node
mbs.AddLoad(Force(markerNumber = mANCFLast, loadVector = [0, -f, 0])) #will be changed in load steps
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
## assemble system and create simulation settings
mbs.Assemble()
simulationSettings = exu.SimulationSettings() #takes currently set values or default values
tEnd = 0.1
h = 1e-4
simulationSettings.timeIntegration.numberOfSteps = int(tEnd/h)
simulationSettings.timeIntegration.endTime = tEnd
simulationSettings.solutionSettings.writeSolutionToFile = True
simulationSettings.solutionSettings.solutionWritePeriod = simulationSettings.timeIntegration.endTime/1000
simulationSettings.displayComputationTime = False
simulationSettings.timeIntegration.verboseMode = 1
simulationSettings.timeIntegration.newton.useModifiedNewton = True
simulationSettings.displayStatistics = True
simulationSettings.displayComputationTime = True
SC.visualizationSettings.nodes.defaultSize = 0.01
simulationSettings.solutionSettings.solutionInformation = "ANCF cantilever beam"
simulationSettings.linearSolverType = exu.LinearSolverType.EigenSparse
doDynamicSimulation = True #switch between static and dynamic simulation
if doDynamicSimulation:
## do dynamic simulation
exu.StartRenderer()
mbs.SolveDynamic(simulationSettings)
SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!
##
else:
## perform static simulation with manual load stepping
simulationSettings.staticSolver.verboseMode = 0
simulationSettings.staticSolver.newton.relativeTolerance = 1e-8
simulationSettings.staticSolver.newton.absoluteTolerance = 1e-3 #1 for 256 elements; needs to be larger for larger number of load steps
#simulationSettings.staticSolver.numberOfLoadSteps = 1
nLoadSteps = 1;
for loadSteps in range(nLoadSteps):
nLoad = 0
loadValue = f**((loadSteps+1)/nLoadSteps) #geometric increment of loads
print('load='+str(loadValue))
mbs.SetLoadParameter(nLoad, 'loadVector', [0, -loadValue,0])
print('load vector=' + str(mbs.GetLoadParameter(nLoad, 'loadVector')) )
mbs.SolveStatic(simulationSettings, updateInitialValues=True)
sol = mbs.systemData.GetODE2Coordinates()
n = len(sol)
print('nEL=',numberOfElements, ', tip displacement: x='+str(sol[n-4])+', y='+str(sol[n-3]))
#MATLAB 1 element: x=0.3622447298905063, y=0.9941447587249748 = paper "on the correct ..."
#2022-03-16:
# nEL= 1 , tip displacement: x=-0.36224472989050654,y=-0.9941447587249747
# nEL= 2 , tip displacement: x=-0.4889263085609102, y=-1.1752228652637502
# nEL= 4 , tip displacement: x=-0.5074287154557922, y=-1.2055337025602493
# nEL= 8 , tip displacement: x=-0.5085092365729895, y=-1.207197756093103
# nEL= 16 , tip displacement: x=-0.5085365799149556, y=-1.207238895003594
# nEL= 32 , tip displacement: x=-0.508537277761696, y=-1.2072398264650905
# nEL= 64 , tip displacement: x=-0.5085373030408489, y=-1.207239853404364
# nEL= 128, tip displacement: x=-0.5085373043168473, y=-1.2072398545511795
# nEL= 256, tip displacement: x=-0.5085373043916903, y=-1.207239854614031
#with second SolveStatic:
#nEL= 256 , tip displacement: x=-0.5085373043209366, y=-1.2072398545457574
#converged: x=-0.508537304326, y=-1.207239854550
#here (OLD):
#1: x=-0.36224472989050543, y=-0.994144758724973
#2: x=-0.4889263083414858, y=-1.1752228650551666
#4: x=-0.5074287151188892, y=-1.2055337022335404
#8: x=-0.5085092364970802, y=-1.2071977560198281
#64: x=-0.5085373029700947, y=-1.2072398533360738
#256:x=-0.5085373043209689, y=-1.2072398545457785
#sol = mbs.systemData.GetODE2Coordinates(exu.ConfigurationType.Initial)
#print('initial values='+str(sol))