ANCFBeamTest.py
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1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2# This is an EXUDYN example
3#
4# Details: Test models for ANCFBeam (2-node 3D shear deformable ANCF beam element
5# with 2 cross section slope vectors);
6# test models: cantilever beam with tip force and torque
7#
8# Author: Johannes Gerstmayr
9# Date: 2023-04-05
10#
11# 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.
12#
13#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
14
15import exudyn as exu
16from exudyn.utilities import *
17
18import numpy as np
19
20useGraphics = True #without test
21#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
22#you can erase the following lines and all exudynTestGlobals related operations if this is not intended to be used as TestModel:
23try: #only if called from test suite
24 from modelUnitTests import exudynTestGlobals #for globally storing test results
25 useGraphics = exudynTestGlobals.useGraphics
26except:
27 class ExudynTestGlobals:
28 pass
29 exudynTestGlobals = ExudynTestGlobals()
30#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
31
32SC = exu.SystemContainer()
33mbs = SC.AddSystem()
34
35compute2D = False
36compute3D = True
37
38#test examples
39#2011 MUBO, Nachbagauer Pechstein Irschik Gerstmayr (2D)
40#2013 CND, Nachbagauer Gruber Gerstmayr (static, 3D); "Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples"
41### not yet: 2013 CND, Nachbagauer Gerstmayr (dynamic, 3D)
42cases = ['CantileverLinear2011', 'Cantilever2011', 'GeneralBending2013', 'PrincetonBeamF2', 'PrincetonBeamF3', 'Eigenmodes2013']
43nElementsList = [1,2,4,8,16,32,64,128,256,512,1024]
44# nElementsList = [8,32, 128]
45nElements = 8
46
47betaList = [0,15,30,45,60,75,90]
48betaDegree = 45
49
50caseList = [0,1,2,3,4]
51case=4
52
53useGraphics = False
54verbose = False
55
56bodyFixedLoad = False
57testErrorSum = 0
58printCase = True
59
60#for nElements in nElementsList:
61#for betaDegree in betaList:
62for case in caseList:
63 if printCase:
64 printCase=False
65 exu.Print('case=', case, cases[case])
66 mbs.Reset()
67
68 computeEigenmodes = False
69 csFact = 1
70 sectionData = exu.BeamSection()
71 fTip = 0
72 MxTip = 0
73 MyTip = 0
74
75 ks1=1 #shear correction, torsion
76 ks2=1 #shear correction, bending
77 ks3=1 #shear correction, bending
78 ff=1 #drawing factor
79
80 #define beam parameters and loads for different cases
81 if case == 0 or case == 1:
82 caseName = cases[case]
83
84 L = 2 #length of beam
85 w = 0.1 #width of beam
86 h = 0.5 #height Y
87
88 fTip = 5e5*h**3
89 if case == 1:
90 fTip *= 1000
91
92 Em = 2.07e11
93 rho = 1e2
94
95 A=h*w
96 nu = 0.3 # Poisson ratio
97 ks2= 10*(1+nu)/(12+11*nu)
98 ks3=ks2
99
100 elif case == 2:
101 L = 2 #length of beam
102 h = 0.2 #height Y
103 w = 0.4 #width Z of beam
104 Em = 2.07e11
105 rho = 1e2
106
107 A=h*w
108
109 nu = 0.3 # Poisson ratio
110 ks1= 0.5768 #torsion correction factor if J=Jyy+Jzz
111 ks2= 0.8331
112 ks3= 0.7961
113
114 MxTip = 0.5e6
115 MyTip = 2e6
116
117 csFact = 10
118 elif case == 3 or case == 4: #Princeton beam example
119 L = 0.508 #length of beam
120 h = 12.3777e-3 #height Y; 12.3777e-3 with Obrezkov's paper
121 w = 3.2024e-3 #width Z of beam
122 Em = 71.7e9
123 ks1=0.198
124 nu = 0.31
125
126 ks2=1
127 ks3=1
128 # ks2=0.9
129 # ks3=0.9
130
131
132 rho = 1e2 #unused
133 A=h*w
134
135 MxTip = 0
136 MyTip = 0
137 if case == 3:
138 fTip = 8.896 #F2
139 elif case == 4:
140 fTip = 13.345 #F3
141 #if kk==0: exu.Print('load=', fTip)
142
143 beta = betaDegree/180*pi #beta=0 => negative y-axis
144 bodyFixedLoad = False
145
146 csFact = 10
147
148 Gm = Em/(2*(1+nu)) # Shear modulus
149
150 #compute sectionData
151
152 # Cross-section properties
153 Iyy = h*w**3/12 # Second moment of area of the beam cross-section
154 Izz = w*h**3/12 # Second moment of area of the beam cross-section
155 J = (Iyy+Izz) # approximation; Polar moment of area of the beam cross-section
156
157 sectionData.stiffnessMatrix = np.diag([Em*A, Gm*A*ks2, Gm*A*ks3, Gm*J*ks1, Em*Iyy, Em*Izz])
158
159
160 rhoA = rho*A
161
162 if False:
163 #linear solution:
164 uzTip = fTip*L**3/(3*Em*Iyy)
165 exu.Print('uz linear=',uzTip)
166 uyTip = fTip*L**3/(3*Em*Izz)
167 exu.Print('uy linear=',uyTip)
168
169 sectionData.inertia= rho*J*np.eye(3)
170 sectionData.massPerLength = rhoA
171
172 sectionGeometry = exu.BeamSectionGeometry()
173
174 #points, in positive rotation sense viewing in x-direction, points in [Y,Z]-plane
175 #points do not need to be closed!
176 lp = exu.Vector2DList()
177 if True:
178 lp.Append([h*ff,-w*ff])
179 lp.Append([h*ff,w*ff])
180 lp.Append([-h*ff,w*ff])
181 lp.Append([-h*ff,-w*ff])
182
183 sectionGeometry.polygonalPoints = lp
184 #exu.Print('HERE\n',sectionGeometry.polygonalPoints)
185 nGround = mbs.AddNode(NodePointGround(referenceCoordinates=[0,0,0])) #ground node for coordinate constraint
186 mnGround = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nGround, coordinate=0))
187
188
189 eY=[0,1,0]
190 eZ=[0,0,1]
191 lElem = L/nElements
192 if compute3D:
193 initialRotations = eY+eZ
194 #create beam nodes and elements
195 n0 = mbs.AddNode(NodePointSlope23(referenceCoordinates=[0,0,0]+initialRotations))
196 nInit = n0
197 for k in range(nElements):
198 n1 = mbs.AddNode(NodePointSlope23(referenceCoordinates=[lElem*(k+1),0,0]+initialRotations))
199
200 oBeam = mbs.AddObject(ObjectANCFBeam(nodeNumbers=[n0,n1], physicsLength = lElem,
201 sectionData = sectionData,
202 crossSectionPenaltyFactor = [csFact,csFact,csFact],
203 visualization=VANCFBeam(sectionGeometry=sectionGeometry)))
204 n0 = n1
205
206
207 mTip = mbs.AddMarker(MarkerNodeRigid(nodeNumber = n1))
208 if fTip != 0:
209 if case < 3:
210 mbs.AddLoad(Force(markerNumber=mTip, loadVector = [0,fTip,0], bodyFixed = bodyFixedLoad))
211 elif case >= 3:
212 mbs.AddLoad(Force(markerNumber=mTip, loadVector = [0,-fTip*cos(beta),fTip*sin(beta)], bodyFixed = bodyFixedLoad))
213
214 if MxTip != 0 or MyTip != 0:
215 mbs.AddLoad(Torque(markerNumber=mTip, loadVector = [MxTip, MyTip,0]))#, bodyFixed = True ))
216
217 for i in range(9):
218 #if i != 4 and i != 8: #exclude constraining the slope lengths
219 if True:
220 nm0 = mbs.AddMarker(MarkerNodeCoordinate(nodeNumber=nInit, coordinate=i))
221 mbs.AddObject(CoordinateConstraint(markerNumbers=[mnGround, nm0]))
222
223
224 # exu.Print(mbs)
225 mbs.Assemble()
226
227 tEnd = 100 #end time of simulation
228 stepSize = 0.5*0.01*0.1 #step size; leads to 1000 steps
229
230 simulationSettings = exu.SimulationSettings()
231 simulationSettings.solutionSettings.solutionWritePeriod = 2e-2 #output interval general
232 simulationSettings.solutionSettings.sensorsWritePeriod = 1e-1 #output interval of sensors
233 simulationSettings.timeIntegration.numberOfSteps = int(tEnd/stepSize) #must be integer
234 simulationSettings.timeIntegration.endTime = tEnd
235 #simulationSettings.solutionSettings.solutionInformation = "This is the info\nNew line\n and another new line \n"
236 simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 0.5
237 #simulationSettings.timeIntegration.simulateInRealtime=True
238 #simulationSettings.timeIntegration.realtimeFactor=0.1
239
240 simulationSettings.timeIntegration.verboseMode = verbose
241 simulationSettings.staticSolver.verboseMode = verbose
242
243 #simulationSettings.parallel.numberOfThreads = 4
244 simulationSettings.timeIntegration.newton.useModifiedNewton = True
245 #simulationSettings.timeIntegration.newton.numericalDifferentiation.minimumCoordinateSize = 1e0
246
247 simulationSettings.timeIntegration.newton.numericalDifferentiation.relativeEpsilon = 1e-4
248 simulationSettings.timeIntegration.newton.relativeTolerance = 1e-6
249
250 # simulationSettings.displayComputationTime = True
251 simulationSettings.linearSolverType = exu.LinearSolverType.EigenSparse
252 # simulationSettings.parallel.numberOfThreads = 4
253
254 #simulationSettings.staticSolver.newton.numericalDifferentiation.relativeEpsilon = 5e-5
255 #simulationSettings.staticSolver.newton.numericalDifferentiation.forODE2 = True
256 #simulationSettings.staticSolver.newton.relativeTolerance = 1e-6
257 # simulationSettings.staticSolver.newton.numericalDifferentiation.relativeEpsilon = 1e-4
258
259 if nElements > 32 and case==0: #change tolerance, because otherwise no convergence
260 simulationSettings.staticSolver.newton.relativeTolerance = 1e-6
261 if case == 1: #tolerance changed from 1e-8 to 5e-10 to achieve values of paper (1024 has difference at last digit in paper)
262 simulationSettings.staticSolver.newton.relativeTolerance = 0.5e-9
263
264
265 simulationSettings.staticSolver.numberOfLoadSteps = 5
266
267
268 #add some drawing parameters for this example
269 SC.visualizationSettings.nodes.drawNodesAsPoint=False
270 SC.visualizationSettings.nodes.defaultSize=0.01
271
272 SC.visualizationSettings.bodies.beams.axialTiling = 50
273 SC.visualizationSettings.general.drawWorldBasis = True
274 SC.visualizationSettings.general.worldBasisSize = 0.1
275 SC.visualizationSettings.openGL.multiSampling = 4
276
277
278 # [M, K, D] = exu.solver.ComputeLinearizedSystem(mbs, simulationSettings, useSparseSolver=True)
279 # exu.Print('M=',M.round(1))
280
281 if useGraphics:
282 exu.StartRenderer()
283 mbs.WaitForUserToContinue()
284
285 # if computeEigenmodes:
286 # nModes = 3*(1+int(compute3D))
287 # nRigidModes = 3*(1+int(compute3D))
288 # if compute2D:
289 # constrainedCoordinates=[0,1,mbs.systemData.ODE2Size()-2]
290 # else:
291 # constrainedCoordinates=[0,1,2,5,mbs.systemData.ODE2Size()-8,mbs.systemData.ODE2Size()-7]
292
293 # # constrainedCoordinates=[]
294
295 # compeig=mbs.ComputeODE2Eigenvalues(simulationSettings, useSparseSolver=False,
296 # numberOfEigenvalues= nRigidModes+nModes,
297 # constrainedCoordinates=constrainedCoordinates,
298 # convert2Frequencies= False)
299
300 # exu.Print('eigvalues=',np.sqrt(compeig[0][nRigidModes:]))
301
302 # if False: #show modes:
303 # for i in range(nModes):
304 # iMode = nRigidModes+i
305 # mbs.systemData.SetODE2Coordinates(5*compeig[1][:,iMode], exudyn.ConfigurationType.Visualization)
306 # mbs.systemData.SetTime(np.sqrt(compeig[0][iMode]), exudyn.ConfigurationType.Visualization)
307 # mbs.SendRedrawSignal()
308
309 # mbs.WaitForUserToContinue()
310
311 # else:
312 mbs.SolveStatic(simulationSettings)
313 # mbs.SolveDynamic(simulationSettings)
314 #mbs.SolveDynamic(simulationSettings, solverType = exu.DynamicSolverType.RK44)
315
316
317 if useGraphics:
318 SC.WaitForRenderEngineStopFlag()
319 exu.StopRenderer() #safely close rendering window!
320
321 ##evaluate final (=current) output values
322 uTip = mbs.GetNodeOutput(n1, exu.OutputVariableType.Displacement)
323
324 errorFact = 1
325 if case != 1:
326 errorFact *= 100
327
328 testErrorSum += np.linalg.norm(uTip)
329
330
331
332 if case < 2:
333 pTip = mbs.GetNodeOutput(n1, exu.OutputVariableType.Position)
334 exu.Print('ne=',nElements, ', ux=',L-pTip[0], ', uy=',pTip[1])
335 elif case == 2:
336 rotTip = mbs.GetNodeOutput(n1, exu.OutputVariableType.Rotation)
337 exu.Print('ne=',nElements, ', u=',list(uTip))
338 # exu.Print('ne=',nElements, ', rot=',rotTip)
339 elif case == 3 or case == 4:
340 exu.Print('ne=', nElements, ', beta=', round(beta*180/pi,1), ', u=',uTip.round(7))
341
342
343exu.Print('Solution of ANCFBeam3Dtest=', testErrorSum)
344exudynTestGlobals.testError = testErrorSum - (1.010486312300459 )
345exudynTestGlobals.testResult = testErrorSum
346
347
348
349# case= 0/CantileverLinear2011
350#NachbagauerPechsteinIrschikGerstmayrMUBO2011 (2D):
351# ne=1, 9.12273046e–8, 6.16666566e–4, 0.000193
352# ne=2, 1.61293091e–7, 7.61594059e–4, 4.831e–5
353# ne=4, 1.81763233e–7, 7.97825954e–4, 1.208e–5
354# ne=256, 1.88847418e–7, 8.09900305e–4, 2.945e–9
355#Exudyn: ksFact=1
356# ne= 1 , ux= 9.122730637578513e-08 , uy= 0.0006166665660910789
357# ne= 2 , ux= 1.612930911054633e-07 , uy= 0.0007615940599560586
358# ne= 4 , ux= 1.8176323512975046e-07 , uy= 0.0007978259537503566
359# ne= 8 , ux= 1.8706537496804287e-07 , uy= 0.0008068839288072378
360# ne= 16 , ux= 1.8840244964124508e-07 , uy= 0.0008091484226773518
361# ne= 32 , ux= 1.887374359021976e-07 , uy= 0.0008097145461515286
362# ne= 64 , ux= 1.888212299849812e-07 , uy= 0.0008098560770202866
363# ne= 128 , ux= 1.8884218011550047e-07 , uy= 0.000809891459736643
364# ne= 256 , ux= 1.8884741770364144e-07 , uy= 0.0008099003054122335
365
366
367# case= 1/Cantilever2011
368#NachbagauerPechsteinIrschikGerstmayrMUBO2011 (2D):
369# ne=1, 0.07140274, 0.54225823, 0.168310
370# ne=2, 0.12379212, 0.65687111, 0.053697
371# ne=4, 0.14346767, 0.69593561, 0.014633
372# ne=1024, 0.15097103, 0.71056837, 2.280e–7
373
374#Exudyn: ksFact=1
375# ne= 1 , ux= 0.07140273975041422 , uy= 0.5422582285449739
376# ne= 2 , ux= 0.12379212054619537 , uy= 0.6568711099777776
377# ne= 4 , ux= 0.14346766617229956 , uy= 0.695935613449867
378# ne= 8 , ux= 0.14904162148449163 , uy= 0.7068152604035266
379# ne= 16 , ux= 0.15048521526298897 , uy= 0.709623891842095
380# ne= 32 , ux= 0.15084943688011565 , uy= 0.7103320154655514
381# ne= 64 , ux= 0.15094070328691145 , uy= 0.7105094267817303
382# ne= 128 , ux= 0.15096353326024237 , uy= 0.7105538037895819
383# ne= 256 , ux= 0.15096924149743085 , uy= 0.7105648993600513
384# ne= 512 , ux= 0.15097066651939461 , uy= 0.7105676689547459
385# ne= 1024 , ux= 0.15097102364723924 , uy= 0.7105683631862169
386
387# case = 2:
388#2013 CND, Nachbagauer Gruber Gerstmayr (static, 3D); "Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Static and Linearized Dynamic Examples"
389#Table 4:
390# SMF
391# 8, 1.0943e-4, 1.8638e-4, 1.8117e-2
392# 32, 1.0943e-4, 1.8625e-4, 1.8117e-2
393# ANSYS
394# 40, 1.0939e-4, 1.8646e-4, 1.8117e-2
395#Exudyn, ksFact=10:
396# ne= 8 , u= [-0.00010900977088157404, -0.0001902100873246334, -0.01811732779800177]
397# ne= 32 , u= [-0.00010941122286522997, -0.00018667435478355072, -0.01811739809277171]
398# ne= 128 , u= [-0.00010943631319815239, -0.000186451835025629, -0.018117402461210096]
399#==> in 2013 paper, element performed slightly better, especially in ux and uy terms
400
401# case = 3:
402#Princeton beam with ANSYS (Leonid Obrezkov / Aki Mikkola / Marko Matikainen et al.,
403# Performance review of locking alleviation methods for continuum ANCF beam elements,
404# Nonlinear Dynamics, Vol. 109, pp. 31–546, May 2022
405# beta=[0 15 30 45 60 75 90];
406if (case==3 or case == 4) and False:
407 # F2=8.896
408 # % ANSYS beam (10-199 el)
409 ANSYSF2y=np.array([1.071417630E-002, 1.061328706E-002, 1.011169630E-002, 8.837226265E-003, 6.604665004E-003, 3.538889001E-003, 0])
410 ANSYSF2z=np.array([0, 4.208232124E-002, 7.939482948E-002, 0.108987937, 0.129887616, 0.142194370, 0.146245978])
411 exu.Print('refsol ANSYS F2=8.896:\n',ANSYSF2y.round(6), '\n', ANSYSF2z.round(6),sep='')
412 # % ANSYS solid (el) (4x12x500) - finer mesh doesn't have much influence see in Size effect file
413 # ANSYS_solid_y=[1.069752828E-002 1.057180106E-002 9.938278402E-003 8.686786771E-003 6.500006282E-003 3.481999513E-003 0];
414 # ANSYS_solid_z=[0 4.101165651E-002 7.696749069E-002 0.105976311 0.127251299 0.139594740 0.143848652];
415
416 # F3=13.345
417 # % ANSYS beam (10-199 el)
418 ANSYSF3y=np.array([1.606423724E-002, 1.645825752E-002, 1.665873206E-002, 1.518618440E-002, 1.157837500E-002, 6.248967384E-003, 0])
419 ANSYSF3z=np.array([0, 6.435812858E-002, 0.117735994, 0.156467239, 0.181861627, 0.196097131, 0.200677707])
420 # % ANSYS solid (el) (4x12x500) - finer mesh see in Size effect file
421 #ANSYS_solid_y=[1.603700622E-002 1.637026068E-002 1.640440775E-002 1.485055210E-002 1.127173264E-002 6.062461977E-003 0])
422 #ANSYS_solid_z=[0 6.270699533E-002 0.113752002 0.153554457 0.179978534 0.192972233 0.197669499])
423 exu.Print('refsol ANSYS F3=13.345:\n',ANSYSF3y.round(6), '\n', ANSYSF3z.round(6),sep='')
424#Exudyn results for Princeton beam:
425#not exactly the same, but around the previous values with HOTINT
426#using 16 elements, csFact=10 (no influence)
427# F2=8.896
428# case= 3, PrincetonBeam
429# ne= 16 , beta= 0.0 , u= [-0.0001352 -0.0107023 0. ]
430# ne= 16 , beta= 15.0 , u= [-0.0022414 -0.0106295 0.0421374]
431# ne= 16 , beta= 30.0 , u= [-0.0076567 -0.0101861 0.0794434]
432# ne= 16 , beta= 45.0 , u= [-0.0143664 -0.0089529 0.1089703]
433# ne= 16 , beta= 60.0 , u= [-0.0204225 -0.0067182 0.1297877]
434# ne= 16 , beta= 75.0 , u= [-0.0245093 -0.0036079 0.1420319]
435# ne= 16 , beta= 90.0 , u= [-0.0259403 -0. 0.1460608]
436
437# F3=13.345
438# case= 4, PrincetonBeam
439# ne= 16 , beta= 0.0 , u= [-0.0003039 -0.0160454 0. ]
440# ne= 16 , beta= 15.0 , u= [-0.005319 -0.0165469 0.064622 ]
441# ne= 16 , beta= 30.0 , u= [-0.0171901 -0.0169316 0.1179818]
442# ne= 16 , beta= 45.0 , u= [-0.0303357 -0.0155488 0.1565214]
443# ne= 16 , beta= 60.0 , u= [-0.0411035 -0.0118996 0.1817173]
444# ne= 16 , beta= 75.0 , u= [-0.0479101 -0.0064334 0.1958343]
445# ne= 16 , beta= 90.0 , u= [-0.0502184 -0. 0.2003738]