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Hence: 11 −8 ES 2× 10 ⋅ 2.5× 10 −1 ω = = = 7.071 s LM 1⋅100 or, in terms of frequency: ω f = = 1.125 Hz 2π The period is: T = 1/ f = 0.889 s The expected behaviour is a sinusoidal oscillation around the static deflection value. The maximum dynamic deflection is twice the static value: dyn sta ∆ L = 2⋅∆ L = 0.4 m Numerical simulation TEST01 Discretize the system by just one Finite Element of the “cable” type (FUN2). These elements do not offer any resistance to bending. In addition, the assumed material (of type FUNE) is linear elastic but with no resistance to compression (only to traction) and the formulation is large-strain as concerns axial deformations. The result is: Linear theory The obtained displacement resembles the expected one. However: • The obtained maximum elongation is larger than the expected value (~0.45 instead of 0.40) • The oscillation period is longer than expected (~0.98 instead of 0.89). 2
The EUROPLEXUS input file for this problem is: TEST - 01 *----------------------------------------------------------------------- ECHO *CONV win *-----------------------------------------------------------Problem type CPLA NONL LAGR *-----------------------------------------------------------Dimensioning DIME PT2L 2 FUN2 1 PMAT 1 ZONE 2 TABL 1 2 FORC 1 TERM *---------------------------------------------------------------Geometry GEOM LIBR POIN 2 FUN2 1 PMAT 1 TERM 0 0 0 -1 1 2 2 *------------------------------------------------Geometrical complements COMP EPAI 2.5E-8 LECT 1 TERM *----------------------------------------------------------Material data MATE FUNE RO 8000. YOUN 2.0E11 NU 0.0 ELAS 2.0E11 ERUP 1.0E0 TRAC 1 2.0E11 1.E0 LECT 1 TERM MASS 100.0 LECT 2 TERM *----------------------------------------------------Boundary conditions LINK COUP BLOQ 2 LECT 1 TERM *----------------------------------------------------------Applied loads CHAR 1 FACT 2 FORC 2 -1.E3 LECT 2 TERM TABL 2 0.0 1.0 10.0 1.0 *----------------------------------------------------------------Outputs ECRI DEPL VITE CONT ECRO TFREQ 0.5 FICH ALIC TEMP FREQ 20 POIN LECT 1 2 TERM ELEM LECT 1 TERM *----------------------------------------------------------------Options OPTI PAS UTIL NOTEST *--------------------------------------------------Transient calculation CALCUL TINI 0. TEND 1.5 PASF 0.1E-3 *=========================================================POST-TREATMENT SUIT Post-treatment ECHO RESU ALIC TEMP GARD PSCR SORT GRAP AXTE 1.0 'Time [s]' *------------------------------------------------------Curve definitions COUR 1 'dy_2' DEPL COMP 2 NOEU LECT 2 TERM COUR 2 'sg_1' CONT COMP 1 ELEM LECT 1 TERM COUR 3 'fe_2' FORC COMP 2 NOEU LECT 2 TERM COUR 4 'fe_1' FORC COMP 2 NOEU LECT 1 TERM DCOU 6 'Max_elon' 2 0.0 -0.4 1.5 -0.4 DCOU 7 'Period' 2 0.889 0.0 0.889 -0.4 *------------------------------------------------------------------Plots trac 1 6 7 axes 1.0 'DISPL. [M]' yzer colo noir roug roug dash 0 2 2 trac 2 axes 1.0 'CONTR. [PA]' yzer trac 3 4 axes 1.0 'FORCE [N]' yzer list 1 axes 1.0 'DISPL. [M]' *--------------------------------------------------Results qualification QUAL DEPL COMP 2 LECT 2 TERM REFE -4.53636E-1 TOLE 1.E-2 CONT COMP 1 LECT 1 TERM REFE 7.48171E+10 TOLE 1.E-2 *======================================================================= FIN 3
Page 1 and 2: European Laboratory for Structural
Page 3 and 4: Proceedings of a Course on: Numeric
Page 5: Programme of the Course 1. Introduc
Page 10 and 11: Credits & Acknowledgments • Struc
Page 12 and 13: Introductory Example (4) 7 Applicat
Page 14 and 15: x Computational Framework • Gover
Page 16 and 17: n+ 1 n ∆t n n+ 1 u = u + ( u + u
Page 18 and 19: Scheme start-up and marching (2)
Page 20 and 21: Stress Update • To solve the equi
Page 22 and 23: Geometric non-linearities (3) Set u
Page 24 and 25: Essential Boundary Conditions Essen
Page 26 and 27: Exercise 0 - Ideal ballistics • M
Page 28 and 29: Exercise 0 - Ideal ballistics (5)
Page 30 and 31: Exercise 1 - Suspended mass (3) •
Page 32 and 33: Exercise 1 - Suspended mass (7) •
Page 34 and 35: Exercise 2 - Wave propagation (4)
Page 36 and 37: Exercise 3 - Impact on Cooling Towe
Page 41 and 42: TITLE: PMAT04: motion of projectile
Page 43 and 44: sinon; tra2 = tra2 et ele; finsi; f
Page 45 and 46: Some results: horizontal and vertic
Page 47: PMAT01E This test is similar to PMA
Page 52 and 53: The stress history is: Note that th
Page 54 and 55: Analytical TEST11 Same as TEST01 bu
Page 56 and 57: Comparison of natural vs. engineeri
Page 58 and 59: The total external forces at the tw
Page 61 and 62: TEST13 Same as TEST01 but uses a 10
Page 63 and 64: The mass returns at the initial pos
Page 65 and 66: TEST22 To verify the independence o
Page 67 and 68: Linear dynamic analysis Consider th
Page 69 and 70: • The two waves f and g propagate
Page 71 and 72: Analytical solution For the bar imp
Page 73 and 74: Note that we have also put the Pois
Page 75 and 76: BARI08 We study the effect of the t
Page 77 and 78: ENDPLAY *==========================
Page 79: BARI10 Same as BARI09 but compares
Page 82 and 83: The system is initially at rest, an
Page 84 and 85: CAST MESH TRID NONL LAGR $ $ Dimens
Page 86: Final deformation (with superposed
Page 90 and 91: Detailed Contents • Modeling the
Page 92 and 93: Modeling the fluid domain • The f
Page 94 and 95: Euler equations (3) • For a compr
Page 96 and 97: Time integration Each time incremen
Page 98 and 99: Time integration (5) 10. Account fo
Page 100 and 101:
Euler Equations (FV) • They are w
Page 102 and 103:
Mesh rezoning - motivations • Rez
Page 104 and 105:
Giuliani’s automatic rezoning •
Page 106 and 107:
• Analytical solution (self-simil
Page 108 and 109:
Shock tube (6) • Influence of pse
Page 110 and 111:
Exercise 2 - Explosion in air-fille
Page 112 and 113:
Exercise 3 - Bubble expansion in a
Page 114 and 115:
Exercise 4 - External blast on two
Page 119 and 120:
Geometric data: The calculation is
Page 121 and 122:
SHOC01 Eulerian, “average” pseu
Page 123 and 124:
COUR 7 'ro_a' ECRO COMP 2 ELEM LECT
Page 125 and 126:
Analytical Conclusion: the pseudo-v
Page 127 and 128:
SHOC13 Eulerian, very low pseudo-vi
Page 129 and 130:
Analytical General conclusions: •
Page 131 and 132:
The inverse path is not so straight
Page 133 and 134:
The input files (mesh generation by
Page 135 and 136:
Geometric data: The calculation is
Page 137 and 138:
COUR 1 'dx_4' DEPL COMP 1 NOEU LECT
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TANK02 Eulerian solution: the whole
Page 141:
The final pressure distribution is:
Page 144 and 145:
TUBE06 Lagrangian solution: the who
Page 146 and 147:
And the final velocity distribution
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The computed displacements are: To
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43 30 30 43 44 31 31 44 45 32 32 45
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Geometric data: External blast in a
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abs4 = dall (p4 d 28 p4u) (p4u d 40
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Geometric data: Internal blast in a
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air = air1 ET air2 ET air3 ET air4
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COURBE 8 'P e_p12' ECROU COMP 1 lec
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3D axisymmetric simulation: JWLS3G
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point lect 1 term elem lect 1 term
Page 169 and 170:
Universitat Politècnica de Catalun
Page 171 and 172:
• Motivation Detailed Contents
Page 173 and 174:
FSI Classification FSI for compress
Page 175 and 176:
The 2-D plane case (2) Use geometri
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Classification of FSI algorithms
Page 179 and 180:
The FSA algorithm (4) The case of s
Page 181 and 182:
The FSCR algorithm Combination of F
Page 183 and 184:
Application to Finite Volumes (3) 2
Page 185 and 186:
Exercise 2 - Explosions in simple d
Page 187 and 188:
Exercise/Example 3 - Wave propagati
Page 189 and 190:
Exercise/Example 4 - CONT problem (
Page 191 and 192:
Exercise/Example 5 - Explosion in a
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Exercise/Example 6 : Woodward-Colel
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Geometry: Exercise/Example 8 Steam
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Exercise/Example 9 Explosion in Sec
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Exercise/Example 9 Explosion in Sec
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Boundary Condition Elements: CLxx (
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Exercise/Example 11 - Perforated Pl
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Exercise/Example 12 - Sloshing (3)
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Page 209:
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DIME PT3L 23 PT2L 143 FL24 145 ED01
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The final pressure field in the flu
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ALE solution with FSA: it is not po
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120 119 138 139 121 120 139 140 122
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and the final velocity field: The s
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The final velocities: The final liq
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*----------------------------------
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TWIS07 We study the phenomenon by a
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This is a well-known reactor safety
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1.53330E+00 1.32310E+01 1.15000E+00
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200 199 239 240 200 200 200 240 241
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*----------------------------------
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The final fluid pressures: CONT02 T
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The final fluid velocities: The fin
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This example consists in a long 3D
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GEOM FL38 flui Q4GS stru TERM COMP
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Detail of first diaphragm: Detail o
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BOUNDARY CONDITIONS: The step is en
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The EUROPLEXUS input file reads: WO
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WOCO3D The mesh generation file (K2
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* RESU ALIC GARD PSCR * SORT GRAP *
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PT3L 16389 PT6L 504 NBLE 16389 NALE
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Final pressure distribution: 4
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BOUNDARY CONDITIONS: The vessel is
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as01=daller c1 c2 c3 c4 plan; * c1=
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*trac oeil cach fluidstr; *opti don
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cam3=cam31 et cam32; camb=cam1 et c
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log 1 dtml REZO GAM0 0.5 FLMP EPS1
Page 272 and 273:
Final structure deformation: Final
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LOADING: The event is initiated by
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FLUT RO .242777373 EINT 6.865E5 GAM
Page 278 and 279:
Final structure velocities: 6
Page 280 and 281:
RESULTS: A paper by Bermudez and Ro
Page 282 and 283:
The applied displacement and the co
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PROBLEM: A rigid tank with a deform
Page 286:
The EUROPLEXUS input file reads: GR
Page 289 and 290:
PROBLEM: A rigid tank with rigid or
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COMP EPAI 0.005 LECT 101 102 103 10
Page 293 and 294:
Numerical Solution (flexible bottom
Page 295 and 296:
! VARI DEPL VITE ECRO ! fich alic t
Page 297 and 298:
The final pressures in the rigid an
Page 299 and 300:
LOADING: A constant gravity in the
Page 301 and 302:
Some results: intermediate and fina
Page 305 and 306:
Universitat Politècnica de Catalun
Page 307 and 308:
ALE description of structures (2)
Page 309 and 310:
Example 1 - Taylor bar impact (3) B
Page 311 and 312:
Example 3 - Coining (3) Influence o
Page 313 and 314:
• Tentative classification: Non-c
Page 315 and 316:
Example 4 - Explosion in a 2D box (
Page 317 and 318:
Example 6 - LOCA in the HDR (2) A -
Page 319 and 320:
Examples of “Slow” Transient Co
Page 321 and 322:
Examples of Fast Transient Impact
Page 323 and 324:
Components of Contact-Impact Method
Page 325 and 326:
Shortcomings • Slender or distort
Page 327 and 328:
Example - Bar impact • (See Part
Page 329 and 330:
Example 7b - Indentation (2) • 2D
Page 331 and 332:
Example 7b - Indentation (6) • 3D
Page 333 and 334:
Smoothed Particles Hydrodynamics (C
Page 335 and 336:
SPH Formulation (2) • Basic idea:
Page 337 and 338:
SPH impact [Courtesy of Samtech/Son
Page 339 and 340:
PRGL01: Example 8 - SPH impacts (Co
Page 341 and 342:
Spectral Elements • Motivation: l
Page 343 and 344:
Spectral Elements (5) Convergence p
Page 345 and 346:
Example 9 - Closed FE/SE interface
Page 347 and 348:
Example 11 - Cylindrical valley 85
Page 349 and 350:
Performance Optimization • All ex
Page 351 and 352:
Time Step Partitioning (4) • Intr
Page 353 and 354:
Time Step Partitioning (8) • Acti
Page 355 and 356:
Treatment of links in partitioning
Page 357 and 358:
Example 12a - Taylor bar impact rev
Page 359 and 360:
Coupling at the Interfaces • Two
Page 361 and 362:
Coupling at the Interfaces (5) MU T
Page 363 and 364:
Coupling at the Interfaces (9) Time
Page 365 and 366:
Multiple scales in time (3) • Exp
Page 367 and 368:
Multiple scales in space • Furthe
Page 369 and 370:
Multiple scales in frequency • So
Page 371 and 372:
Example: power plant 133 Example: p
Page 373 and 374:
Example: aircraft (3) Thanks to CPU
Page 375 and 376:
Example 14 - Domains in 3D • Thic
Page 377:
Example 15 - Bar Impact Revisited (
Page 382 and 383:
* mesh=stru et symax et viti et lil
Page 384 and 385:
The displacements are: 4
Page 386 and 387:
c2=p1 d 8 p2; c3=p2 d 20 p3; c4=p3
Page 388 and 389:
The resulting final deformed mesh w
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TERM *-----------------------------
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Geometric data and materials: The b
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BET0 1 KINT 0 AHGF 0 CL 0.5 CQ 2.56
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INFS02 We use a twice finer fluid m
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FREQ 1 GOTR LOOP 60 OFFS FICH AVI C
Page 401 and 402:
Problem description: This example i
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*----------------------------------
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The final velocities: The final for
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*----------------------------------
Page 410 and 411:
The final deformed mesh is: The fin
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pc = 4.5 -1 -1.5; pd = 5.5 -1 -1.5;
Page 414 and 415:
The initial configuration (with par
Page 417 and 418:
TITLE: Indentation problem. PROBLEM
Page 419 and 420:
cp = p0 d 10 p13; elim tol (piece e
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The final velocities: The final dis
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The input file is: INDE - 13 ECHO !
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The final displacement norm: The fi
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elim tol (piece et cp); c_p = piece
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The final deformed shape is: 13
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Numerical Solutions PRGL01 Simplifi
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FOV 2.48819E+01 SCEN GEOM NAVI FREE
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ROMA01 Final plastic streen in the
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SONA01 7
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Final density in the projectile: Fi
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opti echo 0; opti donn 'D:\Users\Fo
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* opti dime 2 elem qua4; p0 = 0 0;
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The final X-displacement in the hyb
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* opti dime 2 elem qua4; opti titr
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VALLPS This calculation assumes a p
Page 452 and 453:
The receiver signal in the coupled
Page 455 and 456:
Problem description: This example r
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CALC TINI 0. TFIN 40.E-3 *=========
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REPETER BCL2 (2); REPETER BCL3 (2);
Page 461 and 462:
*----------------------------------
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The tip displacement in the referen
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LOG 1 DPSD *-----------------------
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TRAC CACH OEIL2 ZONE1; TRAC CACH OE
Page 471 and 472:
The tip displacement in the referen
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$ INIT VITE 2 -227. LECT VITI TERM
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* AXTE 1000.0 'Time [ms]' * COUR 1
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sq41=sq41 coul 'TURQ'; sq42=sq42 co
Page 481 and 482:
The displacements in the case with
Page 485 and 486:
European Commission DG Joint Resear
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