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VIEW 0.00000E+00 0.00000E+00 -1.00000E+00 RIGH 1.00000E+00 0.00000E+00 0.00000E+00 UP 0.00000E+00 1.00000E+00 0.00000E+00 FOV 2.68819E+01 SCEN GEOM NAVI FREE LINE HEOU POIN SPHP COLO PAPE VECT SCCO FIEL VITE SCAL USER PROG 47 PAS 4 99 TERM TEXT VSCA SLER CAM1 1 NFRA 1 FREQ 10 TRAC OFFS FICH AVI NOCL NFTO 101 FPS 15 KFRE 10 COMP -1 REND GOTR LOOP 99 OFFS FICH AVI CONT NOCL REND GO TRAC OFFS FICH AVI CONT REND ENDPLAY *================================================================= SUIT Post-treatment ECHO * RESU ALIC TEMP GARD PSCR * SORT GRAP * AXTE 1.0 'Time [s]' * COUR 1 'dx_par1' DEPL COMP 1 NOEU LECT par1 TERM COUR 2 'dy_par1' DEPL COMP 2 NOEU LECT par1 TERM COUR 3 'dx_par2' DEPL COMP 1 NOEU LECT par2 TERM COUR 4 'dy_par2' DEPL COMP 2 NOEU LECT par2 TERM COUR 5 'dx_par3' DEPL COMP 1 NOEU LECT par3 TERM COUR 6 'dy_par3' DEPL COMP 2 NOEU LECT par3 TERM * trac 1 2 3 4 5 6 axes 1.0 'DISPL. [M]' yzer COLO vert vert bleu bleu turq turq trac 2 4 6 axes 1.0 'DISPL. [M]' yzer COLO vert bleu turq trac 2 axes 1.0 'Y-DISPL. [M]' xaxe 1 1.0 'X-DISPL. [M]' yzer COLO vert trac 4 axes 1.0 'Y-DISPL. [M]' xaxe 3 1.0 'X-DISPL. [M]' yzer COLO bleu trac 6 axes 1.0 'Y-DISPL. [M]' xaxe 5 1.0 'X-DISPL. [M]' yzer COLO turq list 2 axes 1.0 'Y-DISPL. [M]' xaxe 1 1.0 'X-DISPL. [M]' list 4 axes 1.0 'Y-DISPL. [M]' xaxe 3 1.0 'X-DISPL. [M]' list 6 axes 1.0 'Y-DISPL. [M]' xaxe 5 1.0 'X-DISPL. [M]' * QUAL DEPL COMP 1 LECT par3 TERM REFE 8.831001451D+2 TOLE 1.E-6 DEPL COMP 2 LECT par3 TERM REFE 0.000000000D+0 TOLE 1.E-6 *================================================================= SUIT Post-treatment (rendering on bitmap file) ECHO * RESU ALIC GARD PSCR * SORT VISU NSTO 1 * *================================================================= PLAY CAME 1 EYE 5.09858E+02 1.27465E+02 2.62775E+03 ! Q 1.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 VIEW 0.00000E+00 0.00000E+00 -1.00000E+00 RIGH 1.00000E+00 0.00000E+00 0.00000E+00 UP 0.00000E+00 1.00000E+00 0.00000E+00 FOV 2.68819E+01 SCEN GEOM NAVI FREE LINE HEOU POIN SPHP COLO PAPE VECT SCCO FIEL VITE SCAL USER PROG 47 PAS 4 99 TERM TEXT VSCA SLER CAM1 1 NFRA 1 FREQ 1 TRAC OFFS FICH BMP REND GOTR LOOP 3 OFFS FICH BMP REND GO TRAC OFFS FICH BMP REND ENDPLAY *================================================================= FIN 4
Some results: horizontal and vertical displacement components as a function of time (note that motion is uniform in the horizontal direction since there is no air resistance in the modelled case): Vertical displacement components as a function of time: 5
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: sinon; tra2 = tra2 et ele; finsi; f
Page 47: PMAT01E This test is similar to PMA
Page 50 and 51: Hence: 11 −8 ES 2× 10 ⋅ 2.5×
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 •
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• Analytical solution (self-simil
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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
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Geometric data: The calculation is
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SHOC01 Eulerian, “average” pseu
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COUR 7 'ro_a' ECRO COMP 2 ELEM LECT
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Analytical Conclusion: the pseudo-v
Page 127 and 128:
SHOC13 Eulerian, very low pseudo-vi
Page 129 and 130:
Analytical General conclusions: •
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The inverse path is not so straight
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The input files (mesh generation by
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Geometric data: The calculation is
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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
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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
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The 2-D plane case (2) Use geometri
Page 177 and 178:
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
Page 195 and 196:
Geometry: Exercise/Example 8 Steam
Page 197 and 198:
Exercise/Example 9 Explosion in Sec
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Exercise/Example 9 Explosion in Sec
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Boundary Condition Elements: CLxx (
Page 203 and 204:
Exercise/Example 11 - Perforated Pl
Page 205 and 206:
Exercise/Example 12 - Sloshing (3)
Page 207 and 208:
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
Page 218 and 219:
ALE solution with FSA: it is not po
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120 119 138 139 121 120 139 140 122
Page 222 and 223:
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
Page 252 and 253:
The EUROPLEXUS input file reads: WO
Page 254 and 255:
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
Page 260 and 261:
Final pressure distribution: 4
Page 262 and 263:
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
Page 268 and 269:
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
Page 274 and 275:
LOADING: The event is initiated by
Page 276 and 277:
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
Page 284 and 285:
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
Page 395 and 396:
BET0 1 KINT 0 AHGF 0 CL 0.5 CQ 2.56
Page 397 and 398:
INFS02 We use a twice finer fluid m
Page 399 and 400:
FREQ 1 GOTR LOOP 60 OFFS FICH AVI C
Page 401 and 402:
Problem description: This example i
Page 403 and 404:
*----------------------------------
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The final velocities: The final for
Page 408 and 409:
*----------------------------------
Page 410 and 411:
The final deformed mesh is: The fin
Page 412 and 413:
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
Page 423 and 424:
The input file is: INDE - 13 ECHO !
Page 425 and 426:
The final displacement norm: The fi
Page 427 and 428:
elim tol (piece et cp); c_p = piece
Page 429 and 430:
The final deformed shape is: 13
Page 431 and 432:
Numerical Solutions PRGL01 Simplifi
Page 433 and 434:
FOV 2.48819E+01 SCEN GEOM NAVI FREE
Page 435 and 436:
ROMA01 Final plastic streen in the
Page 437 and 438:
SONA01 7
Page 439:
Final density in the projectile: Fi
Page 442 and 443:
opti echo 0; opti donn 'D:\Users\Fo
Page 444 and 445:
* 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
Page 450 and 451:
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
Page 457 and 458:
CALC TINI 0. TFIN 40.E-3 *=========
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REPETER BCL2 (2); REPETER BCL3 (2);
Page 461 and 462:
*----------------------------------
Page 463 and 464:
The tip displacement in the referen
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Page 467 and 468:
LOG 1 DPSD *-----------------------
Page 469 and 470:
TRAC CACH OEIL2 ZONE1; TRAC CACH OE
Page 471 and 472:
The tip displacement in the referen
Page 473 and 474:
Page 475 and 476:
$ INIT VITE 2 -227. LECT VITI TERM
Page 477 and 478:
* AXTE 1000.0 'Time [ms]' * COUR 1
Page 479 and 480:
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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