Download full text - ELSA - Europa

More documents

Recommendations

Info

• Analytical solution (self-similar): Shock tube (2) • Shock S moves to the right at speed • Contact discontinuity C (particle initially at diaphragm) moves to the right at speed u C • Rarefaction wave R( ab , ) moves to the left at speeds v , v vS a b 35 Shock tube (3) Suggested variations: • Study influence of pseudo-viscosity and upwinding on Eulerian solution • Obtain and discuss Lagrangian solution(s). Hint: try different amounts of pseudo-viscosity • Obtain and discuss ALE solution(s). Compare automatic rezoning and mean-based rezoning • Solve shock tube problem with Finite Volumes 36 18
Shock tube (4) • Assumed parameter values: • Analytical solution: = i 0 λ ρ / ρ = p / p P p / p 1 2 1 2 C 2 37 Shock tube (5) • Discretization: • “Optimal” numerical solution (Eulerian): ‣ C L = 0.5, C Q = 0 ‣ α 0 = 0.2, β 0 = 0 density pressure Internal energy 38 19
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 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 •
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
Page 139 and 140: 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
Page 148 and 149: The computed displacements are: To
Page 150 and 151: 43 30 30 43 44 31 31 44 45 32 32 45
Page 153 and 154: Geometric data: External blast in a
Page 155 and 156: abs4 = dall (p4 d 28 p4u) (p4u d 40
Page 157 and 158:
Geometric data: Internal blast in a
Page 159 and 160:
air = air1 ET air2 ET air3 ET air4
Page 161 and 162:
COURBE 8 'P e_p12' ECROU COMP 1 lec
Page 163 and 164:
3D axisymmetric simulation: JWLS3G
Page 165 and 166:
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
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
Page 193 and 194:
Exercise/Example 6 : Woodward-Colel
Page 195 and 196:
Geometry: Exercise/Example 8 Steam
Page 197 and 198:
Exercise/Example 9 Explosion in Sec
Page 199 and 200:
Exercise/Example 9 Explosion in Sec
Page 201 and 202:
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:
Page 214 and 215:
DIME PT3L 23 PT2L 143 FL24 145 ED01
Page 216 and 217:
The final pressure field in the flu
Page 218 and 219:
ALE solution with FSA: it is not po
Page 220 and 221:
120 119 138 139 121 120 139 140 122
Page 222 and 223:
and the final velocity field: The s
Page 224 and 225:
The final velocities: The final liq
Page 226 and 227:
*----------------------------------
Page 228 and 229:
TWIS07 We study the phenomenon by a
Page 231 and 232:
This is a well-known reactor safety
Page 233 and 234:
1.53330E+00 1.32310E+01 1.15000E+00
Page 235 and 236:
200 199 239 240 200 200 200 240 241
Page 237 and 238:
*----------------------------------
Page 239 and 240:
The final fluid pressures: CONT02 T
Page 241 and 242:
The final fluid velocities: The fin
Page 243 and 244:
This example consists in a long 3D
Page 245 and 246:
GEOM FL38 flui Q4GS stru TERM COMP
Page 248 and 249:
Detail of first diaphragm: Detail o
Page 250 and 251:
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
Page 256 and 257:
* RESU ALIC GARD PSCR * SORT GRAP *
Page 258 and 259:
PT3L 16389 PT6L 504 NBLE 16389 NALE
Page 260 and 261:
Final pressure distribution: 4
Page 262 and 263:
BOUNDARY CONDITIONS: The vessel is
Page 264 and 265:
as01=daller c1 c2 c3 c4 plan; * c1=
Page 266 and 267:
*trac oeil cach fluidstr; *opti don
Page 268 and 269:
cam3=cam31 et cam32; camb=cam1 et c
Page 270 and 271:
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
Page 291 and 292:
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
Page 390 and 391:
TERM *-----------------------------
Page 393 and 394:
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:
*----------------------------------
Page 405:
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
Page 421 and 422:
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;
Page 446 and 447:
The final X-displacement in the hyb
Page 448 and 449:
* 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 *=========
Page 459 and 460:
REPETER BCL2 (2); REPETER BCL3 (2);
Page 461 and 462:
*----------------------------------
Page 463 and 464:
The tip displacement in the referen
Page 465 and 466:
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
show all

Download full text - ELSA - Europa

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?