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The computed displacements are: To see the approximate position of the bubble interface, one may plot the mass fraction distribution of the bubble material component: 6
The input file for the test TUBE04 is: TUBE - 04 *----------------------------------------------------------------------- ECHO *CONV win *-----------------------------------------------------------Problem type AXIS NONL ALE *-----------------------------------------------------------Dimensioning DIME PT2L 107 FL23 12 FL24 84 ZONE 2 NALE 1 NBLE 98 NEPE 1020 ECRO 3264 TERM *---------------------------------------------------------------Geometry GEOM LIBR POIN 107 FL23 12 FL24 84 TERM 0.00000E+00 0.00000E+00 3.14500E+00 0.00000E+00 3.11810E+00 4.10500E-01 3.03780E+00 8.13990E-01 2.90560E+00 1.20350E+00 2.72360E+00 1.57250E+00 2.49510E+00 1.91460E+00 2.22390E+00 2.22390E+00 1.91460E+00 2.49510E+00 1.57250E+00 2.72360E+00 1.20350E+00 2.90560E+00 8.13990E-01 3.03780E+00 4.10500E-01 3.11810E+00 0.00000E+00 3.14500E+00 5.15600E+00 0.00000E+00 5.09970E+00 7.30510E-01 5.00880E+00 1.45180E+00 4.86420E+00 2.15130E+00 4.64850E+00 2.81320E+00 4.34360E+00 3.41610E+00 3.93350E+00 3.93350E+00 3.41610E+00 4.34360E+00 2.81320E+00 4.64850E+00 2.15130E+00 4.86420E+00 1.45180E+00 5.00880E+00 7.30510E-01 5.09970E+00 0.00000E+00 5.15600E+00 7.16700E+00 0.00000E+00 7.11050E+00 1.06860E+00 7.02640E+00 2.12620E+00 6.88680E+00 3.15600E+00 6.65900E+00 4.13330E+00 6.30030E+00 5.02060E+00 5.76190E+00 5.76190E+00 5.02060E+00 6.30030E+00 4.13330E+00 6.65900E+00 3.15600E+00 6.88680E+00 2.12620E+00 7.02640E+00 1.06860E+00 7.11050E+00 0.00000E+00 7.16700E+00 9.17800E+00 0.00000E+00 9.13620E+00 1.42630E+00 9.07480E+00 2.84270E+00 8.96560E+00 4.23180E+00 8.76610E+00 5.56250E+00 8.40820E+00 6.78060E+00 7.78260E+00 7.78260E+00 6.78060E+00 8.40820E+00 5.56250E+00 8.76610E+00 4.23180E+00 8.96560E+00 2.84270E+00 9.07480E+00 1.42630E+00 9.13620E+00 0.00000E+00 9.17800E+00 1.11890E+01 0.00000E+00 1.11680E+01 1.80470E+00 1.11370E+01 3.60290E+00 1.10790E+01 5.38310E+00 1.09600E+01 7.11960E+00 1.07060E+01 8.75410E+00 1.01290E+01 1.01290E+01 8.75410E+00 1.07060E+01 7.11960E+00 1.09600E+01 5.38310E+00 1.10790E+01 3.60290E+00 1.11370E+01 1.80470E+00 1.11680E+01 0.00000E+00 1.11890E+01 1.32000E+01 0.00000E+00 1.32000E+01 2.20000E+00 1.32000E+01 4.40000E+00 1.32000E+01 6.60000E+00 1.32000E+01 8.80000E+00 1.32000E+01 1.10000E+01 1.32000E+01 1.32000E+01 1.10000E+01 1.32000E+01 8.80000E+00 1.32000E+01 6.60000E+00 1.32000E+01 4.40000E+00 1.32000E+01 2.20000E+00 1.32000E+01 6.29420E-06 1.32000E+01 1.32000E+01 1.49000E+01 1.10000E+01 1.49000E+01 8.80000E+00 1.49000E+01 6.60000E+00 1.49000E+01 4.40000E+00 1.49000E+01 2.20000E+00 1.49000E+01 6.29420E-06 1.49000E+01 1.32000E+01 1.66000E+01 1.10000E+01 1.66000E+01 8.80000E+00 1.66000E+01 6.60000E+00 1.66000E+01 4.40000E+00 1.66000E+01 2.20000E+00 1.66000E+01 6.29420E-06 1.66000E+01 1.32000E+01 1.83000E+01 1.10000E+01 1.83000E+01 8.80000E+00 1.83000E+01 6.60000E+00 1.83000E+01 4.40000E+00 1.83000E+01 2.20000E+00 1.83000E+01 6.29420E-06 1.83000E+01 1.32000E+01 2.00000E+01 1.10000E+01 2.00000E+01 8.80000E+00 2.00000E+01 6.60000E+00 2.00000E+01 4.40000E+00 2.00000E+01 2.20000E+00 2.00000E+01 6.29420E-06 2.00000E+01 2 3 1 3 4 1 4 5 1 5 6 1 6 7 1 7 8 1 8 9 1 9 10 1 10 11 1 11 12 1 12 13 1 13 14 1 2 15 16 3 3 16 17 4 4 17 18 5 5 18 19 6 6 19 20 7 7 20 21 8 8 21 22 9 9 22 23 10 10 23 24 11 11 24 25 12 12 25 26 13 13 26 27 14 15 28 29 16 16 29 30 17 17 30 31 18 18 31 32 19 19 32 33 20 20 33 34 21 21 34 35 22 22 35 36 23 23 36 37 24 24 37 38 25 25 38 39 26 26 39 40 27 28 41 42 29 29 42 7
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
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x Computational Framework • Gover
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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) •
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Exercise 2 - Wave propagation (4)
Page 36 and 37:
Exercise 3 - Impact on Cooling Towe
Page 41 and 42:
TITLE: PMAT04: motion of projectile
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sinon; tra2 = tra2 et ele; finsi; f
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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
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The mass returns at the initial pos
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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
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Note that we have also put the Pois
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BARI08 We study the effect of the t
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ENDPLAY *==========================
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BARI10 Same as BARI09 but compares
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The system is initially at rest, an
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CAST MESH TRID NONL LAGR $ $ Dimens
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Final deformation (with superposed
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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
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 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
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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
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
Page 231 and 232:
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
Page 241 and 242:
The final fluid velocities: The fin
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This example consists in a long 3D
Page 245 and 246:
GEOM FL38 flui Q4GS stru TERM COMP
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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
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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
Page 264 and 265:
as01=daller c1 c2 c3 c4 plan; * c1=
Page 266 and 267:
*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
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
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Example 15 - Bar Impact Revisited (
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* mesh=stru et symax et viti et lil
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The displacements are: 4
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c2=p1 d 8 p2; c3=p2 d 20 p3; c4=p3
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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
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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;
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The initial configuration (with par
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TITLE: Indentation problem. PROBLEM
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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
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The receiver signal in the coupled
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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);
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*----------------------------------
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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
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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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