Download full text - ELSA - Europa

More documents

Recommendations

Info

⎧ M1U 1 = F1+ R1 ⎪ ⎨M U = F + R ⎪ CU ⎩ + CU = 2 2 2 2 1 1 2 2 0 Coupling at the Interfaces (3) • It may be useful to split the problem into a free and a link problem by an additive decomposition. Define: 1 U − i,free Mi Fi so that: U −1 i = U i,free + U i,link U M R i,link i i • The problem becomes: Free problem (involves all dofs) ⎧ M1U ⎪ 1,free = F1 ⎨ M U ⎪⎩ = F 2 2,free 2 ⎧ MU 1 1,link = R1 ⎪ ⎨MU = R ⎪ ⎪⎩ CU 2 2,link 2 1 1+ CU 2 2 = 0 Link problem (involves only dofs on interface) 111 ⎧ M1U ⎪ 1,free = F1 ⎨ M 2U ⎪⎩ 2,free = F2 Coupling at the Interfaces (4) ⎧ MU 1 1,link = R1 ⎪ ⎨MU 2 2,link = R2 ⎪ CU ⎪⎩ + CU = 1 1 2 2 0 • The free problem may be solved directly to obtain U i,free • To solve the link problem, we introduce as usual Lagrange multipliers and associated reaction (interaction) forces: so that: R i = C Λ 1 1 2 2 T i T MU 1 1,link −C1 Λ= 0 T MU 2 2,link −C2Λ= 0 CU + CU = 0 Unknowns: U Λ an d U , i,link i 112 56
Coupling at the Interfaces (5) MU T −C Λ= 0 1 1,link 1 T MU 2 2,link −C2Λ= 0 CU 1 1+ CU 2 2 = 0 • We express the unknown velocities U in terms of the i accelerations. By using CD time integration scheme (recall Part 1) n ∆t n U = U + ( U + U) 2 • By introducing the velocity predictor (or mid-step velocity): p n t n n 12 U U + ∆ U ≡U + 2 one gets: p t U ∆ = U + U 2 • By splitting the acceleration this becomes: p t t U U ∆ ∆ = + U free + U link 2 2 113 p t t U U ∆ ∆ = + U free + U 2 2 link Coupling at the Interfaces (6) T MU 1 1,link −C1 Λ= 0 T MU 2 2,link −C2Λ= 0 CU + CU = 0 1 1 2 2 • We see therefore that also the velocities may be formally split into a free and a link part. By defining: p t U free U ∆ + U ∆t (known) → U free link U link 2 2 so that: U = U + U free link one gets for the link problem: ⎧ T ⎪MU 1 1,link −C1 Λ= 0 ⎪ T ⎨MU 2 2,link −C2Λ = 0 ⎪ ∆ t ∆ t ⎪− CU − CU = CU + CU ⎩ 2 2 1 1,link 2 2,link 1 1,free 2 2,free 114 57
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 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 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: Coupling at the Interfaces • Two
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

Create successful ePaper yourself

Delete template?

Save as template?