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RESULTS: Results are in perfect agreement with the analytical solutions. POST-TREATMENT An animation of the computed results from this calculation is made. Numerical Solutions PMAT04 The mesh generation file (K2000): *%siz 100 opti echo 1; * opti titr 'PMAT - 04'; opti dime 2 elem qua4; opti trac psc; opti ftra 'pmat04_mesh.ps'; * p0=0 0; g = 9.80665d0; v0 = 100.; n = 1000; * * First projectile * phi0 = 30.d0; sinp = sin phi0; cosp = cos phi0; tfin = 2.d0 * v0 * sinp / g; dt = tfin / n; * par1 = manu poi1 (p0 plus (0 0)); * x y = coor p0; t = 0.0; i = 0; p2 = p0 plus (0 0); repe loop1 n; i = i + 1; t = t + dt; x = v0 * t * cosp; y = v0 * t * sinp - (0.5d0 * g * t * t); p1 = p2; p2 = x y; ele = manu seg2 p1 p2; si (i ega 1); tra1 = ele; sinon; tra1 = tra1 et ele; finsi; fin loop1; * * Second projectile * phi0 = 45.d0; sinp = sin phi0; cosp = cos phi0; tfin = 2.d0 * v0 * sinp / g; dt = tfin / n; * par2 = manu poi1 (p0 plus (0 0)); * x y = coor p0; t = 0.0; i = 0; p2 = p0 plus (0 0); repe loop2 n; i = i + 1; t = t + dt; x = v0 * t * cosp; y = v0 * t * sinp - (0.5d0 * g * t * t); p1 = p2; p2 = x y; ele = manu seg2 p1 p2; si (i ega 1); tra2 = ele; 2
sinon; tra2 = tra2 et ele; finsi; fin loop2; * * Third projectile * phi0 = 60.d0; sinp = sin phi0; cosp = cos phi0; tfin = 2.d0 * v0 * sinp / g; dt = tfin / n; * par3 = manu poi1 (p0 plus (0 0)); * x y = coor p0; t = 0.0; i = 0; p2 = p0 plus (0 0); repe loop3 n; i = i + 1; t = t + dt; x = v0 * t * cosp; y = v0 * t * sinp - (0.5d0 * g * t * t); p1 = p2; p2 = x y; ele = manu seg2 p1 p2; si (i ega 1); tra3 = ele; sinon; tra3 = tra3 et ele; finsi; fin loop3; * mesh=par1 et par2 et par3 et tra1 et tra2 et tra3; * tass mesh; trac qual mesh; * opti sauv form 'pmat04.msh'; sauv form mesh; * opti trac mif; trac tra2; fin; The EUROPLEXUS input file is: PMAT - 04 ECHO CONV win CPLA NONL LAGR CAST MESH DIME PT2L 3006 PMAT 3 FUN2 3000 ZONE 2 TERM GEOM PMAT par1 par2 par3 FUN2 tra1 tra2 tra3 TERM COMP EPAI 10.0 LECT par1 par2 par3 TERM 1.0 LECT tra1 tra2 tra3 TERM COUL roug LECT par1 TERM jaun LECT par2 TERM rose LECT par3 TERM vert LECT tra1 TERM bleu LECT tra2 TERM turq LECT tra3 TERM MATE FANT 1.0 LECT tra1 tra2 tra3 TERM MASS 1.0 LECT par1 par2 par3 TERM INIT VITE 1 86.6025404D0 LECT par1 TERM VITE 2 50.0000000D0 LECT par1 TERM VITE 1 70.7106781D0 LECT par2 TERM VITE 2 70.7106781D0 LECT par2 TERM VITE 1 50.0000000D0 LECT par3 TERM VITE 2 86.6025404D0 LECT par3 TERM CHAR CONST GRAV 0 -9.80665D0 LECT par1 par2 par3 TERM ECRI DEPL VITE FREQ 100 POIN LECT par1 par2 par3 TERM FICH ALIC TEMP FREQ 1 POIN LECT par1 par2 par3 TERM FICH ALIC FREQ 250 OPTI NOTE PAS UTIL log 1 CALCUL TINI 0. TEND 17.66200291D0 PASF 17.66200291E-3 NMAX 1000 *================================================================= 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 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: TITLE: PMAT04: motion of projectile
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
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Geometric data: The calculation is
Page 121 and 122:
SHOC01 Eulerian, “average” pseu
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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
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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
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
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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
Page 205 and 206:
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
Page 250 and 251:
BOUNDARY CONDITIONS: The step is en
Page 252 and 253:
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
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
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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
Page 274 and 275:
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
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
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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
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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
Page 386 and 387:
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
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
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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
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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
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
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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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