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2.10000E+01 8.33330E+00 2.10000E+01 6.66670E+00 2.10000E+01 5.00000E+00 2.10000E+01 3.33330E+00 2.10000E+01 1.66670E+00 2.10000E+01 0.00000E+00 2.10000E+01 0.0 20.99 2 4 3 1 4 6 5 3 6 8 7 5 8 10 9 7 10 12 11 9 12 14 13 11 14 16 15 13 16 18 17 15 18 20 19 17 20 22 21 19 22 24 23 21 24 26 25 23 26 28 27 25 28 30 29 27 30 32 31 29 32 34 33 31 34 36 35 33 36 38 37 35 38 40 39 37 40 42 41 39 42 44 43 41 44 46 45 43 46 48 47 45 50 52 51 49 52 54 53 51 54 56 55 53 56 58 57 55 58 60 59 57 60 62 61 59 62 64 63 61 64 66 65 63 66 68 67 65 68 70 69 67 71 198 221 72 72 221 341 312 73 74 75 75 73 75 76 76 73 76 77 77 73 77 78 78 73 78 79 79 73 79 80 80 73 80 81 81 73 81 82 82 73 82 83 83 73 83 84 84 73 84 85 85 73 85 86 86 73 86 87 87 73 87 88 88 73 88 89 89 73 89 90 90 73 90 91 91 73 91 92 92 73 92 93 93 73 93 94 94 73 94 95 95 73 95 96 96 73 96 97 97 73 97 98 98 73 98 99 99 73 99 100 100 73 100 101 101 73 101 102 102 74 103 104 75 75 104 105 76 76 105 106 77 77 106 107 78 78 107 108 79 79 108 109 80 80 109 110 81 81 110 111 82 82 111 112 83 83 112 113 84 84 113 114 85 85 114 115 86 86 115 116 87 87 116 117 88 88 117 118 89 89 118 119 90 90 119 120 91 91 120 121 92 92 121 122 93 93 122 123 94 94 123 124 95 95 124 125 96 96 125 126 97 97 126 127 98 98 127 128 99 99 128 129 100 100 129 130 101 101 130 131 102 103 132 133 104 104 133 134 105 105 134 135 106 106 135 136 107 107 136 137 108 108 137 138 109 109 138 139 110 110 139 140 111 111 140 141 112 112 141 142 113 113 142 143 114 114 143 144 115 115 144 145 116 116 145 146 117 117 146 147 118 118 147 148 119 119 148 149 120 120 149 150 121 121 150 151 122 122 151 152 123 123 152 153 124 124 153 154 125 125 154 155 126 126 155 156 127 127 156 157 128 128 157 158 129 129 158 159 130 130 159 160 131 132 161 162 133 133 162 163 134 134 163 164 135 135 164 165 136 136 165 166 137 137 166 167 138 138 167 168 139 139 168 169 140 140 169 170 141 141 170 171 142 142 171 172 143 143 172 173 144 144 173 174 145 145 174 175 146 146 175 176 147 147 176 177 148 148 177 178 149 149 178 179 150 150 179 180 151 151 180 181 152 152 181 182 153 153 182 183 154 154 183 184 155 155 184 185 156 156 185 186 157 157 186 187 158 158 187 188 159 159 188 189 160 161 190 191 162 162 191 192 163 163 192 193 164 164 193 194 165 165 194 195 166 166 195 196 167 167 196 197 168 168 199 169 169 169 199 201 170 170 201 203 171 171 203 205 172 172 205 207 173 173 207 209 174 174 209 211 175 175 211 213 176 176 213 215 177 177 215 217 178 178 217 219 179 179 219 180 180 180 222 223 181 181 223 224 182 182 224 225 183 183 225 226 184 184 226 227 185 185 227 228 186 186 228 229 187 187 229 230 188 188 230 231 189 190 232 233 191 191 233 234 192 192 234 235 193 193 235 236 194 194 236 237 195 195 237 238 196 196 238 239 197 197 239 4
200 199 239 240 200 200 200 240 241 202 202 241 242 204 204 242 243 206 206 243 244 208 208 244 245 210 210 245 246 212 212 246 247 214 214 247 248 216 216 248 249 218 218 249 250 220 220 250 251 251 220 251 222 219 222 251 252 223 223 252 253 224 224 253 254 225 225 254 255 226 226 255 256 227 227 256 257 228 228 257 258 229 229 258 259 230 230 259 260 231 232 261 262 233 233 262 263 234 234 263 264 235 235 264 265 236 236 265 266 237 237 266 267 238 238 267 268 239 239 268 269 240 240 269 270 241 241 270 271 242 242 271 272 243 243 272 273 244 244 273 274 245 245 274 275 246 246 275 276 247 247 276 277 248 248 277 278 249 249 278 279 250 250 279 280 251 251 280 281 252 252 281 282 253 253 282 283 254 254 283 284 255 255 284 285 256 256 285 286 257 257 286 287 258 258 287 288 259 259 288 289 260 261 290 291 262 262 291 292 263 263 292 293 264 264 293 294 265 265 294 295 266 266 295 296 267 267 296 297 268 268 297 298 269 269 298 299 270 270 299 300 271 271 300 301 272 272 301 302 273 273 302 303 274 274 303 304 275 275 304 305 276 276 305 306 277 277 306 307 278 278 307 308 279 279 308 309 280 280 309 310 281 281 310 311 282 282 311 71 283 283 312 313 284 284 313 314 285 285 314 315 286 286 315 316 287 287 316 317 288 288 317 318 289 290 319 320 291 291 320 321 292 292 321 322 293 293 322 323 294 294 323 324 295 295 324 325 296 296 325 326 297 297 326 327 298 298 327 328 299 299 328 329 300 300 329 330 301 301 330 331 302 302 331 332 303 303 332 333 304 304 333 334 305 305 334 335 306 306 335 336 307 307 336 337 308 308 337 338 309 309 338 339 310 310 339 340 311 311 340 198 71 312 341 342 313 313 342 343 314 314 343 344 315 315 344 345 316 316 345 346 317 317 346 347 318 197 199 168 168 219 222 180 180 342 341 348 349 343 342 349 350 344 343 350 351 345 344 351 352 346 345 352 353 347 346 353 354 71 72 283 283 72 312 283 283 355 * added pmat: element 300, node 355 opti echo *--------------------------------------------------Geometric Complements COMP EPAI 2.5E-2 LECT 1 PAS 1 23 24 PAS 1 33 TERM GROU 5 'vessel' LECT 1 PAS 1 23 TERM 'shield' LECT 24 PAS 1 33 TERM 'liqu' LECT 34 35 64 PAS 1 291 298 PAS 1 299 TERM 'bull' LECT 36 PAS 1 63 TERM 'gas' LECT 292 PAS 1 297 TERM COUL jaun LECT liqu TERM roug LECT bull TERM turq LECT gas TERM rose LECT vessel shield TERM *------------------------------------------------------------Grid motion GRIL LAGR LECT 1 PAS 1 48 49 PAS 1 70 74 PAS 1 102 319 335 PAS 1 340 341 PAS 1 347 198 221 355 TERM EULE LECT 348 PAS 1 354 TERM ALE LECT 34 PAS 1 299 TERM AUTO AUTR *----------------------------------------------------------Material data MATE VM23 RO 7800. YOUNG 1.6E11 NU 0.333 ELAS 1.05E8 TRAC 2 1.05E8 .656256E-3 1.6105E10 1.00066 LECT vessel TERM VM23 RO 7800. YOUNG 1.6E11 NU 0.333 ELAS 1.05E8 TRAC 2 1.05E8 .656256E-3 1.6105E10 1.00066 LECT shield TERM FLUT RO 832. EINT 98.68 GAMM 7.15D0 CL 0.5 CQ 2.56 PB 2.71E5 PMIN 0. AHGF 0. ITER 2 ALF0 1. BET0 1. KINT 0 NUM 5 LECT liqu TERM 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 and 44:
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
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• The two waves f and g propagate
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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
Page 90 and 91:
Detailed Contents • Modeling the
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Modeling the fluid domain • The f
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Euler equations (3) • For a compr
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Time integration Each time incremen
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Time integration (5) 10. Account fo
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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
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
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COUR 7 'ro_a' ECRO COMP 2 ELEM LECT
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Analytical Conclusion: the pseudo-v
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SHOC13 Eulerian, very low pseudo-vi
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Analytical General conclusions: •
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The inverse path is not so straight
Page 133 and 134:
The input files (mesh generation by
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Geometric data: The calculation is
Page 137 and 138:
COUR 1 'dx_4' DEPL COMP 1 NOEU LECT
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TANK02 Eulerian solution: the whole
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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
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Universitat Politècnica de Catalun
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• 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
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: Exercise/Example 12 - Sloshing (7)
Page 209: Exercise/Example 12 - Sloshing (11)
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: 1.53330E+00 1.32310E+01 1.15000E+00
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
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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
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The final pressures in the rigid an
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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 (
Page 382 and 383:
* mesh=stru et symax et viti et lil
Page 384 and 385:
The displacements are: 4
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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
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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;
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 !
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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
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
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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 *=========
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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 *-----------------------
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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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