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European Laboratory for Structural
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Proceedings of a Course on: Numeric
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Programme of the Course 1. Introduc
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Credits & Acknowledgments • Struc
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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
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Scheme start-up and marching (2)
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Stress Update • To solve the equi
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Geometric non-linearities (3) Set u
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Essential Boundary Conditions Essen
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Exercise 0 - Ideal ballistics • M
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Exercise 0 - Ideal ballistics (5)
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Exercise 1 - Suspended mass (3) •
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Exercise 1 - Suspended mass (7) •
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Exercise 2 - Wave propagation (4)
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Exercise 3 - Impact on Cooling Towe
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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
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PMAT01E This test is similar to PMA
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Hence: 11 −8 ES 2× 10 ⋅ 2.5×
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The stress history is: Note that th
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Analytical TEST11 Same as TEST01 bu
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Comparison of natural vs. engineeri
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The total external forces at the tw
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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
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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
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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
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Mesh rezoning - motivations • Rez
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Giuliani’s automatic rezoning •
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• Analytical solution (self-simil
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Shock tube (6) • Influence of pse
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Exercise 2 - Explosion in air-fille
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Exercise 3 - Bubble expansion in a
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Exercise 4 - External blast on two
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Geometric data: The calculation is
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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
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The input files (mesh generation by
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Geometric data: The calculation is
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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:
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TUBE06 Lagrangian solution: the who
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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
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FSI Classification FSI for compress
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The 2-D plane case (2) Use geometri
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Classification of FSI algorithms
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The FSA algorithm (4) The case of s
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The FSCR algorithm Combination of F
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Application to Finite Volumes (3) 2
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Exercise 2 - Explosions in simple d
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Exercise/Example 3 - Wave propagati
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Exercise/Example 4 - CONT problem (
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Exercise/Example 5 - Explosion in a
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Exercise/Example 6 : Woodward-Colel
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Geometry: Exercise/Example 8 Steam
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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
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Exercise/Example 12 - Sloshing (3)
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Exercise/Example 12 - Sloshing (7)
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Exercise/Example 12 - Sloshing (11)
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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
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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
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- Page 278 and 279: Final structure velocities: 6
- Page 280 and 281: RESULTS: A paper by Bermudez and Ro
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- Page 284 and 285: PROBLEM: A rigid tank with a deform
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- 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
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- 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 306 and 307: Detailed contents • ALE descripti
- Page 308 and 309: Example 1 - Taylor bar impact 7 Exa
- Page 310 and 311: Example 3 - Coining Bilateral, Plan
- Page 312 and 313: Example 3 - Coining (5) Bilateral,
- Page 314 and 315: Example 4 - Explosion in a 2D box 1
- Page 316 and 317: Example 5 - Explosion in a corridor
- Page 318 and 319: Lagrangian contact • Non-permanen
- Page 320 and 321: Example 6a - Deep drawing A (2) Vel
- Page 322 and 323: Tube Crash (2) 35 Conventional cont
- Page 324 and 325: The Basic Pinball Method [Belytschk
- Page 326 and 327: Hierarchic Pinball Method (2) • H
- Page 328 and 329: Example 7 - Cable impact (2) l L v
- Page 330 and 331: Example 7b - Indentation (4) • 3D
- Page 332 and 333: Example 7b - Indentation (8) • Co
- Page 334 and 335: Why a Particle-Based Method? (2)
- Page 336 and 337: SPH Formulation (4) • To write th
- Page 338 and 339: Bird Strike [Courtesy of Snecma/CEA
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- Page 342 and 343: Spectral Elements (3) • To obtain
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- Page 346 and 347: Example 10 - Sediment valley • Ve
- Page 348 and 349: Example 12 - Matsuzaki valley • M
- Page 350 and 351: Time Step Partitioning (2) • Buil
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Treatment of links in partitioning
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Example 12a - Taylor bar impact rev
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Example 12a - Taylor bar impact rev
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⎧ M1U 1 = F1+ R1 ⎪ ⎨M U = F +
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Coupling at the Interfaces (7) ⎧
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Multiple scales in time • Use app
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Multiple scales in time (5) • The
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Multiple scales in space (3) •
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Example: simplified engine S 1 S 2
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Example: aircraft Material is linea
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Example 13 - Domains in 2D (2) •
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Example 14 - Domains in 3D (3) •
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Geometric data and materials: See s
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sler cam1 1 nfra 20 trac offs fich
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Geometric data and materials: See s
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POIN TOUS CHAMELEM FICH TPLO FREQ 1
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* p6=1.2E-2 0; p7=1.2E-2 1.0E-2; *
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COUR 1 'dx_P1' DEPL COMP 1 NOEU LEC
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p4s=p4 plus (0 0); tol=0.001; c1=p1
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The deformed final mesh at 4 ms wit
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The input file: INFS - 02 *--------
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The final mesh and pressures are: T
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ZONE 2 PMAT 2 Q4GS 3904 ECRO 858884
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The final deformed mesh is: The fin
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Problem description: This example i
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LECT die punch holder TERM MASS 0.1
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Geometric data and materials: See s
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geom !navi free line heou poin sphp
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An example of intermediate velociti
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LOADING: The indenter is pushed int
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The initial configuration (with par
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The reaction force is: Approximate
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The final velocities: 8
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The reaction force is: Approximate
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The initial configuration (with par
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The reaction force is: Approximate
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-5.10000E-01 1.33333E+00 2.00000E+0
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Some hardening quantity in the targ
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Final plastic streen in the target
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Final plastic strain in the target:
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Problem description: This example r
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The input file is: HOLE - 06 $ ECHO
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trac 2 1 AXES 1.0 'DISPL. [M]' yzer
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Problem description: This example r
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* fin lab3; nodf=c1p; * tpln=0.0 40
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The input file is: VALL - PS $ ECHO
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The final displacement norm in the
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VEC1=2. 0.; * P1=P11; R1=P13; S1=P1
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S3=P33 PLUS VEC1; * N1=2; N2=3; N3=
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CHPO2=CHPO2 / SCAL1; TSTAT2 . &BCL9
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AXTE 1E3 'Temps (ms)' *------------
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The final displacement field in the
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P9=40. 5. 5.; P14=20. 5. 5.; * BASE
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CLIM1=(P5 ET P6 ET P7 ET P8); CLIM1
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SUIT Post-treatment ECHO RESU ALIC
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The final displacement field in the
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tol=0.01E-3; * base=p0 d 5 p1; stru
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eli=stru elem i; si (ega j 0); sq42
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h3=8.1e-3; h4=16.2e-3; h5=24.3e-3;
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The characteristic displacements in
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The final yield stress field in the
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The mission of the Joint Research C