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The final bubble material mass fraction (giving an idea of the size and form of the bubble): An intermediate-time view of the liquid sodium mass fraction: 12
This example consists in a long 3D metallic pipe with a square cross section of 3× 3 units, sealed at both ends, containing a gas at room pressure. At the initial time, two “explosions” take place at the ends of the pipe, simulated by the presence of the same gas, but at a much higher initial pressure. The gas starts flowing through the pipe, but its motion is partly affected by the presence of internal structures within the pipe: a diaphragm (#1) with a square central hole near the first extremity, and two diaphragms (#2 and #3) that obstruct one half of the flow section, creating a sort of labyrinth, at the second extremity. All the pipe walls, and the internal structures, are deformable and characterized by an elastoplastic behaviour. The pressures and structural material properties are so chosen that very large motions and relatively large deformations occur in the structure. The whole model measures 18× 18× 18 units. The above figure shows the deformed shapes of the pipe, with superposed fluid pressure maps. The displacements are the real ones (not scaled up). Note the strong wave propagation effects, the partial wave reflections at obstacles, and the “ballooning” effect of the thin pipe walls in regions at high pressure. This is a severe test, among other things, for the automatic rezoning algorithms, which must keep the fluid mesh reasonably uniform under large motions. Details of the pressure drop across the various obstacles and of the deformation of diaphragms and pipe walls are also illustrated. It may be interesting for users to note that the EUROPLEXUS input file for this application consists of less than 60 lines of data. The mesh is prepared by a preprocessor and the two domains, structure and fluid, are meshed separately (but with matching nodes in this first example). Suitable FSI conditions are then computed by the code in a totally automatic way and without any user directive or intervention. 1
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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 (
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 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: The final fluid velocities: The fin
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
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Numerical Solution (flexible bottom
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! 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
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Some results: intermediate and fina
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Universitat Politècnica de Catalun
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ALE description of structures (2)
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Example 1 - Taylor bar impact (3) B
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Example 3 - Coining (3) Influence o
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• Tentative classification: Non-c
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Example 4 - Explosion in a 2D box (
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Example 6 - LOCA in the HDR (2) A -
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Examples of “Slow” Transient Co
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Examples of Fast Transient Impact
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Components of Contact-Impact Method
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Shortcomings • Slender or distort
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Example - Bar impact • (See Part
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Example 7b - Indentation (2) • 2D
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Example 7b - Indentation (6) • 3D
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Smoothed Particles Hydrodynamics (C
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SPH Formulation (2) • Basic idea:
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SPH impact [Courtesy of Samtech/Son
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PRGL01: Example 8 - SPH impacts (Co
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Spectral Elements • Motivation: l
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Spectral Elements (5) Convergence p
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Example 9 - Closed FE/SE interface
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Example 11 - Cylindrical valley 85
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Performance Optimization • All ex
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Time Step Partitioning (4) • Intr
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Time Step Partitioning (8) • Acti
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Treatment of links in partitioning
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Example 12a - Taylor bar impact rev
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Coupling at the Interfaces • Two
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Coupling at the Interfaces (5) MU T
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Coupling at the Interfaces (9) Time
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Multiple scales in time (3) • Exp
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Multiple scales in space • Furthe
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Multiple scales in frequency • So
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Example: power plant 133 Example: p
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Example: aircraft (3) Thanks to CPU
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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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*----------------------------------
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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
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The displacements in the case with
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European Commission DG Joint Resear
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