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This is a well-known reactor safety benchmark problem from the 1970’s/80s. Geometric data: Simplified sodium-cooled fast breeder reactor (axisymmetric) with internal shield. The roof is rigid. Materials The explosive bubble is made of a misture of molten fuel and fluid sodium (corium). The pool is filled by liquid sodium. An argon cover gas fills the region below the roof. The tank and inner shield are made of elasto-plastic steel. Numerical Solution CONT01 We use the standard single-component fluid material model. This means that the two fluid-fluid interfaces are treated as Lagrangian. Due to sliding of the sodium/argon interface along the tank, the FSA model may not be used alone to describe fluidstructure interactions (use is made of Lagrangian sliding locally). The input file is: CONT - 01 *----------------------------------------------------------------------- ECHO !CONV win *-----------------------------------------------------------Problem type AXIS NONL ALE lagc *-----------------------------------------------------------Dimensioning 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
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
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Page 228 and 229: TWIS07 We study the phenomenon by a
Page 232 and 233: DIME PT2L 293 PT3L 70 ZONE 3 ED41 3
Page 234 and 235: 2.10000E+01 8.33330E+00 2.10000E+01
Page 236 and 237: FLUT RO 2.4278E3 EINT 0. GAMM 0.75D
Page 238 and 239: The final mesh (colors indicate mat
Page 240 and 241: GRIL LAGR LECT stru TERM ALE LECT f
Page 242 and 243: The final bubble material mass frac
Page 244 and 245: Geometric data: Materials The explo
Page 246: Some results: global deformed mesh
Page 249 and 250: The well-known Woodward-Colella tes
Page 251 and 252: Numerical Solutions WOCO2D The mesh
Page 253 and 254: ECHO * RESU ALIC GARD PSCR * SORT G
Page 255 and 256: The EUROPLEXUS input file reads: WO
Page 257 and 258: This example is a patch of four sho
Page 259 and 260: CONT SPLA NX 1 NY 0 NZ 0 LECT symx
Page 261 and 262: TITLE: Cavi51: steam explosion in a
Page 263 and 264: p10p=p10 plus p0; p11=0.75 0 1.7; p
Page 265 and 266: *opti donn 5; * vol3=vol2 syme plan
Page 267 and 268: si (nn2 ega 1); str2=ei; sinon; str
Page 269 and 270: The EUROPLEXUS input file reads: CA
Page 271 and 272: Some results: final pressure distri
Page 273 and 274: TITLE: PPLA04: unsteady flow throug
Page 275 and 276: liq2=daller c1 c2 c3 c4 plan; lag=l
Page 277 and 278: Some results: final fluid pressure:
Page 279 and 280: PROBLEM: A deformable tank complete
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s1 = p5 d 4 p9; s2 = p9 d 16 p12; s
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The final pressure distribution in
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RESULTS: Linear theory predicts a 1
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The velocity at 200 ms is presented
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compute a reasonable initial distri
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FSA LECT 2 3 4 5 6 7 8 9 10 11 12 1
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$ $ $ 91 92 93 94 95 96 97 98 99 10
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The computed displacements of the t
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TITLE: OILCUP2: uniformly accelerat
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2526 2527 2528 2529 2530 2531 2532
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Intermediate and final oil mass fra
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Detailed contents • ALE descripti
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Example 1 - Taylor bar impact 7 Exa
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Example 3 - Coining Bilateral, Plan
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Example 3 - Coining (5) Bilateral,
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Example 4 - Explosion in a 2D box 1
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Example 5 - Explosion in a corridor
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Lagrangian contact • Non-permanen
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Example 6a - Deep drawing A (2) Vel
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Tube Crash (2) 35 Conventional cont
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The Basic Pinball Method [Belytschk
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Hierarchic Pinball Method (2) • H
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Example 7 - Cable impact (2) l L v
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Example 7b - Indentation (4) • 3D
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Example 7b - Indentation (8) • Co
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Why a Particle-Based Method? (2)
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SPH Formulation (4) • To write th
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Bird Strike [Courtesy of Snecma/CEA
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Example 8 - SPH impacts (2) SONA01:
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Spectral Elements (3) • To obtain
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Spectral Elements (7) Coupling betw
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Example 10 - Sediment valley • Ve
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Example 12 - Matsuzaki valley • M
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Time Step Partitioning (2) • Buil
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Time Step Partitioning (6) • This
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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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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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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 initial configuration (with par
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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
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