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Geometric data: For the fluid domain, same as exercise 2 of Part II. The structure is a thin shell of 0.01 units thickness Materials For the fluid domain, same as exercise 2 of Part II. The structure material is a steel with the following characteristics: density 7800, 11 8 Young’s modulus 1.6× 10 , Poisson’s coefficient 1/3, elastic limit 1.05× 10 , and a bilinear elasto-plastic traction curve characterized by the following points 8 ( σε): , 1.05× 10 , 0.65626× 10 −3 10 , 1.6105× 10 , 1.00066. Numerical Solution TANK04 We use the FSA directive to prescribe the fluid-structure interaction along the external edge of the fluid domain. The input file is: TANK - 04 *----------------------------------------------------------------------- ECHO *CONV win CAST mesh *-----------------------------------------------------------Problem type DPLA NONL ALE *-----------------------------------------------------------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
Page 159 and 160: air = air1 ET air2 ET air3 ET air4
Page 161 and 162: COURBE 8 'P e_p12' ECROU COMP 1 lec
Page 163 and 164: 3D axisymmetric simulation: JWLS3G
Page 165 and 166: 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
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 215 and 216: ECHO RESU ALIC TEMP GARD PSCR SORT
Page 217 and 218: The displacements of the horizontal
Page 219 and 220: 0.00000E+00 7.11050E+00 1.06860E+00
Page 221 and 222: scen geom navi free !vect scco scal
Page 223 and 224: Alternative 2 Use multi-phase multi
Page 225 and 226: Geometric data: Complex shell-like
Page 227 and 228: At 0.5 ms, spurious (non-physical)
Page 229: Here is an example of the computed
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
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TITLE: Cavi51: steam explosion in a
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p10p=p10 plus p0; p11=0.75 0 1.7; p
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*opti donn 5; * vol3=vol2 syme plan
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si (nn2 ega 1); str2=ei; sinon; str
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The EUROPLEXUS input file reads: CA
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Some results: final pressure distri
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TITLE: PPLA04: unsteady flow throug
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liq2=daller c1 c2 c3 c4 plan; lag=l
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Some results: final fluid pressure:
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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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