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LOADING: The indenter is pushed into the piece at constant imposed speed (linear displacement in time), until it reaches an indentation depth equal to the radius of the indenter. INITIAL CONDITIONS The indenter has an initial velocity equal to the imposed indentation velocity (to avoid an initial error in the energy balance). CALCULATION: The calculation is performed up to 50 ms. At the final time, the indenter has reached a depth equal to its radius. RESULTS: The computed resultant contact force is in good agreement with the approximate analytical solution up to an indentation depth equal to approximately 1/2 of the indenter radius. For larger indentations, the analytical (linear) solution is no longer valid. POST-TREATMENT Several animations of the computed results from this calculation are available on the EUROPLEXUS Consortium Web site. REFERENCES: The indentation problem is detailed in the following EDF document: N. Tardieu, B. Serre: "Indentation elasto-plastique d'un bloc par un indenteur spherique elastique", Code_Aster, Manuel de Validation, Report V6.04.506, December 2002. This calculation is detailed in: F. Casadei: "Validation of the EUROPLEXUS Pinball Impact-Contact Model on an Indentation Problem", Technical Note in press, July 2007. (available on the EUROPLEXUS Consortium Web site). Numerical Solutions INDE10 2D axisymmetric solution. The mesh generation file is: *%siz 50 opti echo 1; opti dime 2 elem qua4; p0 = 0 0; p1 = 0 -1.5; p2 = 1.5 -1.5; p3 = 1.5 0; pc = 0 0.5; p13 = 0.375 0; tol = 1.e-5; piece = dall (p0 d 40 p1) (p1 d 40 p2) (p2 d 40 p3) (p3 d 40 p0) plan; sphere = manu poi1 pc; opti trac psc ftra 'vl_jrc_inde10_msh.ps'; trac qual (piece et sphere); tout = piece et sphere; axe = tout poin droi p1 pc tol; base = piece poin droi p1 p2 tol; 2
cp = p0 d 10 p13; elim tol (piece et cp); c_p = piece elem appu larg cp; mesh = tout et axe et base et c_p; tass mesh; opti sauv form 'vl_jrc_inde10.msh'; sauv form mesh; list (nbno mesh); list (nbel mesh); fin; The input file is: INDE - 10 ECHO !CONV WIN NONL AXIS CAST mesh DIME PT2L 1682 Q42L 1694 PMAT 1 ZONE 2 TERM GEOM Q42L piece PMAT sphere TERM COMP EPAI 1.0 LECT piece sphere TERM COUL rose LECT piece TERM turq LECT sphere TERM MATE MASS 650.D0 LECT sphere TERM VM23 RO 7800 YOUN 2.1E11 NU 0.3 ELAS 5.E7 TRAC 2 5.E7 2.38095E-4 5.E7 1.0 LECT piece TERM OPTI PINS CNOR NCOL RCEL LINK COUP BLOQ 1 LECT axe base TERM 2 LECT base TERM DEPL 2 -1.D0 FONC 1 LECT sphere TERM PINB BODY DIAM 1.D0 LECT sphere TERM BODY MLEV 4 LECT c_p TERM FONC 1 TABL 2 0. 0. 2. 20. INIT VITE 2 -10. LECT sphere TERM REGI 'r_piece' RESU LECT c_p TERM 'r_base' RESU POIN LECT base TERM ECRI DEPL VITE FEXT TFRE 0.005 FICH ALIC TFRE 25.E-5 OPTI CSTA 0.5 LOG 1 CALCUL TINI 0. TFIN 50.E-3 FIN 3
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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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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
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The EUROPLEXUS input file reads: WO
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WOCO3D The mesh generation file (K2
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* RESU ALIC GARD PSCR * SORT GRAP *
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PT3L 16389 PT6L 504 NBLE 16389 NALE
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Final pressure distribution: 4
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BOUNDARY CONDITIONS: The vessel is
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as01=daller c1 c2 c3 c4 plan; * c1=
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*trac oeil cach fluidstr; *opti don
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cam3=cam31 et cam32; camb=cam1 et c
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log 1 dtml REZO GAM0 0.5 FLMP EPS1
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Final structure deformation: Final
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LOADING: The event is initiated by
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FLUT RO .242777373 EINT 6.865E5 GAM
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Final structure velocities: 6
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RESULTS: A paper by Bermudez and Ro
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The applied displacement and the co
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PROBLEM: A rigid tank with a deform
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The EUROPLEXUS input file reads: GR
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PROBLEM: A rigid tank with rigid or
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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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Page 373 and 374: Example: aircraft (3) Thanks to CPU
Page 375 and 376: Example 14 - Domains in 3D • Thic
Page 377: 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
Page 386 and 387: 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
Page 397 and 398: INFS02 We use a twice finer fluid m
Page 399 and 400: FREQ 1 GOTR LOOP 60 OFFS FICH AVI C
Page 401 and 402: Problem description: This example i
Page 403 and 404: *----------------------------------
Page 405: The final velocities: The final for
Page 408 and 409: *----------------------------------
Page 410 and 411: The final deformed mesh is: The fin
Page 412 and 413: pc = 4.5 -1 -1.5; pd = 5.5 -1 -1.5;
Page 414 and 415: The initial configuration (with par
Page 417: TITLE: Indentation problem. PROBLEM
Page 421 and 422: The final velocities: The final dis
Page 423 and 424: The input file is: INDE - 13 ECHO !
Page 425 and 426: The final displacement norm: The fi
Page 427 and 428: elim tol (piece et cp); c_p = piece
Page 429 and 430: 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
Page 439: 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 *=========
Page 459 and 460: REPETER BCL2 (2); REPETER BCL3 (2);
Page 461 and 462: *----------------------------------
Page 463 and 464: The tip displacement in the referen
Page 465 and 466: Problem description: This example r
Page 467 and 468: 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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Problem description: This example r
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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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