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explicit dynamics
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EXPLICIT DYNAMICS
with
ANSYS/LS-DYNA
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Training Manual
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What is ANSYS/LS-DYNA?
• General purpose explicit dynamic finite element program
• Used to solve highly nonlinear transient dynamic problems
– Efficient for a wide range of contact types
– Advanced material modeling capabilities
– Robust for very large deformation analyses
• Seamless interface of the ANSYS and LS-DYNA programs
– Full integration of the LS-DYNA solver into ANSYS
– All pre and post-processing performed using standard ANSYS conventions
– GUI has look and feel of general ANSYS
– Supports capability of implicit - explicit sequential solutions
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Benefits of ANSYS/LS-DYNA
• Excellent combination of explicit and implicit solution technology
• ANSYS Pre and Post Processing:
– All explicit dynamic specific commands begin with EDxx prefix
– Customized ANSYS GUI for efficient execution of explicit problems
– Supports all ANSYS Solid Modeling and Boolean Operations
– Allows direct geometry import from IGES, Pro/E, ACIS, Parasolid, etc.
– Supports all ANSYS automatic meshing features
– APDL and design optimization can be used
– Supports all general postprocessing features and animation macros
– Specialized time-history postprocessing
• LS-DYNA Solver
– Fastest explicit solver in marketplace
– More features than any other explicit code
– Full version of LS-DYNA (with airbags, seatbelts, explosives, etc.)
– Full versions of LS-TAURUS and LS-POST postprocessors
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Applications of ANSYS/LS-DYNA
• Crashworthiness Analysis
– ANSYS/LS-DYNA:
• Full Car Crash
• Car Component Analyses
• Crash in ALL Vehicle Industries
– Car
– Truck
– Bus
– Train
– Ship
– Aircraft
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(continued)
Applications of ANSYS/LS-DYNA
• Manufacturing Process Simulation
• Deep drawing
• Hydro forming
• Superplastic forming
• Rolling
• Extrusion
• Stamping
• Machining
• Drilling
• Almost all forming processes have been simulated with LS-DYNA
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• Pipe whip (ANSYS News 3/93):• Impact of a pipe with a rotational
velocity of 50 rad/sec• CPU time (SGI Octane R12000) < 20
seconds
(continued)
Applications of ANSYS/LS-DYNA
• Contact/Impact– Drop test – Pendulum impact test– Jet engine fan
containment
• A wide range of contact types are possible
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PUNCH
DIE
BLANK
STATIC ‘QUASI’ STATIC DYNAMIC
Structural Problems Metal Forming Impact Problems
F = 0 F 0 F = ma
IMPLICIT METHODEXPLICIT METHOD
Comparison of Implicit and Explicit Methods
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Comparison of Implicit and Explicit Methods
Implicit Time Integration:
• Inertia effects ([C] and [M]) are typically not included
• Average acceleration - displacements evaluated at time t+t:
Linear Problems:– Unconditionally stable when [K] is linear
– Large time steps can be taken
Nonlinear problems:– Solution obtained using a series of linear approximations (Newton-
Raphson)
– Requires inversion of nonlinear stiffness matrix [K]
– Small iterative time steps are required to achieve convergence
– Convergence is not guaranteed for highly nonlinear problems
att
1tt FKu
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Comparison of Implicit and Explicit MethodsExplicit Time Integration
• Central difference method used - accelerations evaluated at time t:
where {Ftext} is the applied external and body force vector,
{Ftint} is the internal force vector which is given by:
• Fhg is the hourglass resistance force (see ELEMENTS Chapter) and Fcont is the contact force.
• The velocities and displacements are then evaluated:
intt
extt
1t FFMa
contacthgn
T FFdBF
int
tttttt tavv 2/2/
2/2/ ttttttt tvuu
where tt+t/2=.5(tt+ tt+ t) and tt- t/2=.5(tt- tt+ t)
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Explicit Time Integration (continued):
• The geometry is updated by adding the displacement increments to the initial geometry {xo}:
Comparison of Implicit and Explicit Methods
• Nonlinear problems:
– Lumped mass matrix required for simple inversion
– Equations become uncoupled and can be solved for directly (explicitly)
– No inversion of stiffness matrix is required. All nonlinearities (including contact) are included in the internal force vector.
– Major computational expense is in calculating the internal forces.
– No convergence checks are needed
– Very small time steps are required to maintain stability limit
ttott uxx
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t t crit 2
max
Stability Limit
Implicit Time Integration
• For linear problems, the time step can be arbitrarily large (always stable)
• For nonlinear problems, time step size may become small due to convergence difficulties
Explicit Time Integration
• Only stable if time step size is smaller than critical time step size
• Where max = largest natural circular frequency
• Due to this very small time step size, explicit is useful only for very short transients
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• Critical time step size of a rod
– Natural frequency:
• Critical time step:
– Courant-Friedrichs-Levy-criterion
– Δt is the time needed of the wave to propagate through the rod of
length l
Note: The critical time step size for explicit time integration depends on element length and material properties (sonic speed).
l
c=ω 2max with
ρ
Ec= (wave propagation velocity)
c
lt=Δ
Critical Time Step Size
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• ANSYS/LS-DYNA checks all elements when calculating the required time step. For stability reasons a scale factor of 0.9 (default) is used to decrease the time step:
• The characteristic length l and the wave propagation velocity c are dependent on element type:
clt 9.0
ρ
Ec=elementtheoflength=l
)-1ρ(
E
)LL(LmaxA2
)LLL(LmaxA
2
3214321
νc=
,,l=shells: triangular for ,
,,,l=
L1
L4
L3
L2
A
Shell elements:
Beam elements:
ANSYS/LS-DYNA Time Step Size
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File Organization
ANSYS /SOLU or LS-DYNAsolver taskreads jobname.K
ANSYS /PREP7 INTpreprocessingwrites jobname.K(standard LS-DYNA input)
ANSYS Resultsjobname.rstBinary Result FileEDRST,FREQ
ANSYS/POST26EDREAD, ...
LS-TAURUSLS-POST phs3
LS-TAURUS, LS-POST, ASCIIGLSTAT, MATSUM, …ASCII Result FilesEDOUT,File
ANSYS/POST1
ANSYS Resultsjobname.hisTime History DataEDHIST,Comp and EDHTIME,FREQ
LS-TAURUS & LS-POST phs1
LS-TAURUS & LS-POST binary d3plotBinary Result Filessimilar to jobname.rst
LS-TAURUS & LS-POST phs2
LS-TAURUS and LS-POST binary d3thdtBinary Result Filessimilar to jobname.his
ANSYS/POST26
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(continued)
File OrganizationDescription of ANSYS Files Generated During an ANSYS/LS-DYNA run:
Jobname.k• LS-DYNA input stream that is automatically generated upon execution of the ANSYS
SOLVE command.
• Contains all geometry, load, and material data that exists in the ANSYS database
• The file is 100% compatible with LS-DYNA version 950e
• File can also be manually generated using the EDWRITE command: Solution: Write Jobname.k
Jobname.rst• Explicit dynamics results file that is nearly
identical to standard ANSYS .rst
• Primarily used to review results in the general ANSYS postprocessor (POST1)
• Contains results at a relatively small number of time steps (e.g., 10 - 1000)
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(continued)
File OrganizationDescription of ANSYS Files Generated During an ANSYS/LS-DYNA run:
Jobname.his
• Explicit dynamics time history results files used in POST26
• Contains results for a subset of nodes and/or elements of the model
• Typically will contain results at significantly more time steps than Jobname.rst
Time history ASCII files
• Specialized files containing additional information about the explicit analysis
• User must specify which files are written before solution
• ASCII files include:
GLSTAT: Global energies
MATSUM: Material energies
SPCFORC: Nodal constraint reaction forces
RCFORC: Resultant contact interface forces
RBDOUT: Rigid body data
NODOUT: Nodal data
ELOUT: Element data
etc....
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(continued)
File Organization
• Since the LS-TAURUS and LS-POST postprocessors automatically come with ANSYS/LS-DYNA, the following two DYNA results files are easily generated during an explicit dynamic analysis:
• D3PLOT– LS-TAURUS and LS-POST binary results file
– Similar to ANSYS Jobname.rst
• D3DHDT– LS-TAURUS and LS-POST time-history results file
– Similar to ANSYS Jobname.his