LS-DYNA ENVIRONMENT
Feb 2011
LS-DYNA Implicit Static Analysis
Introduction
Implicit Analysis Introduction
LS-DYNA ENVIRONMENTPage 1
Implicit Analysis Introduction
This introduction to the use implicit analysis in LS-DYNA focuses on linear and
non-linear static analysis for a range of different analysis types including.
• Simple static analysis
• Eigenvalue analysis
• Buckling analysis
• Frequency Response analysis
An implicit dynamic option is also available in LS-DYNA, however this is not
covered in this introduction at present.
Implicit Analysis Introduction
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Implicit vs. Explicit
Applications
Implicit
• Low rate dynamic analyses
• Linear and non-linear Static analysis
• Modal and vibration analysis
• Strength and buckling
• Springback
• Gravity loading & Pre-loading
Explicit
• High rate dynamic analyses
• Car crash
• Impact / Penetration problems
• Explosives
Advantages / Disadvantages
Implicit• Unconditionally stable (no timestep limit)
• Can be used for static analysis
• Relatively inexpensive for long duration analyses
• Often requires a large amount of memory
• Can have problems with strongly non-linear models
Explicit• Computationally fast
• Robust even for strongly non-linear models
• Conditionally stable (timestep limit)
• Expensive to conduct long duration
analyses
Implicit Analysis Introduction
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Implicit Analysis – Double Precision
When running an implicit analysis the Double Precision version of the LS-DYNA
executable is recommended.
ls971_s_R4.2.1_win32_p.exe Single Precision SMP version
ls971_d_R4.2.1_win32_p.exe Double Precision SMP version
mpp971_s_R4.2.1_win32_p.exe Single Precision MPP version
mpp971_d_R4.2.1_win32_p.exe Double Precision MPP version
Implicit Analysis Introduction
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Implicit Analysis – Time / Timesteps
In an implicit static analysis a termination time and a timestep are specified by the
user. However, for implicit static, time doesn’t have any actual meaning as the
analysis is trying to achieve static equilibrium at each timestep.
The terminology time is used however as Implicit and Explicit share a large number
of the same keywords within LS-DYNA.
Example – Model 1 and 2 will give the same results.
Model 1
Termination time = 1.0sec
Time step = 0.1sec
Model 2
Termination time = 100sec
Time step = 10sec
Forc
e
Time0.2 1.0F
orc
eTime20 100
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Implicit Analysis – Memory
Typically an implicit analysis requires more memory than an explicit analysis to
solve, because of this the analysis can run in one of two different modes.
In CoreIf the machine has sufficient memory and enough was specified when submitting
the job the analysis will run using the machine’s internal memory only.
Out of CoreIf sufficient memory was not specified when submitting the job the analysis will
run using scratch files stored on the hard disk.
In the ‘Out of Core’ mode the analysis will take a lot longer due to the amount of
additional time it takes to read and write data to the hard disk.
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Implicit Analysis – Memory
Which mode the analysis is running in can be determined from the otf file (d3hsp).
Search for ‘BEGIN’ to find the start of the first timestep.
BEGIN implicit statics time step 1
=================================================================
time = 2.00000E-01
current step size = 2.00000E-01
Solving linear system with real*8 BCSLIB-EXT
stiffness matrix data
-----------------------------------------------------------
number of equations = 113058
stiffness coefficients = 3.0 Mw
Memory Requirements: incore out-of-core
TOTAL for linear algebra = 30.5 10.7 Mw
TOTAL for entire job = 49.4 29.6 Mw
TOTAL available = 100.0 100.0 Mw
an INCORE solution will be performed
In Core Mode Out of Core ModeBEGIN implicit statics time step 1
============================================================
time = 2.00000E-01
current step size = 2.00000E-01
Solving linear system with real*8 BCSLIB-EXT
stiffness matrix data
--------------------------------------------------------
number of equations = 113058
stiffness coefficients = 3.0 Mw
Memory Requirements: incore out-of-core
TOTAL for linear algebra = 30.6 8.4 Mw
TOTAL for entire job = 49.4 27.2 Mw
TOTAL available = 40.0 40.0 Mw
an OUT-OF-CORE solution will be performed
*** Warning The stiffness matrix for this job is being factorized in out-of-core mode (using disk files), which may severely decrease performance. For best performance, increase available memory usingthe command line option memory=nnnM, where for this job nnn is at least 49400401 (adding an additional 10% is recommended).
Implicit Analysis Introduction
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Implicit Analysis – Control Cards
There are a number of *CONTROL_IMPLICIT cards that need to be set in order to
run an implicit analysis.
*CONTROL_IMPLICIT_GENERAL
This is used to turn on the implicit solver (IMFLAG=1) and to set the initial timestep (DT0).
If the timestep selected is too large then LS-DYNA may be unable to converge on a solution
and will error terminate. If this is the case then either the timestep has to be reduced or the
*CONTROL_IMPLICIT_AUTO card (see later slide), which allows LS-DYNA to automatically
adjust the timestep, can be used.
*CONTROL_IMPLICIT_SOLUTION
This is used to specify whether the analysis should be linear static or non-linear static
(NSOLVR).
In general for a non-linear analysis the default solution method (NSOLVR=2) is perfectly
adequate.
If contact is specified in the model then the analysis is non-linear regardless of the loading or
material properties.
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Implicit Analysis – Control Cards
*CONTROL_IMPLICIT_SOLVER
This is used to specify the linear equation solver used to perform the stiffness matrix inversion
(LSOLVR).
In general the default solver (LSOLVR=4) is perfectly adequate, however the BCSLIB-EXT
solver (LSOLVR=6) can also be useful if the model is large.
*CONTROL_IMPLICIT_EIGNEVALUE
This card is used to activate an eigenvalue analysis (modal analysis). For this type of analysis
only this control card and *CONTROL_IMPLICIT_GENERAL are required.
The NEIG value is used to specify the number of eigenvalues (modes) to be calculated. The
other options allow the user to specify particular frequency ranges to analyze.
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Implicit Analysis – Control Cards
*CONTROL_IMPLICIT_AUTO
This card is optional and is used to specify how LS-DYNA can adjust the timestep to achieve a
solution.
The initial timestep is specified on the *CONTROL_IMPLICIT_GENERAL card, and then a max
and min timestep are given on this card along with an optimum number of iterations (ITEOPT)
to solve each timestep and an allowable iteration window (ITEWIN).
When this card is activated, if LS-DYNA fails to converge for a particular timestep, rather than
error terminating it will try again using a smaller timestep size.
Also after an iteration has converged LS-DYNA will increase or reduce the timestep if the
number of iterations was less than or greater than the optimum ± iteration window.
See the *CONTROL_IMPLICIT_AUTO
section in the LS-DYNA Keyword Manual
for more details.
ITEOPT
Num
be
r o
f It
era
tio
ns
ITEOPT + ITEWIN
ITEOPT - ITEWIN
Non adjustment zone
Reduce timestep size
Increase timestep size
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Implicit Analysis – Element Formulation
Particular element formulations (ELFORM on the *Section card) are recommended
for implicit analyses to give the most accurate results.
Linear Analyses (including eigenvalue)
Solid Elements – Element formulation type 18
Shell Elements – Element formulation type 18 to 21
Non-Linear Analyses
Solid Elements – Element formulation type 2
Shell Elements – Element formulation type 16 or type 6
Rather than modifying an existing explicit model the *CONTROL_IMPLICIT_EIGENVALUE
card options ISOLID, IBEAM, ISHELL, ITSHELL can be used to automatically reset the
element type.
Note: As long as NEIG=0 on the *CONTROL_IMPLICIT_EIGENVALUE card LS-DYNA will
not run an eigenvalue analysis.
Implicit Analysis Introduction
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Implicit Analysis – Contact
Contact in an implicit analysis can be more problematic than in an explicit analysis.
This is generally due to the difficulty of detecting when parts actually come into
contact with each other given the larger timesteps used in an implicit analysis.
As such a smaller timestep size may be needed at the point when contact occurs to
correctly pick up the interaction between the parts (See *CONTROL_IMPLICIT_AUTO card).
In the contact definitions on optional card C there is the IGAP option for implicit
analysis. This option can help to improve convergence, however it does produce a
‘sticky’ contact which can resist the contact re-opening or sliding. This option is on
by default (IGAP=0 or IGAP=1)
Some general recommendations are;
• Set ORIEN=2 on the *CONTROL_CONTACT card.
• Possibly switch to non-automatic type contacts if convergence problems are occurring. (Note: The
SHLTHK option on the *CONTROL_CONTACT card may need to be set to allow for shell thicknesses)
• If possible have a small initial penetration between parts and use the IGNORE option on the
*CONTROL_CONTACT card to prevent LS-DYNA adjusting the geometry to correct for this.
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Implicit Analysis – Loading
In an implicit analyses it is better to use displacement loading rather than force
loading as it supplies a more stable behaviour, particularly with structures that could
buckle or suddenly collapse.
If a particular force loading is required then a load limiting spring can be added
between the node the displacement load is applied to and the actual loading device.
Loading Plate
Load Limiting
Spring
Displacement
Loading Node*Mat_Spring_Nonlinear_Elastic (S04)
Stiffness Curve
Forc
e
Displacement
Required Load
Required Load
Structure
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Implicit Analysis – Implicit-Explicit switching
On the *CONTROL_IMPLICIT_GENERAL card in addition to selecting an explicit or
implicit analysis there is also the option of an analysis that switches between the two
methods either automatically or according to a curve.
For IMFLAG = 4 or 5 When the implicit analysis fails to converge LS-DYNA will switch to explicit for a short time
interval and then return to the implicit analysis. This can help in cases with buckling or
sudden contacts as the short explicit step allows the analysis to get past these instabilities.
For IMFLAG = -n (n = load curve id)Using this option the user can specify a curve to control the implicit-explicit switching. The
curve is analysis method vs time (0=explicit, 1=implicit)
Time
Me
tho
d
1
0
Implicit Explicit Implicit
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Implicit Analysis – Dynamic Relaxation
Implicit can also be used for dynamic relaxation instead of the standard method (explicit +
damping) by setting IDRFLG = 5 on the *CONTROL_DYNAMIC_RELAXATION card.
The termination time for the implicit dynamic relaxation is set using the DRTERM option on the
*CONTROL_DYNAMIC_RELAXATION card.
The other *CONTROL_IMPLICIT cards are defined as normal, apart from the IMFLAG option on
the *CONTROL_IMPLICIT_GENERAL card which is set to zero (i.e. explicit for the main
analysis).
When using dynamic relaxation be aware of the SIDR option on the *DEFINE_CURVE cards
which is used to specify if a given curve is used in the main analysis or the dynamic relaxation.
Only the final state of the dynamic relaxation is written to the ptf (d3plot) file as time=0.0.
However the *DATABASE_BINARY_D3DRLF card can be used to output an rlf (d3drlf) file that
contains the data from the dynamic relaxation phase, this file can be viewed the same as the ptf
file.
For an implicit dynamic relaxation the DT/CYCL option on the *DATABASE_BINARY_D3DRLF
card specifies the number of implicit steps between outputs.
Implicit Analysis Introduction
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Example 1: Simple Cantilever Beam Analysis
A simple cantilever beam modelled in shell
elements is fixed at one end and a load
applied at the other.
Load (W) = 0.778N
Length (L) = 300mm
Width (b) = 40mm
Thickness (d) = 1mm
I (2nd Moment of Area)
= b d3 / 12
= 40 * 13 / 12
= 3.333
End deflection
= W L3 / 3 E I
= 0.778 * 3003 / 3 * 210e3 * 3.333
= 10.00mm
mm
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Example 2: Suspension Gravity Load Analysis
Modelling Points
• *CONTROL_IMPLICIT_GENERAL card used to specify an implicit analysis.
• Shell element type 16 specified on *SECTION_SHELL card.
*CONTROL_IMPLICIT_GENERAL
1 0.5 0 0 0 0 0 0
*SECTION_SHELL_TITLE
1mm
1 16 0.0 0 0.0 0.0 0 0
1.0 1.0 1.0 1.0 0.0 0.0 0.0
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Example 2: Suspension Gravity Load Analysis
An implicit dynamic relaxation is carried out to pressurize a tyre and then apply a
gravity load to the suspension system. *BOUNDARY_PRESCRIBED_MOTION
cards are used to hold parts of the model still during the dynamic relaxation phase.
The main explicit analysis then drives the suspension system forward over a kerb.
Initial
State
Tyre
pressurizing
Gravity
loading
Tyre and suspension system
model
Implicit dynamic relaxation stage Main explicit stage
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Example 2: Suspension Gravity Load Analysis
Modelling Points
• Implicit dynamic relaxation specified on the *CONTROL_DYNAMIC_RELAXATION
card.
• SIDR option on the *DEFINE_CURVE cards used to specify whether the curve is
used in the dynamic relaxation or the main explicit phase.
*CONTROL_DYNAMIC_RELAXATION
0 0.0 0.0 10.0 0.0 0 0.0 5
*DEFINE_CURVE_TITLE
DR Gravity
1 1 0.0 0.0 0.0 0.0 0
0.0 0.0
5.0000000 0.0
9.0000000 9810.0000
11.000000 9810.0000
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Example 2: Suspension Gravity Load Analysis
• LCIDDR option on the *LOAD_BODY card used to specify a separate gravity
loading curve for the dynamic relaxation phase.
• Various *BOUNDARY_PRESCRIBED_MOTION cards are used to fix parts during
the dynamic relaxation phase.
• *DATABASE_BINARY_D3DRLF card used to output the results from the dynamic
relaxation phase.
*LOAD_BODY_Z
3 0.0 1
*BOUNDARY_PRESCRIBED_MOTION_RIGID
10 3 2 100001 0.0 0 5.0 0.0
10 1 2 100001 0.0 0 0.0 0.0
*DATABASE_BINARY_D3DRLF
1
Implicit Analysis Introduction
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Example 3: Roll Cage Loading Analysis
A load of 25kN is applied to a simple shell model of a roll cage using a rigid plate.
As it is recommended to use displacement loading in implicit analyses a load limiting
spring is setup between the loading plate and the node on which the displacement
load is applied.
Loading
Plate
Load Limiting Spring
Displacement
Loading Node
Spring
Stiffness
Curve
Fo
rce
Displacement
25kN
-25kN
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Example 3: Roll Cage Loading Analysis
Modelling Points
• *CONTROL_IMPLICIT_AUTO option used to improve convergence.
• *BOUNDARY_PRESCRIBED_MOTION used to specify the displacement loading.
*CONTROL_IMPLICIT_AUTO
1 50 20 1.0E-4 1.0E-2 0.0
*BOUNDARY_PRESCRIBED_MOTION_NODE
7591 2 2 1 -1.0 0 0.0 0.0
7591 3 2 1 -1.0 0 0.0 0.0
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Example 3: Roll Cage Loading Analysis
If the load limit is increased to 50kN, the structure is unable to support the full load
and starts to collapse at a force of about 45kN.
Spring
Stiffness
Curve
Fo
rce
Displacement
50kN
-50kN
The displacement loading can also be
increased to see the collapsed shape.• Set *Boundary_Prescribed_Motion to 500mm
• Reduce initial timestep to 0.02sec
Force applied to the roll cage
(Spring Force)
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Example 4: Springback Analysis – Two Stage
In stage 1 an explicit forming analysis is carried out. At the end of the analysis the
final state (coords, stress, strain) for the formed part is written out to the ‘dynain’ file
using the *INTERFACE_SPRINGBACK_LSDYNA card. The ‘dynain’ file is written in
keyword format so it can used as input for further analyses.
Implicit Analysis Introduction
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Example 4: Springback Analysis – Two Stage
In stage 2 an implicit springback analysis is carried out to calculate the final deformed
shape of the part. The ‘dynain’ file containing the deformed geometry, stress and
strain data for the formed part is copied across from stage 1 and referenced as an
Include file in stage 2.
Initial State (from forming analysis) Final State (after springback)
Displacement Displacement
Von Mises Stress Von Mises Stress
Implicit Analysis Introduction
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Example 4: Springback Analysis – Two Stage
Modelling Points
• Additional constraints are added to the formed part in stage 2 to hold it during the
springback phase.
*BOUNDARY_SPC_NODE
4424 0 1 0 0 0 0 0
4392 0 1 1 1 1 1 1
4753 0 0 0 1 0 0 0
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Example 5: Springback Analysis – Seamless
In this example an explicit forming analysis and implicit springback analysis are
carried out in one single run using the *INTERFACE_SPRINGBACK_SEAMLESS
card and the *CONTROL_IMPLICIT_GENERAL card with IMFLAG=2.
Stresses at end of explicit forming stage
(time = 0.005)
Stresses at end of implicit springback stage
(time = 0.007)
Implicit Analysis Introduction
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Example 5: Springback Analysis – Seamless
Modelling Points
• Death time (DT) option used to turn off the contacts at the end of the forming stage
• Additional constraints added to hold the formed part during the springback phase
using the *INTERFACE_SPRINGBACK_SEAMLESS card.
*CONTACT_SURFACE_TO_SURFACE_ID
1Blank to Die
1 2 0 0 0 0 1 1
0.2 0.2 0.0 0.0 0.0 0 0.0 5.0E-3
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0 0.0 0 0.0 0.0 0 0 0
*INTERFACE_SPRINGBACK_SEAMLESS
1000 0 0 0
4424 1.0 0.0
4392 7.0 7.0
4753 3.0 0.0
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Eigenvalue Analysis
In order to carry out an Eigenvalue analysis the *CONTROL_IMPLICIT_GENERAL
and *CONTROL_IMPLICIT_EIGENVALUE cards need to be included in the model.
Shell element types 18-21 and solid element type 18 should be used in eigenvalue
analyses (ELFORM on the *Section card) to get the most accurate results.
A ptf (d3plot) file is output from the analysis, however the actual eigenvalue results
are stored in the ‘eigout’ and ‘d3eigv’ files.
Implicit Analysis Introduction
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Eigenvalue Analysis
The eigout file is a text file containing the numerical results of the analysis.
r e s u l t s o f e i g e n v a l u e a n a l y s i s:
problem time = 1.00000E-01
(all frequencies de-shifted)
|------ frequency -----|MODE EIGENVALUE RADIANS CYCLES PERIOD
1 3.639766E+03 6.033048E+01 9.601893E+00 1.041461E-012 2.182026E+04 1.477168E+02 2.350986E+01 4.253534E-02
MODAL PARTICIPATION FACTORS
MODE X-TRAN Y-TRAN Z-TRAN X-ROT Y-ROT Z-ROT
1 -0.353256E-12 0.662843E-12 -0.207698E-01 -0.451023E-17 0.148055E-07 0.363606E-182 -0.454327E-13 -0.102060E-13 0.831329E-13 0.209197E-07 0.391772E-16 -0.231701E-18
MODAL EFFECTIVE MASS
MODE X-TRAN Y-TRAN Z-TRANEff. Mass Accum. % Eff. Mass Accum. % Eff. Mass Accum. %
1 1.247900E-25 0.00% 4.393605E-25 0.00% 4.313862E-04 62.09%2 2.064130E-27 0.00% 1.041617E-28 0.00% 6.911077E-27 62.09%
MODE X-ROT Y-ROT Z-ROT Eff. Mass Accum. % Eff. Mass Accum. % Eff. Mass Accum. %
1 2.034215E-35 0.00% 2.192032E-16 0.00% 1.322093E-37 0.00%2 4.376333E-16 0.00% 1.534857E-33 0.00% 5.368548E-38 0.00%
Implicit Analysis Introduction
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Eigenvalue Analysis
The d3eigv file is a plot state file similar to the ptf file that allows the various mode
shapes to be visualized. Each state represents a particular mode and can be
animated in Oasys D3PLOT
The Modeshape animation
style is recommend for
viewing these results
Anim → Style → Modeshape
Implicit Analysis Introduction
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Example 6: Eigenvalue Analysis
A simple plate is modelled using shell elements with one edge fixed and the first
eight eigenvalue modes are calculated.
Implicit Analysis Introduction
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Example 6: Eigenvalue Analysis
Modelling Points
• *CONTROL_IMPLICIT_EIGENVALUE card used to define and eigenvalue
analysis.
• Shell element type 18 specified on *SECTION_SHELL card.
*CONTROL_IMPLICIT_EIGENVALUE
8 0.0 0 0.0 0 0.0 0 0.0
0 0 0 0 0
*SECTION_SHELL
1 18 0.0 0 0.0 0.0 0 0
1.0 1.0 1.0 1.0 0.0 0.0 0.0 0
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Eigenvalue Analysis – Stress output
The MSTRES option on the *CONTROL_IMPLICIT_EIGENVALUE card can be
used to calculate the stress based on the eigenvalue displacements for each mode
shape. This is only available for linear element (shell element type 18 and solid
element type 18).
This function is available from LS-DYNA 971 R.4.2.1
Implicit Analysis Introduction
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Example 7: Eigenvalue Analysis – Stress output
A simple plate is modelled using shell elements and fixed out the outer edge. The
first four eigenvalue modes calculated along with the resulting stresses.
You may need to change
from the shell element mid
surface to the top or bottom
surface to see the results
Implicit Analysis Introduction
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Example 7: Eigenvalue Analysis – Stress output
Modelling Points
• MSTRES option set on the *CONTROL_IMPLICIT_EIGENVALUE card.
*CONTROL_IMPLICIT_EIGENVALUE
4 0.0 0 0.0 0 0.0 0 0.0
0 0 0 0 1
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Intermittent Eigenvalue Analysis
There is the option to carry out an eigenvalue analysis at particular points during a
standard explicit or implicit analysis, with the resulting eigenvalues being affected by
the changing geometry and stress state of the model.
An example is a wire being stretched were the greater the tension in the wire the
higher the frequency of the resulting eigenvalues.
This type of analysis is activated by setting the NEIG option on the
*COTNROL_IMPLICIT_EIGNEVALUE card to a negative value and either
IMFLAG=1 or 6 on the *CONTROL_IMPLICIT_GENERAL card.
The negative NEIG value references a curve where each point on the curve is
X value = time at which to calculate the eigenvalues.
Y value = number of eigenvalues to calculate.
At each stage during the analysis when the eigenvalues are calculated a separate
eigout and d3eigv file are output.
Implicit Analysis Introduction
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Example 8: Intermittent Eigenvalue Analysis
In this example a simple plate is held at one edge and pulled in the x-direction. As
the plate is stretched the eigenvalues are calculated at 0sec, 0.05sec and 0.1sec
Time Mode 1 Mode 2
0.00 sec 9.60 Hz 23.51 Hz
0.05 sec 976 Hz 979 Hz
0.10 sec 1263 Hz 1270 Hz
Time = 0.0sec
Time = 0.1sec
Mode Shape Stress State
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Example 8: Intermittent Eigenvalue Analysis
Modelling Points
• Explicit with intermittent eigenvalue analysis specified on the
*CONTROL_IMPLCIT_GENERAL card
• *CONTROL_IMPLICIT_EIGENVALUE card references a curve (id 10) that define
the times for the eigenvalue analysis
*CONTROL_IMPLICIT_GENERAL
6 0.1 0 0 0 0 0 0
*CONTROL_IMPLICIT_EIGENVALUE
-10 0.0 0 0.0 0 0.0 0 0.0
0 0 0 0
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Example 8: Intermittent Eigenvalue Analysis
• Curve used to define when an eigenvalue analysis is carried out (x value) and the
number of modes to calculate (y value).
*DEFINE_CURVE
10 0 0.0 0.0 0.0 0.0 0
0.0 4.0000000
5.0000001E-2 4.0000000
9.8999999E-2 4.0000000
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Frequency Response Analysis
From LS-DYNA 971 R5 a frequency response analysis method will be available.
This can be used to calculate the spectrum of structural response for an applied unit
harmonic excitation.
*CONTROL_FREQUENCY_RESPONSE_FUNCTION
This card specifies the excitation and output nodes along with the frequency range to be
studied and also the level of damping to be added to the model.
The control cards for an eigenvalue analysis also need to be included in the model covering the
range for the frequency response analysis
(*CONTROL_IMPLICIT_EIGENVALUE, *CONTROL_IMPLICIT_GENERAL)
Note
From LS-DYNA 971 R5.1 onwards the keyword name will be changed
from - *CONTROL_FREQUENCY_RESPONSE_FUNCTION
to - *FREQUENCY_DOMAIN_FRF
Implicit Analysis Introduction
LS-DYNA ENVIRONMENTPage 41
Example 9: Frequency Response Analysis
A simple plate model is excited at one point and the response output at one of the
corner nodes.
Input Node
Output Node
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LS-DYNA ENVIRONMENTPage 42
Example 9: Frequency Response Analysis
Modelling Points
• *CONTROL_FREQUENCY_RESPONSE_FUNCTION cards used to specify the
excitation, frequency range, damping and response output.
• Number of modes specified on the *CONTROL_IMPLICIT_EIGENVALUE cards
are sufficient to cover the range of frequencies being investigated.
*CONTROL_IMPLICIT_EIGENVALUE
100 0.0 0 0.0 0 0.0 0 0.0
0 0 0 0 0
*CONTROL_FREQUENCY_RESPONSE_FUNCTION
131 0 -3 3 0 2000.0 0 100
1.0E-2 0 0 0.0 0.0
1 1 3 1
1.0 400.0 400 0 0 0
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Buckling Analysis
A buckling analysis can be carried out in LS-DYNA implicit using the
*CONTROL_IMPLICIT_BUCKLING card.
The model is setup as a static analysis with a load applied that is close to the
buckling load. LS-DYNA will initially solve this static loadcase and then analyze the
buckling loadcase using the results from the end of the static analysis to generate
the geometric stiffness terms.
It is recommended that the load applied in the static analysis is close to the buckling
load of the structure. This is to ensure that enough of a deflection is applied to the
structure to allow the buckling analysis to find a solution.
The eigenvalues written to the ‘eigout’ file represent the multipliers applied to the
base load (static analysis load) to achieve the various buckling modes. The buckling
mode shapes are written to the ‘d3eigv’ file.
*CONTROL_IMPLICIT_BUCKLINGThis card is used to specify the number of buckling modes to be output.
Implicit Analysis Introduction
LS-DYNA ENVIRONMENTPage 44
Example 10: Buckling Analysis
In this simple example a tube modelled in shell elements is pinned at each end and
loaded in compression. Once the implicit static loading (50kN) is complete a buckling
analysis is then carried out.
Length (L) = 5000mm
Radius (r) = 50mm
Wall Thickness = 5mm
I (2nd Moment of Area)
= π/4 * ( router4 - rinner
4)
= 0.7854 * (514 – 494)
= 785e3
Buckling Load (n=1)
= π2 E I / L2
= π2 * 210e3 * 785e3 / 50002 = 65.1kN
Buckling Load (n=2)
= 4 π2 E I / L2
= 4 * π2 * 210e3 * 785e3 / 50002 = 260.3kN
Mode 1Load = 50kN * 1.271
Load = 63.5kN
Mode 2Load = 50kN * 5.044
Load = 252.2kN
Implicit Analysis Introduction
LS-DYNA ENVIRONMENTPage 45
Modelling Points
• The *CONTROL_IMPLICIT_BUCKLE card is used to specify the number of
buckling modes to be calculated when the static analysis is finished.
• The *CONTROL_IMPLICIT_GENERAL card is used to setup the initial static
analysis.
• A base compression load of 50kN is applied to the end of the beam during the
static analysis.
Example 10: Buckling Analysis
*CONTROL_IMPLICIT_GENERAL
1 0.1 0 0 0 0 0 0
*LOAD_NODE_POINT
55852 1 1 -1.0 0
*CONTROL_IMPLICIT_BUCKLE
8
Implicit Analysis Introduction
LS-DYNA ENVIRONMENTPage 46
Appendix A – Element types in LS-DYNA Implicit
The following element types are available in implicit LS-DYNA 971.
Solid Elements
1, 2, 3, 4, 10, 13, 15, 16, 17, 18, 101-105
Shell Elements (2D Solids)
2, 4, 6, 10, 12, 13, 15, 16, 17, 18, 20, 21, 22, 25, 26, 27, 101-105
Beam Elements (2D shells)
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12
Thick Shell Elements
2, 3
Implicit Analysis Introduction
LS-DYNA ENVIRONMENTPage 47
Appendix B – Material types in LS-DYNA Implicit
The following material types are available in implicit LS-DYNA 971.
Solid Elements
1-7, 10-24, 26, 27, 30, 31, 33, 35, 36, 38, 41-53, 57, 59, 60-65,
70, 72, 73, 75-85, 87-89, 91, 92, 96, 98, 99, 100, 102-107, 109-112,
115, 124, 126-129, 141-145, 151, 152, 159, 161, 167, 173, 177-181,
183, 192, 193
Shell Elements
1-4, 6, 9, 18, 20-24, 27, 30, 32, 34, 36, 37, 41-50, 54, 55, 60, 76, 77,
81, 89, 91, 92, 98, 99, 103, 104, 106, 107, 116-118, 122, 123, 125,
133, 135-137, 181
Beam Elements
1, 3, 4, 6, 9, 18, 20, 24, 41-50, 100
Discrete Beam Elements
66-71, 74, 93-95, 97, 146, 196
Implicit Analysis Introduction
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Appendix B – Material types in LS-DYNA Implicit
Resultant Beam Elements
28-29, 166
Cohesive Elements
138, 184, 185
2D Solid Elements
1-7, 9, 12, 13, 18, 20, 21, 24, 26, 27, 41-50, 57, 60, 63, 77, 81, 82
103, 104, 106, 107, 167
Implicit Analysis Introduction
LS-DYNA ENVIRONMENTPage 49
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