Implicit Analysis Intro 02-2011

LS-DYNA ENVIRONMENT

Feb 2011

LS-DYNA Implicit Static Analysis

Introduction

Implicit Analysis Introduction

LS-DYNA ENVIRONMENTPage 1


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 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 – 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 – 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



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.



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 – 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.




*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.




*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



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 – 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.



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



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



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.



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



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.


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




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




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




• 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



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




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




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)



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.




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




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



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)



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



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.



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%



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



Example 6: Eigenvalue Analysis

A simple plate is modelled using shell elements with one edge fixed and the first

eight eigenvalue modes are calculated.



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



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



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



Example 7: Eigenvalue Analysis – Stress output

Modelling Points

• MSTRES option set on the *CONTROL_IMPLICIT_EIGENVALUE card.


4 0.0 0 0.0 0 0.0 0 0.0

0 0 0 0 1



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.



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




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


6 0.1 0 0 0 0 0 0


-10 0.0 0 0.0 0 0.0 0 0.0

0 0 0 0




• 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



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



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



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.


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



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.



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



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


1 0.1 0 0 0 0 0 0

*LOAD_NODE_POINT

55852 1 1 -1.0 0

*CONTROL_IMPLICIT_BUCKLE

8



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



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



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



Contact Information

UK:

Arup

The Arup Campus

Blythe Valley Park

Solihull, West Midlands

B90 8AE

UK

T +44 (0)121 213 3399

F +44 (0)121 213 3302

[email protected]

For more information please contact the following:

www.arup.com/dyna

China:

Arup

39/F-41/F Huai Hai Plaza

Huai Hai Road (M)

Shanghai

China 200031

T +86 21 6126 2875

F +86 21 6126 2882

[email protected]

India:

nHance Engineering Solutions Pvt. Ltd (Arup)

Ananth Info Park

HiTec City

Madhapur

Hyderabad - 500081

India

T +91 (0) 40 44369797 / 8

[email protected]

Implicit Analysis Intro 02-2011

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Transcript of Implicit Analysis Intro 02-2011