9-finite element analytical tecniques

8/12/2019 9-Finite Element Analytical Tecniques

1/89

FiniteElementAnalytical

StructuralDesign


2/89

Slide2 of88

Three types of models are used to simulate vehicle structures

Lumped Parameter (LP) models Hybrid models

FE models

Heuristic beam models and

Continuum mechanicsbased models which use beam, solid and shell

elements

Most detailed models (LP or FE) are approximations of a highly

complex nonlinear system subject to large and unstable elastic

plastic deformations


3/89

Slide3 of88

1970 1985:

Essentially one of genesis and growth, develop some understandingof an extremely complex structural mechanics problem

numerical techniques to simulate deformations, including folding

and buckling of a car structure during first 50 to 100 ms of a crash

test

Solutions obtained by using beam element models in conjunction

with nonlinear joint formulations

Solutions based on first principles by modeling the car body as acontinuum, and thus, automating the task of attributing discretized

stiffness values to the structural com onents


4/89

Slide4 of88

Discretized stiffness based on

quasistatic beam element formulation

implicit FE techniques

finite difference methods

implicit/explicit FE formulations

Explicit FE time integration

First crash model simulated a headon collision of a vehicle fronts ruc ure w a r g wa , us ng mp c so ver

Development of an implicitexplicit integration FE PAMCRASHcode, applied to analyze the response of an Apillar, and next to the

r g ron quar er o a un o y passenger ve c e s ruc ure The quasistatic analysis was accomplished by an iterative

incremental force/displacement analysis


5/89

Slide5 of88

Some features of the solvers:

Combined time integration with shell elements

nodetosegment contact force transmissions

ane s ress e as op as c y

Continuum approach remained mainly in research

As there is high degree of interaction between the different panels

of an automobile structure, it is necessary to consider the full

vehicle in a single model to predict the energy absorption of the

individual parts during a crash.

The inability to fulfill this requirement brought the continuum

approach and thus, the finite element approach, to automotive


6/89

Slide6 of88

1985 to present:

Breakthroughoffiniteelementmethodsinthemid1980s VectorizedSuperComputers+explicitFE

Fromaninitialvelocityof13.4m/s

2,272shell+106beamelements

as c as ccons u vemo e w s ra n ar en ng ors ee metalbehavior

TablefromPriyaPrasad(2005)


7/89

Slide7 of88

MercedesBenz, Porsche, BMW, Audi, Volkswagen, Opel

and Ford of Germany

Objective :investigatethepotentialofthefiniteelement

methodtopredictthebucklingbehaviorofanautomotivecarbodyduringanovernightcomputersimulation

Accuracy:sufficientlyrealisticpredictionofthevehicles

deformation mode

Efficiency:abilityoftheanalysttoprovideresultwithinreasonable

deadlines


8/89

Slide8 of88

ESIofParisandEschborn VWpolo

mo e s zeso , to , s e e ements

use

of

explicit

finite

element

methods

due

to

the

g v g

implicitintegrationtechniquestosolvethese

Usingexplicitelementbyelementtechniques


9/89

Slide9 of88

Vectorization of the software PAMCRASH and CRASHMAS

for ESI and IABG, respectively) and consequentoptimization with respect to the particular features of the

ray ar ware u ma e y a owe or run mes a

satisfied the original FAT overnight performance criterion.

Since 1986 the develo ment of simulation technolo for

crashworthiness industrial rather than technological

In the late 1980s, numerical simulation was almost

exclusively a research activity involving very few engineers,and hardly affecting the design cycle


10/89

Slide10 of88

Numerical simulations have taken up a substantial part of the

increased workload of crashworthiness engineers

Numerical simulations have not lowered the normal workload of

prototypes)

Simulation: rapidly performing important simulations in parametric

s u es or qu c e m na on rom pro o yp ng ose es gns w c

have a high probability of not satisfying the testing criteria

Mainstreamuseofnumericalsimulationasadirectsupportforthe

designteamrequirestherapiddevelopmentoffullvehicleFEmodelsattheveryearlystagesofthedesign(bottleneckto

analystsworkplan)


11/89

Slide11 of88

When a safet related roblem a ears in a rotot e

during a test, it is simulation that allows for diagnosisof the cause of the problem and selection of an

amount of time.

In addition to structural analysis, occupant simulationis increasingly performed using finite element models

The extensive use of numerical simulation has enabled

safer cars and trucks in less time without acorresponding increase in test facilities


12/89

Slide12 of88

nonlinearproblemsinstructuralmechanics

stampedthinshellpartsandsubsequently

assembled b various weldin and fastenin

techniques

strengthgrades,aluminiumand/orcomposite

materials


13/89

Slide13 of88

Structure experiences high impact loads which produce localized plastic.

Can ultimately lead to large deformations and rotations with contact andstacking among the various components.

Deformations initiall involve wave effects associated with hi h stresses.

Once these stresses exceed the yield strength of the material and/or itscritical buckling load, localized structural deformations occur during a few

wave transits in the structure., .

Of particular interest here are structural integrity and associatedkinematics and stacking of components, forces transmitted through thevarious members, stresses, strains, and energy absorption.

Crash event may be considered as a low to mediumdynamic event (5100 mph), persisting for a short duration

of 100200 ms

,


14/89

Slide14 of88

Solvesnumericallyasetofnonlinearpartialdifferentialequationsofmotioninthespacetimedomain

Coupledwithmaterialstressstrainrelations

conditions

Solutionfirstdiscretizestheequationsinspacebyormu at ngt epro em nawea var at ona orm

andassuminganadmissibledisplacementfield

Yieldssetofsecondorderdifferentiale uationsintime

Systemofequationsissolvedbydiscretizationinthetimedomain


15/89

Slide15 of88

Techni ues to solve e uations:

Technique is labeled implicit if the selected integration

parameters render the equations coupled, and in thiscase e so u on s uncon ona y s a e.

If the integration parameters are selected to decouple

it is conditionally stable.

FE simulation for structural crashworthiness by explicit

solvers appears to be first introduced by Belytschko Later, Hughes discussed the development of mixed

.


16/89

Slide16 of88

The explicit FE technique solves a set of hyperbolic wave equations

in the zone of influence of the wave front, and accordingly does not

require coupling of large numbers of equations.

,

provide a solution for all coupled equations of motion, which

require assembly of a global stiffness matrix. e me s ep or mp c so vers s a ou wo o ree or ers o

magnitude of the explicit time step.

For crash simulations involving extensive use of contact, multiple

material models and a combination of nontraditional elements,explicit solvers are more robust and computationally more efficient

than implicit solvers.


17/89

Slide17 of88

Ma+Cv+Kx=F

SolveforxusinginversionofK

SolveforausinginversionofMmatrix

matrix

IfK(x),iterationsareinvolved

,becomeslumped,andinversionistrivial

Inte rationisdoneusin

(BackwardEulerMethod)

Unconditionallystable

CentralDifferenceorForwardEuler

ConditionallyStable

Sincewesolveforx,itisimplicitandlessernumberof

iterations

Canbeusedonlyforshortdurationsimulations

Tinytimesteps


18/89

Slide18 of88


19/89

Slide19 of88


20/89

Slide20 of88


21/89

Slide21 of88

Solutionproceeds tothenextstepandhencefornext


22/89

Slide22 of88

Explicit integration method a numerical technique to integrate a

system of ordinary differential equations from the spatial

discretization of a continuum

expressed at a moment in time where the displacements of all

spatial points are already known

Central differencing technique allows the analyst to determine the

displacements at the next timestep and repeat the process.

Since the displacements are known at the time for which thedynamic equilibrium of the system is solved, this process requires

the only inversion of the mass matrix, M.


23/89

Slide23 of88

If a lumpedmass approach is used, the mass matrix is diagonal and no

matrix inversion is necessary

If carefully implemented, explicit integration is second order accurate. It is

the elementbyelement nature of the explicit algorithm that allows for

the best characterization of this solution technique

Since stresses are calculated in each element separately from the

corresponding nodal displacements and/or velocities, each timestepsimulates the effect of the loads on one side of the element upon the

opposing sides, thus representing the stress wave propagation through

the element

T e

on y

raw ac s

o

t e

exp icit

a gorit m

are

t e

con itiona

sta i ity

andtheclearinabilityofthemethodologytotreatstaticproblems.


24/89

Slide24 of88

Courants condition: Timesteps determined by dividing thee emen c arac er s c eng roug e acous c wave spee

through the material of which the element is made.For typical automotive applications using mild steel elements (c=

,analysis time step of 1 microsecond.

Analysis timestep should not exceed the smallest of all element

The re uirement is e uivalent to sa in that the numerical timestep of the analysis must be smaller than, or equal to, the timeneeded for the physical stress wave to cross the element.

Due to this restriction, it is clear that explicit methods are best

su te to treat pro ems o s ort urat on an t us, g oa ngvelocity and problems of a highly nonlinear nature that requiresmall timesteps for accuracy reasons.


25/89

Slide25 of88

4noded Belytschko and Tsay shell

Bilinearly interpolated isoparametric element, the lowest order ofinterpolation functions available is used

integration point in the center of the element

Elastoplastic bending problems is possible by defining userdefinednumber of integration points through the thickness of the element,

all placed along the element normal in the element center

Faster to compute four underintegrated elements than a single

fully integrated element with four integration points : symmetries inthe straindisplacement matrix that arise in the case of under

inte rated finite elements


26/89

Slide26 of88

Drawback of the underinte ration :number of zero

energy or hourglass modes Simplifications in the evaluation of the element strain

sp acemen ma r x, cer a n e orma on mo es resuin a zerostrain calculation, and consequently, no

stresses and nodal forces are calculated Nodal velocities can easily and rapidly diverge towards

infinity as long as they remain parallel to the hourglass

element)

Hour lass instabilit is the ma or drawback


27/89

Slide27 of88

Hour lass instabilities revented b the use of

perturbation hourglass resistance techniques Detecting the presence of the hourglass mode in the

element deformation pattern, and consequently, applying

an external force field to ensure that the corresponding

velocities and or dis lacements remain bounded

It cannot be stressed enough that the hourglass forces

result from an artificial external force field and do not form

equi i rium wit stresses in t e materia Consequently they remove kinetic energy from the


28/89

Slide28 of88

techniquesarechoseninawaytooptimize

Compromisingthematerialstiffnessinthe

Continuityoftheoutofplanedisplacement

acrosstheelementboundaries

l d f


29/89

Slide29 of88

A corotational local system for objectivity.

All element strains and stresses are calculated in a localreference system following element normal and theelement 12 side.

No spurious strains and stresses are calculated if theelement is subjected to large rigid body rotational motions.

small shear deformations. In practice, this is not a problemfor solving crashworthiness problems since no largemembrane shear deformations occur in sheet metal.

It may cause hourglass modes to appear due toexaggerated rotations of the stress tensor.

Slid 30 f 88


30/89

Slide30 of88

Element formulation is based on a strict uncoupling of membrane and

bending effects.

The membrane strains and stresses calculated as resulting from the loads

parallel to the local xy planeplane stress element.

Formulation limited to small bending strains since no thickness changes

considered.

Bendin stresses result from loadin alon the local zaxis and bendinmoments around the local x and yaxes.

The bending strains in all integration points away from the element mid

lane are calculated usin the ReissnerMindlin e uations and thus the

assumption is made implicitly that the element is flat. All four nodes are in the same plane and a single normal is valid for the

entire surface of the element.

Slid 31 f 88


31/89

Slide31 of88

Bel tschko and Tsa shell element is thus the sumof a plane stress membrane element and aReissnerMindlin plate element.

.

In warped element, loads parallel to the local xy

missed by the current element formulation.

Warped Belytschko and Tsay elements severely

un erest mate t e structure s en ng st ness. This is why this element fails the twisted beam

Slide 32 of 88


32/89

Slide32 of88

Essentially, plastic hinges develop very rapidly over the full sectiono e n roug y mm s ee me a o owe y arge r g o y

rotations of the parts between the hinges. Objectivity of the element is thus the primary requirement, and this

.

As long as the time for the development of the individual plastichinges is small compared to the duration of the global event, the

bending stiffness plays a less important role. The small membrane deformation behavior and buckling behavior

of the sheet metal is in line with the assumptions of the Belytschkoand Tsay shell.

r angu ar

e ements

were

o ta ne

y

ar trar y

co aps ng

two

nodesofafournodeshellelement.

Slide 33 of 88


33/89

Slide33 of88

The lanestress lasticit attheindividualintegrationpointsoftheelementisbasedonthemembranecomponentsofthestresstensoronly

2

xx+2

yyxxyy+32

xy 2

y

strainandthestrainrate

Caremustbetakentoaccountforthenatureof

theplasticdeformationandthusaflowofthematerialatconstantvolumemustbesimulated.

Slide 34 of 88


34/89

Slide34 of88

Usually, a Newton iteration technique involving theunknown throughthe thickness strain in the element is

performed. A noniterative, radial return approach will lead to a

deformation pattern involving a nonzero volumetric plasticstrain.

Poisson coefficient of the material during plasticdeformation equal to the elastic Poisson coefficient

Computertimesaving approach implemented in mostexplicit finite element codes and approximation do not

affect much results of crashworthiness simulations(indication for small deformation nature of the problem)

Slide 35 of 88


35/89

Slide35 of88

were nodetosegment contacts:

physical surfaces, a socalled masterslave contact

definition exists If they are on the same physical surface, a so

called single surface contact definition exists

where the nodes of the surface are not permittedto penetrate the shell elements that they define

Slide 36 of 88


36/89

Slide36 of88

the spatial discretization of the structure

elements that are generated in the model as soon

as a enetration is detected and automaticalldeleted from the model as soon as that very

penetration has been annihilated

Contact stiffness controlled by the user, who

multi lies this default valuewith a enalt factor

Slide37 of88


37/89

Increase the penalty factor to avoid deep penetrations results in

unrealistic simulation results

An upper bound for stiffness required to maintain stability of

A contact spring stiffness is so decided that it operates at the

stability limit and will stop penetration of the slave node throughe mas er segmen n a s ng e mes ep.

The penetration in a typical crash analysis where nodal velocities

are of the order of 10 m/s is:

10*0.000001=0.000010m=0.01mm Safetyfactorof10withrespecttothestabilitydoesnotaffect

Slide38 of88


38/89

The main problems in contact algorithms originate in the nodetosegmen na ure o e mo e e n on, as we as n e searc

algorithms that define which nodes are in contact with whichsegments

of detecting edgetoedge or edge to segment penetrations.

For each slave node

Find the nearest master node n e neares mas er segmen connec e o s mas er no e

Works well for smooth surfaces

Not for irregular meshes and high curvatures

time consuming part of the explicit solvers for many years, evenafter the introduction of the bucket sort algorithms

Slide39 of88


39/89

Earl searchal orithmsdetectedanearestmasternodefor

eachslavenodeandselectedasinglenearestmaster

segmentfromallsegmentsconnectedtothenearest

mas erno e.

Analgorithmthatworksverywellforthesimulationofthe

contact of two smooth convex surfaces but fails in mansituationsthatoccurinthehighcurvaturefailuremodes

Inmultipleimpacts andhighcurvaturesinthemesh,as

wellasirregularmeshes:detectionofawrongneighborsegment,allowingnumerouspenetrationstoremain

.

Slide40 of88


40/89

ModelsDevelopmentBetween1987

and1997 The stateoftheart model size for a full vehicle crashworthiness model

grew y a ac or o , rom , o , e emen s

Homogeneous models to cover all load cases for frontal, side and rearimpact simulations by a single model.

10 mm. larger than 10 mm do not provide enough accuracy

below 5 mm make the element size smaller than the spot weld connections no er approac r c e emen mo e ng a so ma e more sense.

If the total sheet metal surface of a bodyinwhite is about 25square meters, it is expected that model sizes between 250,000and 500 000 elements for a full bod inwhite

Limit that should sensibly be used with shell elements. (Eachelement represents between 0.5 and 1 gram of steel)

Slide41 of88


41/89


and1997 Mesh is able to smoothly represent

the deformed shape of the car body

Five elements (half a wavelength)necessary to represent the width of a

.

DaimlerChryslerCorporation

geometry

The simulation result remains mesh

de endent

The predicted accelerations and

energy absorption will continue to

change until mesh convergence is

reac e

This point lies between 10 and 16

elements per buckle EvolutionofmodelsizeandCPU

from1988to1998


Slide42 of88


42/89


and1997

Meshandelementqualityareofutmost

crashworthinesssimulation

Fromacoarsean roug approx mat onto

highlypreciseandarigorousapproach

Meshingforcrashworthinesshasbecomeaprofessioninitsownright

Slide43 of88


43/89

Every sheet metal component in the car body is meshed separatelyus ng sur ace a a.

For a precise model of the sheet in the midplane, offsets of thesurface data are carefully performed.

as much as possible parallel and orthogonal to the incomingpressure wave and using triangles only where necessary.

Trian les are found in areas of mesh transition or areas of hi hdouble curvature (warpage) only.

At the assembly of the individual sheets, offsets may be necessaryin order to guarantee a minimum gap between all parts so that non t a penetrat ons are generate .

These gaps are also necessary to ensure a good performance of thecontact algorithms and avoid deep penetrations through the

.

Slide44 of88


44/89

Currentlynoclearlysuperiormethodcanbedistinguished

Oneissueistherealrotationalstiffnessofthespotweld

Anotherproblemliesinthedesiretomakethespotweldelement location inde endent of the finite element meshonbothflanges.

Flangesarecurrentlymeshedwithtwoelementsoverthe

spotweldelementsprovesaratherelusivegoal.

Inamodernvehiclemodel,between3,000and5,000spot

locations

Slide45 of88


45/89

Moreandmorecareisbeengiventomodelingofthemanyothervehiclecomponents

Caremustbegiventotheconnectionsbetweencar

bushings rubberpartsrequireaprohibitivelyfinemesh

betweenthebodyinwhiteandsubframe

canseverelyinfluencetheaccelerationresponseinthe

Rigidbodyconnectionaswellasaspringelementconnectionwillbothleadtoerroneousresults

Slide46 of88


46/89

Necessary to accurately model the mass, rotational inertia and center ofgrav ty pos t on o t e eng ne an transm ss on oc .

The engine mounts modeled similar to the subframe mounts.

Decisive factor in determining the relative rotation between powertrain and .

A cylindrical shell model with 5 or 6 elements over the circumference istypically used to model driveshafts in order to simulate potential contacts

with brackets in the car body. Spherical joints connect the driveshafts to the wheel knuckles and to the

transmission block.

To avoid small timesteps, rigid body definitions are usually superimposed on .

For smooth contact forces between engine block and structure, the externalgeometry of the engine block is accurately modeled using elements of a sizenot much larger then the ones used for the car body

Slide47 of88


47/89

Axle modeled using shell elements starting from CAD surface or line data.

For a typical McPherson front axle, this subsystem has modeling of the wheel

knuckle, suspension strut, lower control arm and stabilizer bar. A detailed shell model to ensure that all potential contacts with structural

parts can occur in the model.

The stabilizer bar is modeled as a cylindrical bar with 5 or 6 shells over the

circumference. If these elements have a very small dimension, mass scaling or other

techniques can be used to prevent a dramatic decrease in the calculated

stable timestep.

T e ru er us ings in t e c assis mo e are not mo e e in etai , as t e

subframe and engine mounts.

A series of revolute, cylindrical and spherical joints provide the correct hinges

e ween e c ass s par s as we as e ween c ass s an car o y s ruc ure.

Slide48 of88


48/89

The wheels are connected to the axle models.

The wheels consist of detailed geometrical models for

wheel rim, brake disk and outer tire. The wheel rim and the brake disk are usuall ri idl

connected to the wheel rim, thus preventing the wheelfrom rotating.

are performed, but is acceptable for crash simulationsnecessary to account for the correct inertial response ofthe wheel.

The wheel can become a major load path in offset or

oblique frontal crash events.

.

Slide49 of88


49/89

Theairinthetireissimulatedusin theairba al orithms

oftheexplicitcodes

Thepressureofaconstantamountofairinthetireasa

functionofthecompressedvolume,assumingisothermal

orisentropicconditions.

themselves.

Existingtiremodelsarefartoocomplextobeincorporated

infullvehiclecrashmodels,andresearchisneededtogeneratereasonableandefficientapproximations.

Slide50 of88


50/89

Thesteeringrackanditsconnectionstothewheelknucklemodeleds m ar o e ron an rearax es.

Acorrectmodelingofoutercontoursreleasingthecorrectdegreesoffreedomintheconnectionsusingjointand/orspringelementsis.

Adetailedmodelisbuiltthatcouplesthetranslationalmotionofthesteeringracktotherotationofthewheels inthestudyof

frontaloffsetandobliqueimpacts. Veryoften,asteeringrackmodelthatisfixedtothesubframe

structureisused,thuseffectivelyblockingthewheelrotation.

Thesteeringcolumnisusuallymodeledasasetofcylindricaltubess ng neac ot er.

Itisthisslidingmotionthatsimulatesthetelescopicdeformationofthesteeringcolumnasthedummyhitsthesteeringwheel.

Slide51 of88


51/89

Enginemotioniscrucialforthedummyresponseinthepassenger.

Enginemotionisatleastpartlydeterminedbycontactswiththestructureandothercomponentslocatedunderthehood.

Com onentsincludethebatter radiator airconditionin unit automaticbrakingsystemunit,ventilatorsandelectroenginesattheradiator,radiatorbracketandlightbrackets.

Someofthesearemildsteelstructuresandcanbemodeledassuch.

oftheirstiffnessaslongastheresultingstrengthisconsiderablyhigherthanthatofthesurroundingstructuralparts.

Anexceptionistheradiatormodel,whichmustcrushundertheimpactoft eengine oc an somew at ampitsacce erationresponse.

Equivalentmodelsbasedonforcedisplacement curvesdeterminedinadroptest

Slide52 of88


52/89

Structural model of the doors sufficient for the simulation of frontal and

For side impact load cases, door inner components must be carefullymodeled.

Hin es and locks must be modeled in such a wa that the correctrotational degrees of freedom are released between the door model andthe model of the bodyinwhite.

Door structures are mostly quite weak with respect to bending.

,motors, loudspeakers and the window glass provide the flexural stiffnessof the entire component, and thus, determine the critical timing of theimpact between door and occupant.

T e inertia response o t e oor structure is important in etermining t e

velocity of impact with the dummy. The mass of the door as well as the masses of its individual components

should be carefull checked.

Slide53 of88


53/89

Windshieldandbumperaremodeledinfrontalimpact,whereasthefueltankandsparewheelandtireare

typicallypresentinrearimpactmodels.

simulationoffrontalandsideimpactandthefrontseatsareessentialinallmodels.

modeledandacarefulmasscheckistypicallyperformedatthisstage.

erema n ngmassesaretrace an oca ya e tothemodelasdensityincreasesand/ornodaladdedmasses

Slide54 of88

Software Development Between 1987


54/89

SoftwareDevelopmentBetween1987

and1997 Modeling technology has evolved towards ever larger and more

e a e numer ca mo e s o e ve c e n a ques or moreaccuracy and more reliability in the results.

Software development trying to run and manage these models with,

technology.

A first important focus point of development was on animation

packages for rapid postprocessing for visualization of the simulatedcrash event and the deformation modes of the car body and fordisplay of plastic strain, stresses and energy densities over theindividual parts.

components that absorb more or less energy Interactive preprocessing software of the models to quickly

incor orate structural chan es

Slide55 of88



55/89


and1997 Effort has been to increase the efficiency of the solvers

Explicit finite element codes have been optimized to the point that theyrun in a 99 percent Vectorized mode.

The elementbyelement nature of the codes lends itself particularly wellfor Vectorized rocessin considerin the nodal force assembl and thesearch algorithms in the contactimpact routines.

Parallelization of the codes achieving ever better scaling performance onboth shared memory and distributed memory machines.

algorithms by socalled segmentbased search algorithms.

The old algorithms based on the search of a nearest master node for everyslave node are always computertime consuming even if bucket sortingimproves t is situation.

With the new segmentbased search methods, an algorithm wasintroduced that is not only computationally much more efficient, but alsoim roves on man of the shortcomin s of older al orithms.

Slide56 of88



56/89


and1997 Techniques developed in order to allow explicit simulations to run with a

.

The stable time step of the analysis is linearly dependent upon the shortest

mesh dimension in the model. As deformation changes (reduces) this dimension, a drop of the timestep

seems mathematically unavoidable.

Indeed it is not possible to keep a constant timestep during a crashsimulation with highly deforming shell elements without changing the physics

of the problem. Small strain formulations where the influence of the change in geometry upon

the element stiffness is ignored from a certain point on (or during the entireanalysis), to a controlled reduction of the materials elastic modulus as itplastically deforms.

The most widely used method is mass scaling.

As an element dimension decreases, the corresponding material density ornodal masses are increased in such a way that the resulting time step remainsconstant.

Slide57 of88



57/89


and1997 The basic technology of explicit finite element codes same

uring t e ast eca e.

One of the major improvements in accuracy was thereplacement of degenerated quadrilateral elements by a true

r ang e e emen as propose y e y sc o.

This element is free of hourglass modes and has a bendingresponse equivalent to the flat quadrilateral Belytschko and

say e emen .

Major improvement with respect to a degenerated quad butstill must be used with care and in limited numbers mainly

inplane shear stiffness that can be too high in certain cases

Slide58 of88



58/89


and1997 A large number of special purpose options were added

to the codes in order to fulfill crashspecific functions

in the models. Such as ri id bodies but s rin elements s ot weld

elements, joint elements and occupant simulationoriented options such as seatbelt, and airbag models.

These mainl im rove the a lication sco e of thecodes.

It seems that the simulations have arrived at a

of the simulation is no longer the mesh, but rather, thenumerical algorithms that are used in the explicit finite

.

Slide59 of88


59/89

An finite element simulation activit can be seenas a chain with two links.

The first link is the numerical model, essentially ahypercomplicated massspring system whosedynamic behavior is an approximation of the

continuum the car that is to be modeled.The second link is the software or the numerical

algorithm to perform a numerical time integration of

The solution obtained on the computer is an

Slide60 of88


60/89

The main problem with early simulation work was clearlythe coarseness of the shell element mesh representing the

car body. This resulted in simulation of the low curvature (high

wavelength) buckling modes only, and thus constantlyoverestimated the energy absorption in the structure sincehigh curvature modes were precluded from the simulation

y e ou ay o e mes .

Too coarse meshes generally resulted in too stiff behaviorof the energy absorbing, highly deforming structural parts.

The weak link in the chain was clearly the mode, and anyadditional loss of accuracy due to the use of very simplealgorithms was almost welcome.

Slide61 of88


61/89

Some of the algorithmic deficiencies tended to compensate for theerrors ue o e coarseness o e n e e emen mes . Penetrations allowed due to failing contact algorithms and zero energy

modes in underintegrated shell elements

of more accurate algorithms rather than in further refinement ofthe models.

In other words, the algorithms have become the weak link in thechain.

Improved algorithms for shells and contacts have been available inexplicit codes for quite a while, but have not been used extensively

,

of numerical robustness.

Slide62 of88


62/89

Approximately half of all numerical problems in modern crashworthiness .

The complex surfaces with high double curvature are discretized by large finite

elements, resulting in a polygonal surface with lots of links and edges. Edgetoedge penetrations can go undetected since they cause no nodal

penetrations through any of the segments.

It makes the model less stiff than the actual structure where no penetrationscan occur.

Conse uent movements of the enetrated se ments can easil lead im actsof nodes on segments from the wrong side.

Suanomalies in the models will lead to local instabilities, hourglassing due tothe extreme outofplane loads and potentially abort the simulation

rematurel .

Classical contact algorithms set the tangled nodes free and allow penetrationwithout any further checks resulting in a further loss of realism.

Edgetoedge algorithms are currently being introduced into all commercial.

Slide63 of88


63/89

Increasingly finer models allows for detection of the influence ofe zeroenergy mo es an e correspon ng per ur a on

hourglass forces in the numerical models.

The perturbation hourglass forces are nodal forces introduced

in the element from becoming unbounded.

Although these forces are supposed to make up for the missing

element stiffness, they do not correspond to a stress in theelement, and thus constitute an external force field of ratherarbitrary magnitude controlled by userdefined coefficients.

Due to the introduction of this force field, a perturbationstabilized

compared to reality.

Slide64 of88


64/89

Full integration using fourGauss integration points in the element of the.

Unfortunately, straightforward solution does not work.

Fully underintegrated elements with uniform bilinear interpolation sufferfrom another drawback called shear lockin .

Shear locking occurs when nonzero outofplane shear strains arepredicted by the element in conditions of pure bending resulting in anoverlystiff element response.

deflections are interpolated with higher order rather then bilinearfunctions, formulations that exhibit no shear locking are possible.

However, complexity increases which decreases element performance.

Development of a fullyintegrated element that avoids all shear lockingand maintains the simplicity of uniform bilinear interpolation has provento be a challenging task.

Slide65 of88


65/89

Severalsolutionsexisttoneutralizehourglassmodesusinguniformbilinearinterpolationwhileavoiding

shearlocking.

(SRI)elements.

Thissolutionconsistsofperformingafullintegration

areducedintegrationfortheoutofplaneshearstrains.

esee ementse ect ve yavo s ear oc ng orrectangularelementsbutsomeproblemsstilloccurinirregularmeshes

Slide66 of88


66/89

Assumednaturalcoordinatestrain (ANS) elements.

soparametr c coor nate e s no onger erent ate , ut mproveestimates of the outofplane shear strain field are used directly.

This approach leads to a formulation without shear locking independently ofthe quadrature rule used and both reduced integration and full integrationimplementations exist in most commercial explicit finite element codes.

A reduced integration ANS element does not solve the original hourglassproblem and would not suffer from shear locking.

The advanta e of the ANS a roach for these elements lies in the im rovedaccuracy obtained in irregular meshes.

In particular, the ANS element passes the Kichhoff patch test, whereaselements with classical quadrature of the shear strains always fail this ratherelementar re uirement.

A very efficient fullyintegrated ANS element exists in the LSDYNA code,which overcomes all hourglassing and shear locking problems at a cost ofroughly three times the original Belytschko and Tsay shell element

Slide67 of88


67/89

If full integration is still perceived as not efficient enough to allow

parame r c s u es on argesca e cras wor ness mo e s ovehicles, a more economical approach may be given by physical

stabilization. ,

used and an approximate analytical integration is performed overthe element of the nonconstant part of the strain

The constitutive law is invoked in order to estimate hourglassstresses resulting in a set of nodal forces that are supposed tocorrect missing stiffness components of the element rather exactly.

This approach is much more efficient than fullor reducedselective

time then the original Belytschko and Tsay element. The elementalso passes the Kichhoff patch test

Slide68 of88


68/89

Nexttotheexistenceofzeroenergymodes,asecondpotentialproblemis

itslimitationtoflatgeometries.

TheuseoftheMindlinplatetheorywherethefiberdirectionisassumed

tocoincidewiththenormaltotheplatesurface.

Inwarpedelements,bendingstraincanbeunderestimatedfortwo

reasons.

Rotations

normal

to

the

element

will

not

cause

any

curvature

to

be

calculated

although

theserotationsmaynotbeparalleltothenodaldrilldegreesoffreedom(fiber

direction)inallnodesoftheelement.

Forceloadsintheelementplaneshouldalsocausebendingstrainsinawarpedelement

andwillfailtodosowhentheunmodifiedBelytschkoandTsayelementisused.

Those

effects

will

lead

to

the

failure

of

the

so

called

twisted

beam

test

by

thiselement.

Slide69 of88


69/89

It should be emphasized strongly that none of the improvements

described above affect the original assumption that only small

deformations exist within a single shell element.

deficiencies of the element formulations within this framework.

Thus, the use of more sophisticated elements does not allow the

use o coarser mes es.

All rules developed earlier to determine mesh density of a

crashworthiness model still apply.

A good crashworthiness simulation can only be obtained if themesh is able to smoothly represent the deformed geometry of the

car bod .


70/89

Slide71 of88


71/89

Components are typicallyes e n o quas s a c an

dynamic modes

Dynamic

to the ground on a load celland loading is typically appliedfrom the gravitational fall of a

the component.

Sled test: Component mountedhorizontally onto the sled

Railtestsetup SledTest

to impact a rigid or deformablesurface with the componentmaking first contact.

FigurefromPriyaPrasad(2005)

Slide72 of88


72/89

TheraildeformationsexhibitedRailres onse

curvatures,rotationatthefree

endandplastichingeatthefixedend.

peakforceincreasedwithimpactspeedfrom50to60kPa,duetostrainrateeffectsofthematerial

TheFEsimulationcorres ondin to8.2m/simpactagreedquitewellwiththetestresultwhenthestrainrateeffectswereincludedinthesimulation.

Increasingthenumberofshellelementsfrom2,000to3,000showedminorinfluenceonthe

SrailfinaldeformationsInitialimpact

speedsof2,4.5and8.2m/sintoa

rigidwall.


Slide73 of88


73/89

MeasuredandFEcalculatedforcesMidRaildeformations

easure an ca cu a e orcesagreemen

LiketheSrailresponse,thepeakforceincreasedwith

increasingtheimpactspeedduetostrainrateeffects.


Slide74 of88


74/89

Impact speed was 13.4 m/s.

In this simulation, no strain rate effects were included in the

analysis since the midrails were manufactured from high strength

steel, which typically exhibits little strain rate effects


Slide75 of88


75/89

insizeandcomplexity

since1980s

Detailmodelingof

vehiclestructuresan

integralstepinthe

vehicledesignprocess

Offsetimpact

requirements

FordTaurusmodel(2001)hasover1.5Millionelements


Slide76 of88


76/89

Approx.10mmx10mmshellelementsinfrontstructureforplastichingesandbuckling

Theengineandtransmissionsimulatedbyrigidshell

inertiaattheenginesCGlocation

Coarsermeshforstructurebehinddashpanel

era atorus ngso e ements

Twofrontdoorsincludedwithhinges

Aninstrumentpanelwasalsoincludedalongwithappropriatestructuresforkneerestraint.

Slide77 of88


77/89

ModelStatistics: ContactDefinitions

61,500shellelements

500solidelements

25beamelements

Arigidwallinfrontofthevehiclewithstickcondition.

Automaticcontactsurfacesweredefinedinsixzonesasfollows:

,

15joints

40concentratednodalmasses

Frontleftcorner(uptofrontbodyhingepillar)

Frontrightcorner(uptofront

body

hinge

pillar) 200parts

66,000nodes

Frontcenter(includeuptothemiddleoftheengine)

Rearcenter(frommiddleoftheenginetothefirewall)

Driversidecentrepillartodoor

Passengersidecentrepillartodoor

Slide78 of88


78/89

CRAY YMP8E system.

Time step was approximately 0.7 s

A 100 ms simulation was completed in

about 45 hours on one processor. Was necessary to refine the radiator

model for severe hourglassing

Intermediate vehicle configurations(not shown) exhibited realistic

se uential deformations as seen in

0) and final (at

100 ms) vehicle

deformed shapes

highspeed film analysis of barriercrashes.

Time histories of the global energybalance velocit at the front rockerand barrier force provided very

reasonable results, comparable to testdata

Initialimpactvelocity13.4m/sFigurefromPriyaPrasad(2005)

Slide79 of88

IntegratedVehicleOccupant


79/89

RestraintsModel

and

structural

codes,

task,sincerigidbodyequationsofmotionare

Severalcodesweredeveloped,most

prom nent scuss onsonones ng eco e was

fromOveArup, SchelkleandRemensperger.

Slide80 of88


80/89

Vehicleincludingabodyin Modelstatistics:w es ruc ureo a our oorpassengersedan,

Engine,transmission,etc.,

70,000shellelements

9,000

solid

elements 300beamelements

, ,

Bucketcarseatstructurewiththeseatcushion,

Ener absorbin steerin

1,300spotwelds

300parts

91,000

nodescolumnwithasteeringwheelandfoldedairbag,

Instrumentpanel,includinga

20contactsegments

r vers e nee o ster,

Doorstructure,and HybridIIIdummy


Slide81 of88


81/89

approximately constant throughout

the 100 ms duration

testdata,particularlyatthepointwhere

thevehiclevelocitycrossesthezeroline


Slide82 of88


82/89

The pulse shape with itstwo peaks and the times at

which they occurred isconsistent withexperimental data.

The first peak force almost

obtained from one test.

However, the second peak

test value due to inexactmodeling of the engineto

. Barrierunfilteredforcetimepulse


Slide83 of88


83/89

Fullrigidbarrier Vehicle+

Dummy(HIII)


Slide84 of88


84/89

Requiresa detailed


Slide85 of88


85/89

Requiresa detailed

FEmodel


Slide86 of88


86/89

Differencein

frontaldeformations

corresponding

totheprevious

fourimpact

Frontalvehicledeformations


Slide87 of88


87/89

Although the FE technology for structural mechanicswas introduced in the early sixties, it took about 25

years of additional development to apply it successfullyto crashworthiness simulation of automobilestructures.

The developments were mainly in nonlinear problem

,integration, explicit time integration, plasticity, andcontactimpact treatments.

was indeed indispensable for the development of fullscale vehicle models.

Slide88 of88


88/89

The midei hties to the midnineties time s an can be

characterized as the renaissance period of FE

crashworthiness models.

Generic and actual components of vehicle structures as

well as fullscale vehicle models were developed to

s mu a e ron a , s e, rear ve c e mpac w arr ers.

Vehicletovehicle collisions were also developed and

. ,

dummy and air bag models were created and theirres onses were validated a ainst ex erimental data

Slide89 of88


89/89

In 1995 a rocess was established to inte rate vehicle

structure, instrument panel, steering assembly, driver

air bag and Hybrid III dummy models in a single FEmodel.

This process centered on integrating existing

componen s an su sys em mo e s an c ear ydemonstrated that explicit FE technology can simulate

resulting from a vehicle crash in a single integratedmodel, although the results are preliminary.

9-finite element analytical tecniques

Documents