Perugia Stress Evaluation

7/27/2019 Perugia Stress Evaluation

1/20

STATE OF STRESS EVALUATION OF STRUCTURAL ELEMENTS BYMODAL SYNTHESIS

F. Ambrogi 1, C. Braccesi 2, F. Cianetti 2

1 Mechanical Dynamics S.r.l. Italy, Via Palladio 98, 33010 Tavagnacco (UD) - Italy2Dipartimento di Ingegneria Industriale, Universit degli Studi di Perugia

Via G. Duranti 1, 06100 Perugia - ItalyE-mail: [email protected]

ABSTRACT

In this paper various modalities of determination of stress time histories obtained by meansof numerical simulation (MB modelling of mechanical systems combined with FE modelling oftheir components) are shown. A stress evaluation procedure, implemented by the authors fora particular MBS/FEM environment is shown. Meaningful comparisons are proposedbetween various procedures of stress calculation, using as reference a simple notched bar,whose finite element model has been validated by means of comparison with experimental

result in literature. Analogous and further considerations on damage are developed on asimple articulated mechanical system, analysed within MBS/FEM, using the hypothesis ofhigh cycle fatigue.

INTRODUCTION

In analysing the fatigue life of components belonging to mechanical systems subjected to

variable loads in time, the evaluation of damage by means of numerical simulation isincreasingly accompanying the traditional means which use experimental tests in laboratoryor on field. Figure 1 represents a plot of the phases of a typical evaluation procedure toevaluate damage and thus the fatigue life of a mechanical component. The typical operativeprocedure is to define the structural loadings, to evaluate the state of stress and strain andfinally, to assess damage and to predict life. The experimental approach, in particular, needsthe measure of the operative loads, the measure of local strain by means of strain gaugesplaced in crucial points along the structure, the tests on the material to assess its fatiguebehaviour and then, to use the typical estimation algorithms for damage. The numericalassessment procedure differs from the experimental one at least in the first two phases sinceit uses dynamical models and simulations of the system to define the operative loads andalso finite element models of the components to assess the state of stress.As regards the latter approach, the FE model (FEM) integrated in the multibody model (MBS)allows to quickly obtain useful data to assess damage and also to define important tests toevaluate (accelerated tests) the fatigue life of a mechanical component subjected to


2/20

implemented by the authors for a specific MBS/FEM simulation environment is beingillustrated.

Fig.1 - Plot of a typical assessment procedure of damage

Important comparisons are suggested between the different stress evaluation modalitiesusing, as reference point, a simple notched bar the finite element model which has beenassessed comparing with the experimental results found in literature.Further and analogous considerations have been developed on a simple articulatedmechanical system, analysed in the MBS/FEM integrated environment, on which damageassessments were made assuming high cycle fatigue.

EVALUATING BY MEANS OF NUMERICAL SIMULATION OF THE STATE OF STRESSOF MECHANICAL COMPONENTS SUBJECTED TO FATIGUE

In order to develop a hypothetical automatic evaluation process of damage and therefore, ofthe fatigue life of a mechanical component by means of numerical simulation, in high and lowcycle fatigue, it is necessary to know the time histories of stress and /of strain. Whenassessing damage the time histories can then be processed by Rainflow counting method

M

ck ck

kp kp

m m

Experimental approach

Numerical approach

,

t

N

t

,

t

,

103 10 5 10 710 9

,

n

System (Loads) Component (Stress/Strain) RainFlow

Damage

Load Spectrum

Life

ComponentSystem Material

MBS FEM

=i i

i

N

nD


3/20

mentioned in the introduction, the process needs FE modelling of the component. In order forit to be tuned enough to realistically simulate the state of stress and in particular, the stress

concentration conditions, the FE model results usually to be very expensive to use andmanage; anyhow, it needs a thorough experimental validation. Furthermore, it is necessaryto model the dynamics of the entire mechanical system (MBS) in order to simulate itsoperations correctly and therefore the state of loadings which will involve the component. Forthis modelling phase, a full validation of the multibody model is difficult to achieve. For thisreason, numerical evaluation of the damage and of the fatigue life of mechanicalcomponents by numerical simulations should always be considered in qualitative terms andtherefore used mainly in the decisional phase of design choices.

From a methodological point of view, when modelling the component behaviour two maincases emerge: the dynamics of the component is negligible, that is its frequency content isoblivious to the external loads dynamic; the dynamics of the component is fundamental, thatis its first frequency falls into the dynamic range of the external actions. A third possibilitycould also emerge: it is not possible to assess beforehand the relation between input andoutput dynamics.

Negligible dynamics: static approach

Lets consider the case when the dynamics of the component is negligible. The component isintroduced in the multibody model of the system as a rigid body and is subjected to a seriesof external loads L1, L2, LS.. The time histories of these ones L1 (t), L2 (t), LS (t) areavailable as simulation outputs. In this case, when assuming elastic material behaviour, andafterwards applying the necessary corrections in the case plastic material and of low cyclefatigue, the principle of an overlapping effect is valid so that it is only necessary to solve theelastic problem for each L1, L2, LSload, applied separately but assumed united.In every p point of the body, the coefficients cij,k(p) are obtained relating to the kth load whichlink intensity with the state of stress generated in point p. From a formality point of view, in a

generic point of the body, the state of stress generated by the kth load equals:

)p()p( ,, kijkij c= (1)

When the effects are overlapped, the pseudo-stress elastically calculated equals:

=

=S

k

kkijij Lc1

, )t()p()pt,( (2)

Therefore, S elastic problems were solved with a unitary load and a simple linear combination

was carried out to attain the state of stress and strain all along the structure.

Relevant dynamics: modal approach

In the case that the dynamic behaviour of the component is important, in compliance with the


4/20

+= bB con q= (3)

Fig.2 - Deformation state of the flexible component

0Q1j

FLLdtd i

m

j

T

i

j

iii

==

++

DD con 0j =

con i = 1,,n + 6, j = 1,,m e [ ]kqzyx =

(4)

The method above expressed is difficult due to the choose of the best sets of generalisedmodal coordinates, i.e. of the modal forms to consider in modelling the behaviour of the

flexible body.So, by means of MBS simulation, the displacement of the generic point of the model can beexpressed by modal overlap:

=

=n

i

i

1

i )t(q)t( (5)

and, similarly, if the corresponding modal forms expressed in terms of stressk are known,

the tensor of the state of stress can be attained in every point:

=

=n

k

kij

1

k )t(q)t( (6)

Therefore it can be said that even when the dynamic contribution of the component ispresent, the stresses are in all points linear combinations according to known coefficients of

p*

b3

b1

b2

o

r

n3

n1

n2

o

=

=n

i

i rr1

i )t(q)()t,(


5/20

known in literature allowing to attain contemporarily a good modelling not only of the staticbehaviour but also of its dynamics doesnt affect the calculation of the entire numerical

procedure in a considerable way.Various modal synthesis methods exist in literature such as Craig-Bampton [12,13,14],MacNeal-Rubin [13,14] and Benfield-Hruda [13] which are all based on a certain selectionof the generalised modal coordinates that is of the modal forms to consider when modellingthe behaviour of the flexible body. In particular, a method of modal synthesis has beendeveloped based on Craig and Bamptons. On the one hand, this method allows to reduce toa minimum the number of generalised coordinates and on the other, to allow more freedomin defining the boundary conditions of the boundary points (constraints or applying forces

points) by completely describing the effects of local flexibility. The motion of the flexiblestructural component, characterised by N degree of freedom and with fixed boundary points(or interface) is described by the combination ofPnormal modes and by Sstatic correctionmodes. The former are the results of a modal analysis of the body, considering its boundarydofs as being fixed, whereas the latter are static deformed S obtained by imposing a unitarydisplacement for each degree of freedom of the interface and keeping all the others fixed.The modal transformation which characterises this model is described in (7) in which the

physical coordinates x are approximised with a modes summation and p represents the

new coordinate system; I indicates the degrees of freedom of the internal points (equal toR=N-S) and B the boundary dofs (equal to S). The C (SxS) represents the static correctionmodes and matrix N (RxR) the normal modes. Of this last matrix only P modes (< R) isconsidered of the latter.

pp

p0I

x

xx

I

B

NCI

B

=

=

= (7)

fff

pp

k00k

pp

mmmmpKpM

I

B

I

B

NN

BB

I

B

NNNB

BNBB

=

=

+

=+

DDDDDD (8)

The motion equation of the flexible body can be expressed as in (8), where the mass andstiffness matrixes are generalised.For a simpler management of the flexible body, compared to the C&B s original model, anorthonormalisation of the reduced system is carried out in the multibody simulation codes.

This last phase yields a diagonal model, that is a ~

modal matrix image of the free-freebehaviour of the flexible body, but with an elastic contribution of its deformability in theboundary points. (5) and (6) thus are still valid where the modal matrix in terms of

displacement is represented by ~

in terms of stress

~is attainable by applying the

transformation used to orthonormalise the displacement modes at the matrix of the stress

modes corresponding to .

Thi d l d li f th t i ld th lt ill t t d i f ll i


6/20

procedure of image generation of the component for the multibody environment; finally it willonly be necessary to have the MBS simulation results, in terms of loads in one case and in

terms of lagrangian coordinates for the other, in order to carry out a simple linearcombination to have the state of stress and strain in each point of the structure.Therefore, the strenght of this approach is in the possibility to faithfully simulate not only thestatic conditions of the mechanical component but also its dynamical ones in terms ofdisplacement and strain/stress by simply considering a modal model of the flexible body witha number of freedom degrees equal to (P+S) obtained from P normal modes and S staticmodes.In cases where it is difficult to assess the dynamical contribution of the component this typeof approach allows to simulate the behaviour with a relatively higher computational burden(modal analysis to obtain P normal modes).Another consideration should be made for this aspect of modelling. Theoretically, it isdefinitely more correct to model the component inside the dynamic model as a flexible partand not as a rigid one. This allows, as will be shown in this paper, to have a loads distributioninside the structure which allows for the elasticity of the single flexible components. Ofcourse this does not mean that the evaluation of the state of stress cannot be carried outanyhow with a "static" approach that is considering the load histories and the cij,kcoefficients.When considering the calculation burden, this method appears to need not only the modal

model of the component, even if only with a modal base composed of sole static correctionmodes, but also to carry out a set of static analyses to achieve cij,k coefficients: the modalapproach would directly yield the correct evaluation of the loads condition and the state ofstress.It must be pointed out that the above described modalities are directly applicable to the studyof high cycle fatigue by solely supplying the state of stress in the elastic field. Obviously, asregards low cycle fatigue the elastic tensor of pseudo stress must be modified in anelasticplastic tensor; as far as the procedure is concerned, this can be attained for instance,

by Jiangs transformation or by more approximative approaches such as Neubers law orRamberg-Osgoods formula: these are not however the topics of this paper.

Stress Recovery Procedure

Basing on what we have already shown we implemented a procedure to calculate stresswhich, starting from Adams MBS model of the system and Ansys FE model of component,lets to compute automatically the stress state of the whole system (or a part of it) usingstatic and/or Modal MCS.

Analyzing the system it allows to identify the points where forces are applied and get theirtime histories. Furthermore it is possible to get modal coordinates time histories of modalcoordinates, both orthonormalized and un-orthonormalized (split in original normalconstrained modes and static correction modes). It is possible to export modal shapes of apart or of the whole model. Lastly it is possible to compute, directly within the software, amodal superposition of modes, in terms of displacement, and export time histories of the

h l d l f i E fil b d i bi ii f


7/20

counting algorithm, got load spectra at critical points of the flexible component letting toevaluate, chosen the fracture criterium and material properties, the damage, i.e. using the

Miner damage cumulation law.

Fig.3 Stress Recovery toolkit capabilities

RESULTS

The methodology set up in aMBS/FEM simulation environment(Adams/Ansys) was analysed andverified on a simple in plane

mechanism. The system is a slider-crank (fig.3) with no physicalcomparison with real slider-cranks,but nevertheless suitable in thiscontext to point out each time themethodological problems inreconstructing the state of stress andin assessing damage. In MBS

simulations the connecting rod andthe crank are considered to bealternating rigid and flexible; the stateof stress was set up in time by thestatic approach and the MCSmodal described previously. Two

MMBBSS ((AAddaammss))

TTiimmee DDoommaaiinn AAnnaallyysseessLLkk((tt))TTiimmee HHiissttoorriieessqqkk((tt)) TTiimmee HHiissttoorriieess ((OOrrtthhoo))qqkk((tt))TTiimmee HHiissttoorriieess((ddeeOOrrtthhoo))MMooddaall MMooddeell

kk FFuullll oorrRReedduucceedd MMooddeell MMooddeess ((OOrrtthhoo))MMooddaall LLiinneeaarrSSuuppeerrppoossiittiioonn ((OOrrtthhoo))

uuiijj ((tt)) FFuullll oorrRReedduucceedd MMooddeell DDiisspp.. TTiimmee HHiissttoorryy

FFEEMM ((AAnnssyyss))

TTiimmee ddoommaaiinn AAnnaallyysseessoonn FFuullll oorrRReedduucceedd MMooddeellSSRR ((bbyy aapppplliieedd ddiisspp..uuiijj ((tt)) ))SSttaattiicc LLiinneeaarrssuuppeerrppoossiittiioonnoonn FFuullll MMooddeell

SSttaattiicc aannaalliisseess ((LLkk== 11 ))SSRR bbyy ssuuppeerrppoossiittiioonn ((LLkk((tt)) ffrroomm MMBBSS))MMooddaall LLiinneeaarrssuuppeerrppoossiittiioonn ((OOrrtthhoo))oonn FFuullll oorrRReedduucceedd MMooddeell

MMooddeess RReeccoovveerryy ffrroomm MMBBSS ((bbyy aapppplliieedd DDiisspp..kk ))MMooddeell SSRR bbyy ssuuppeerrppoossiittiioonn ((OOrrtthhooqqkk((tt)) ffrroomm MMBBSS))MMooddaall LLiinneeaarrssuuppeerrppoossiittiioonn ((ddeeOOrrtthhoo))oonn FFuullll MMooddeellSSRR bbyy ssuuppeerrppoossiittiioonn ((ddeeOOrrtthhooqqkk((tt)) ffrroomm MMBBSS))

rb

rmmm mb

D d

r

M

N

M

N

Fig.3 Slider-crank sketch

R/d = 0.05D/d = 1.3


8/20

those attained numerically (fig.4).Table 1 shows the results in terms of

concentration factors as concerns the elasticstatic analysis performed in FE environmentand by the "static" reconstruction and the"MCS modal" approaches. As regards the"MCS modal" reconstruction and the staticone obtained from the loads assessed on aflexible model of the component, a modalmodel based on a modal base composed ofonly static modes was used. It is thereforeobvious that there is perfect agreementamong the results. The dynamic behaviourof the two components was then analysedand therefore the ability to reconstruct the dynamics in stress by the methods describedpreviously. The comparison was carried out by using an FE harmonic analysis of the twomodels, considering a bending state of stress and an axial one separately. As far as theprocedure of reconstructing in the multibody code is concerned homologous transientdynamical analyses were adopted by using a random loads as input (with frequency constant

up to 200Hz) and by processing afterwards the results with classical experimental signalanalysis procedures so that a comparison was possible in the frequency field. As regards theconnecting rod, the flexible model was performed with a modal base composed of, not onlyby the same family of static correction modes as before but also by ten normal ones. Theresults show how the MCSmodal reconstruction and thestatic one on the rigid andflexible model, coincide in

static conditions (0HZ fre-quency); they remarkablydiffer however in the flexiblemodel case (fig.5).In this case, it is obvious howby only considering the modalmodelling it is possible tocorrectly simulate the com-

ponent behaviour in terms ofstress both in static anddynamic conditions. As far asthe crank is concerned, theextreme rigidity and therefore,the high frequencies whichcharacterise its modes allow

Table 1 Stress Concentration Factors

Analysis BendingMoment

AxialForce

Theory 1 2.225 2.450

FEM 2.243 2.588

Static approach 2.243 2.588

MCS approach 2 2.243 2.588

1 Experimental data [1]2

Obtained only using the static correction modes

110

120

130

140

150

160

170

Bending - FRF Concentrated Smises

Mag.dB

ofFouriertransform

Static approach (flexible model)

Static approach (rigid model)

FEM

MCS


9/20100

200

(Pa)

Time histories tensione sul piano critico (intaglio manovella)

25

30

Rainflow Matrix Manovella (Mflex/Brig)

In order to verify the correctness of this approachand especially the correctness of the rigid

modelling of the component, some comparisonswere made among the several stress recoverymodalities from the transient analyses carried outon the kinematism with constant rotational speed ofthe connecting rod. The rotational frequency waslargely lower to crank first free-free natural one.The system was characterised by perfect internalconstraints, except for the connecting rod/cranknode modelled with clearance and Hertz contact.The simulations carried out in this work show alsohow it is surely more correct to always model thecomponent, inside the dynamical model, as aflexible part of the component rather than as a rigidone. In fact, in this way, it is possible to considerthe elastic behaviour variations of the system asfunction of the elasticity introduced by the single flexible components. In our testing system,the crank is a component which singularly shows high rigidity (fig.6a). Its elasticity,

introduced by a "MCS modal" model only by static corrections modes, is enough todetermine a noticeable variation in the behaviour of the system both in terms of naturalfrequencies (fig6) and then, in terms of loads, stress and damage. In fact, by comparing twosystem models, the former which assumes the two components as rigid and the latter whichconsiders the flexible connecting rod it can be seen how there are remarkable behaviouraldifferences. When analysing the section of time histories relative to 10 slider-crank cycles, forthe two models, in the notch, have been evaluated: the critical plane, the stress time historyrelative to this plane (fig7), the rainflow matrix of this stress history (fig8), the load spectrum

(fig9), and in the assumption of Miners damage cumulation law, by using Miners curvemodified by Haibach, the damage and the components life have been evaluated. Thesecomparisons have demonstrated the previous statements, supplying a life of 8.6105repetitions for model with rigid crank, and 2.4105 for the model with flexible one.In the case of the latter model (flexible component with high rigidity) the use of the staticapproach results to be equivalent to the MCS modal as far as the choice of reconstructionmodality of the state of stress is concerned.As regards the connecting rod, the model with both components being rigid, and the model

Fig.6 - (a) Crank first mode (free-free) (b) System first mode (M flexi-

ble, B rigid)

(a) (b)

M M

B

1132 Hz 14 Hz

M rig , B rig


10/20

0 20 40 60 80 100 1200

50

100

150

200

250

Spettri di carico ponderati

cycle number

c

yclicstressamplitude(MPa)

Fig.9 Weighted load spectra

for a flexible connecting rod wereconsidered, the latter being modelled by

static modes and 15 normal modes.Furthermore, the excitation low frequencycontent, mostly represented by therotational frequencies of the crank, showsfor this component also, assumed to behighly flexible that the static reconstructionis similar enough to the one carried out byMCS modal modelling. It is also obviousthat, as shown in the analyses performedon the single components (fig 5), when inpresence of excitation with a frequencycontent distributed in a significant range,the MCS modal model is the only analysismodality which correctly reconstructs thecomponent behaviour in terms of strain andstress.

CONCLUSIONS

This work has shown how a correct evaluation of the mechanical component damage, evenwith high rigidity, belonging to articulated and complex mechanical systems, needs its flexiblemodelling.Future developments in research can finalise the criteria for the analysis and the synthesis ofload and stress histories triggered by numerical simulations and/or experimental acquisitions,

and of algorithms to automatically evaluate damage.

REFERENCES

1) Collins J.A., Failure of materials in mechanical design, John Wiley & Sons, 1992;

2) Shigley J.E., Mischke C.R., Mechanical Engineering Design, Ed. McGraw-Hill, Inc.;

3) Shabana A.A., Dynamics of multibody systems, John Wiley & Sons, 1998;

4) M.A. Miner, Cumulative damage in fatigue, Journal of applied mechanics, 1945;5) Atzori B., Tovo R., I metodi per il conteggio dei cicli di fatica: stato dellarte, problemi e

possibilit di sviluppo, ATA, Aprile 1994, vol.47, n.4;

6) M. Brokate, K. Dressler, P. Krejc, Rainflow counting and energy dissipation for hysteresismodels in elastoplasticity, Eur. J. Mech., 15, n.4, 705-737, 1996;

7) K. Dressler, B. Grnder, M.Hack, V.B. Kttgen, Extrapolation of Rainflow Matrices,

M rig , B rig

M flex , B rig


11/20

Universit degli Studi di PerugiaUniversit degli Studi di Perugia -- Dipartimento di Ingegneria Industr ialeDipartimento di Ingegneria Industr iale

1 5 t h 1 5 t h Eu r o p e a n A d am s Us e r s Co n f e r e n ce Eu r o p e a n A d am s U se r s Co n f e r e n ce 2 0 0 0 2 0 0 0

Roma, 15Roma, 15--1717novembernovember20002000

St a t e o f s t r e s s St a t e o f s t r e s s e v a l u a t i o n e v a l u a t i o n o fo fs t r u c t u r a l s t r u c t u r a l e l e m e n t s e l e m e n t s b y m o d a l b y m o d a l s y n t h e s i s s y n t h e s i s

F.F.AmbrogiAmbrogi11,, C.C. BraccesiBraccesi22, F., F. CianettiCianetti22

11 Mechanical DynamicsMechanical Dynamics S.r.l.S.r.l. ItalyItalyVia Palladio 98, 33010Via Palladio 98, 33010 TavagnaccoTavagnacco (UD)(UD)

22 Dipartimento di Ingegneria Industriale, Universit degli Studi dDipartimento di Ingegneria Industriale, Universit degli Studi di Perugiai PerugiaVia G. Duranti 1, 06125 PerugiaVia G. Duranti 1, 06125 Perugia

EE--mail:mail: cianficianfi@@unipgunipg..itit


12/20


M

ck ck

kp kpm m

Experimental approach

Numerical approach

,

t

N

t

,

t

,

10 3 10 5 10 7 10 9

,

n

=i i

i

N

nD

System (Loads) Component (Stress/Strain) RainFlow

Damage

Load Spectrum

Life

ComponentSystem Material

MBS FEM

Damage evaluationDamage evaluation procedureprocedure

StressStress RecoveryRecovery


13/20


SystemSystemSystem ComponentComponentComponent

,

t

N

t

)p(c)p( k,ijk,ij =

==

S

1k kk,ijij

)t(L)p(c)pt,(

)p(c k,ij

(FEM)(FEM)

Lk = 1

Lk(t)

(MBS)(MBS)


Neglegible dynamicsNeglegible dynamics:: staticstatic approachapproach

LoadsLoads Stress /Stress / StrainStrain



14/20


System(with flexible components)SystemSystem((with flexible componentswith flexible components)) ComponentComponentComponent

,

t

Lagrange CoordinatesLagrange Coordinates

qk(t)

Relevant dynamicsRelevant dynamics:: modalmodal approachapproach


+=bB

q=

=

=

n

1i

ii )t(q)r()rt,(

Stress /Stress / StrainStrain

(FEM)(FEM)

(MBS)(MBS)

k,ij

=

=

n

1k

kk,ijij )t(q)pt,(


15/20


,

t

Stress /Stress / DeformationDeformationRainFlowRainFlow

MaterialMaterialMaterial

,

n

SpectraSpectra

,

10 3 10 5 10 7 10 9

=i i

i

NnD

LifeLife

DamageDamage

(MBS)(MBS)with Flexible bodieswith Flexible bodies

Damage EvaluationDamage Evaluation


16/20


11321132 HzHz

FirstFirst naturalnatural modemode

ofoffreefree--free crankfree crank

MM

BB

Why use Flexible ApproachWhy use Flexible Approach ??

1414 HzHz

MM

FirstFirst naturalnatural mode ofmode of

system in asystem in a particularparticular

configurationconfiguration

Weighted loads spectraWeighted loads spectra

Stress TimeStress Time historieshistories onon notch critical planenotch critical plane

Rigid crankRigid crank: life of: life of8.6108.61055 cyclescycles

Flexible crankFlexible crank: life of: life of2.4102.41055 cyclescycles

ADAMS & ANSYSADAMS & ANSYS Integrated ToolsIntegrated Tools


17/20


)(tqk)(tLk ,,

k)(, pc kij ,,

SystemSystem(MBS)(MBS) (FEM)(FEM)

ComponentComponent

ADAMS & ANSYSADAMS & ANSYS Integrated ToolsIntegrated ToolsforforStressStress RecoveryRecovery (SR) and(SR) and Damage EvaluationDamage Evaluation (DE)(DE)

MBS (MBS (AdamsAdams))

AutomaticAutomatic ProcedureProcedure

TimeTime Domain AnalysesDomain Analyses

LLkk(t)(t) TimeTime HistoriesHistories

qqkk(t)(t) TimeTime HistoriesHistories ((OrthoOrtho))qqkk(t)(t) TimeTime HistoriesHistories ((deOrthodeOrtho))

ModalModal ModelModel

kk Full orFull orReducedReduced ModelModel ModesModes ((OrthoOrtho))

Modal LinearModal LinearSuperposition (Superposition (OrthoOrtho))

uu ijij (t)(t) Full orFull orReducedReduced ModelModel DispDisp. Time. Time HistoryHistory

FEM (FEM (AnsysAnsys))

AutomaticAutomatic ProcedureProcedure

TimeTime domaindomainAnalysesAnalyses

on Full oron Full orReducedReduced ModelModel

SR (SR (by applied dispby applied disp.. uu ijij (t)(t) ))Static LinearStatic Linearsuperpositionsuperposition

on Full Modelon Full Model

Static analisesStatic analises ((LLkk= 1 )= 1 )

SRSR byby superposition (superposition (LLkk(t)(t) fromfrom MBS)MBS)

Modal LinearModal Linearsuperposition (superposition (OrthoOrtho))

on Full oron Full orReducedReduced ModelModelModes Recovery fromModes Recovery from MBS (MBS (by applied Dispby applied Disp.. kk ))

Model SRModel SR byby superposition (superposition (OrthoOrtho qqkk(t)(t) fromfrom MBS)MBS)

Modal LinearModal Linearsuperposition (superposition (deOrthodeOrtho))


SRSR byby superposition (superposition (deOrthodeOrtho qqkk(t)(t) fromfrom MBS)MBS)



18/20


ADAMS & ANSYS& Integrated ToolsgforforStressStress RecoveryRecovery (SR) and(SR) and Damage EvaluationDamage Evaluation (DE)(DE)

MBS (MBS (AdamsAdams) GUI) GUI

TimeTime Domain AnalysesDomain Analyses

LLkk(t)(t) TimeTime HistoriesHistories

qqkk(t)(t) TimeTime HistoriesHistories ((OrthoOrtho))

qqkk(t)(t) TimeTime HistoriesHistories ((deOrthodeOrtho))

ModalModal ModelModel

kk Full orFull orReducedReduced ModelModel ModesModes ((OrthoOrtho))

Modal LinearModal LinearSuperposition (Superposition (OrthoOrtho))

uu ijij (t)(t) Full orFull orReducedReduced ModelModel DispDisp. Time. Time HistoryHistory



19/20


FEM (FEM (AnsysAnsys)GUI)GUI

TimeTime domaindomainAnalysesAnalyses


SR (SR (by applied dispby applied disp.. uu ijij (t)(t) ))

Static LinearStatic Linearsuperpositionsuperposition


Static analisesStatic analises ((LLkk= 1 )= 1 )

SRSR byby superposition (superposition (LLkk(t)(t) fromfrom MBS)MBS)

Modal LinearModal Linearsuperposition (superposition (OrthoOrtho))


Modes Recovery fromModes Recovery from MBS (MBS (by applied Dispby applied Disp.. kk ))

Model SRModel SR byby superposition (superposition (OrthoOrtho qqkk(t)(t) fromfrom MBS)MBS)

Modal LinearModal Linearsuperposition (superposition (deOrthodeOrtho))


SRSR byby superposition (superposition (deOrthodeOrtho qqkk(t)(t) fromfrom MBS)MBS)

ggforforStressStress RecoveryRecovery (SR) and(SR) and Damage EvaluationDamage Evaluation (DE)(DE)

1122



20/20


=i i

i

N

nD

)(tqk)(tLk ,,

k)(, pc kij ,,

SystemSystem(MBS)(MBS) (FEM)(FEM)ComponentComponent

MaterialMaterial Stress LifeStress Life

StrainStrain LifeLife

WhlerWhlerMinerMinerm.,m., HaibachHaibach,, Liu ZennerLiu Zenner

MinerMiner

RambergRamberg--OsgoodOsgood

NeuberNeuber

MansonManson--CoffinCoffin

SmithSmith--WatsonWatson--TopperTopper

Critical planeCritical plane

Critical pointsCritical points

ggforforStressStress RecoveryRecovery (SR) and(SR) and Damage EvaluationDamage Evaluation (DE)(DE)

Weighted Load spectrumWeighted Load spectrum

Rain Flow MatrixRain Flow Matrix of Stress THof Stress TH

Stress TH onStress TH on critical planecritical plane

Documents

Perugia Stress Evaluation