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ABSTRACT

Utilizing the Finite Element Method (FEM), two

evolving CAE methods have recently reached a

high level of efficiency and accuracy to optimize

the properties of components in respect ofstiffness, stress level or fatigue resistance.

The first type of CAE-methods is a family of

optimization methods known as (parameter-free)

shape and topology optimization. Very

remarkable and useful results can be generated

with these methods to reach considerable

stiffness increases or stress and weight

reductions.

The second CAE-method is fatigue lifeprediction which gives reasonable accurate

outputs for component life if input data like stress

history and material properties are well known.

State of the art algorithms and software can

handle a combination of complex load histories,

detailed material description and large FEM-

data to give reliable results in short time.

It will be demonstrated, using test cases and real

world components, that combining these two

CAE-methods can significantly increase theoptimization level in respect to lifetime or weight.

In the case of combining topology optimization

with fatigue life prediction, which is a rather new

idea, it can be detected that both material type

(brittle / ductile) and loading history often have a

decisive influence on the resulting design of

components. Compared to common usage of

FEM-based optimization, higher savings of

weight can be obtained by including fatigue life

prediction.

INTRODUCTION

The reduction of vehicle weight is, at leastsince the drastic raise of fuel prices in theseventies, a basic requirement for thedevelopment of any new component or wholevehicle. Nevertheless there is a generatendency in the opposite direction. Reasonscan be found in additional features for morecomfort and safety as well as increased enginetorque.

In order to safe weight, the use of high strengthmaterials is a solution to realize lightweighstructures. For components undergoing cyclicloading, one has to consider that the effect onfatigue life by stress concentrations in notchesgenerally increases with the use of highstrength materials. Vehicles have to withstanddifferent types of loading requirementsincluding effects from notches, weld seams andspot joints. How can engineers handle thesemultiple goals during the developmentprocess?

Generally there are two methods available forthis optimization process: test and numerica

simulation.By performing tests for complete vehicles orcomponents, many influences can beconsidered without any mathematical modelUnfortunately, experimental tests give only poorinformation about over-designed areas and areexpensive and time consuming.

Numerical simulation and optimization can helpto achieve a quicker engineering process andis the only way to get higher levels of

2004-32-0085 / 20044372

Combining FEM-Optimization and Durability Analysisto Reach Lower Levels of Component Weight

Klaus Puchner, Christian Gaier and Helmut DannbauerMAGNA STEYR, Engineering Center Steyr, Austria

Copyright 2004 SAE International and Copyright 2004 Society of Automotive Engineers of Japan, Inc.

performance at a lower weight. The following

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disciplinary optimization is about to be usedsoon. These other disciplines can be NVH andcrash-safety for instance.

FATIGUE LIFE PREDICTION

The structural stress distribution from a finiteelement analysis, the loading of the part, e.g.from a Multi Body Simulation or measurementsof a test drive as well as the material propertiesare the basic input data for fatigue lifeprediction.

During the analysis, many things have asignificant effect on the predicted fatigue lifeand have to be considered including, forexample:

Dynamic stress

Mean stress

Notch sharpness

Temperature of operation

Surface conditions

Joints (e.g. welds, rivets)

Plastic effects

Material properties

Durability analysis can be done in differentregimes. This means basically defining acriterion of failure for a component. In groundvehicle industry the failure criterion is alwaysthe appearance of cracks with a technical size(detectable by visual inspection and a few mmlength). In aerospace industry, due to muchhigher importance of low weight and adaptedmaintenance systems, the criterion is also oftenrelated to a safe crack length.For predicting crack initiation, different regionsof load level and cycle number candistinguished. At very high load levels andconsequently very low cycle numbers (

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The analysis was performed for 2 differentmaterials; steel and gray cast iron respectively,see figures 6 and 7.

Fig. 6: Shape and damage values for steel

Fig. 7: Shape and damage values for gray cast

It can be observed that the usage of fatigueresults rather than using direct finite element

analysis results generates two completelydifferent designs for the 2 material each. Forobvious reasons, this could not be achieved byonly changing the modulus of elasticity andPoissons ratio which is necessary to run thefinite element analysis. The tiny changes instress would create no effect during topologyoptimization. Furthermore, a very good materialutilization in both designs can be observed,which is expressed by very uniform damagedistributions.

EXAMPLE 2

In the second example, a shape optimizationshall be performed for the critical area of awheel carrier. Three forces are acting on thiscomponent with three different andindependent time histories. Since the loadingcondition is changing in time, it would beimpossible to use the resulting stress or strain

history for optimization. Instead it would benecessary to select a few stress distributions atdiscrete instances. The introduction of multi-axial fatigue life prediction eliminates thisdifficult task and computes one single damagevalue per node. Therefore damage can beeasily used for the automatic optimizationprocess.

Fig. 8: Example 2 Shape optimization osuspension component

Contrary to the topology optimization in theexample 1 where a global design wascreated, the area for which the shapeoptimization is performed is restricted to a

known critical area as shown in figure 9.

Fig. 9: Critical area for damage

A comparison of the damage distributions forboth, the original and the modified design isshown in figure 10 and 11. It can be seen thatthe max. damage was reduced from D = 0.0383in the original design to D = 0.00224 in theoptimized design which is a reduction of

about 96%.

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Fig. 10: Critical area, damage original design

Fig. 14: Critical area, damage new design

As it turnes out, the integration of fatigue life

prediction i.e. the usage of damage or safetyfactors as the design optimization criteriaimproves the quality of structural optimizationresults. The reasons can be found in:

Adequate interpretation of static anddynamic loads

Consideration of load histories

Consideration of material properties

CONCLUSION

Today, the use of numerical analysis methodsplays an important role in the developingprocess in automotive industry and there is awide range of possible applications. Fatiguelife prediction and automatic optimization are

powerful software tools which help theengineers to improve products to a higher levemore quickly.

While shape and dimension optimization toolsare in use for years already, the increasedcomputer power recently enables theintegration of topology and shape optimizationat the very beginning of a design processTherefore, new designs can be created and alarge optimization potential can be utilized.The effectiveness of these approaches wasdemonstrated with examples.

CONTACT

Klaus Puchner, Dr. Christian Gaier and HelmutDannbauer are members of the EngineeringCenter Steyr, located at Steyrer Strasse 32, St.Valentin, Austria, Europe. The EngineeringCenter Steyr is part of the MAGNA STEYRgroup.

REFERENCES

1. FKM-Richtlinie, Festigkeitsnachweis,Forschungsheft 183-2, Vorhaben Nr. 154,Frankfurt. 1994.

2. Eichlseder, W. Rechnerische Lebens-daueranalyse von Nutzfahrzeugkompo-nenten mit der FE-Methode, Dissertation,TU Graz. 1989.

3. Kttgen, V.B., Oliver, R., Seeger T.,

Schwingfestigkeitsnachweise frSchweissverbindungen auf Grundlagertlicher Beanspruchungen, Forschungs-hefte, Heft 143, FKM, Frankfurt. 1989.

4. Radaj, D., Gestaltung und Berechnung vonSchweisskonstruktionen, Ermdungs-festigkeit, DVS, Dsseldorf, 1985.

Other fatigue influence factors can beconsidered

5. Grn F., Form- und Topologieoptimierungunter Bercksichtigung der Betriebsfestig-keit , DA MU Leoben, 2002.