Institute for Structural Analysis
Umformsimulation mit LS-DYNA und ETA/DYNAFORMInstitute for Structural Analysis
Beurteilung und Beeinflussung der Beurteilung und Beeinflussung der Zuverlässigkeit von Tiefziehprozessenin der frühen Entwurfsphasein der frühen Entwurfsphase
Stephan PannierWolfgang GrafMichael KaliskeMichael Kaliske
Kathrin GrossenbacherMarkus GanserMarkus GanserArnulf Lipp
Martin LiebscherMartin LiebscherHeiner Müllerschön
Introduction
Motivation
charge A too many rejects in reliablecharge Bcharge A y j
production process production processcharge B
• numerical verification afterwards
• source of trouble - delivery tolerances
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Introduction
Definition
reliability analysis
reliability analysis
reliability analysis
design process manufacturing
t
• reliability analysis in an early design stages
modifications of design parameters easier
less expensive modifications
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• identification of alternative design spaces
Introduction
Example
• e.g. input: 2 draw bead forces, 1 binder forceresult: thinning of blank
• simple deep drawing example – 3 input quantities, 1 results quantity
result: thinning of blank
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Introduction
Example
• e.g. input: 2 draw bead forces, 1 binder forceresult: thinning of blank
• simple deep drawing example – 3 input quantities, 1 results quantity
result: thinning of blank
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Introduction
Solution statement
reliability assessment
no rejects rejectsno rejects
identification of permissible design and uncertainty ranges
j
unmodifieddesign
and uncertainty ranges
design specification of alternative design spaces
• preconditionspreconditions
rare, vague information about uncertainty ranges
arbitrary structural behavior, no one-to-one functions
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applicability of alternative design ranges in industrial environment
Institute for Structural AnalysisInstitute for Structural Analysis
Reliability analysis
Reliability analysis
Uncertainty modeling
uncertainty
aleatoric epistemic
randomness perception/evaluation
objective data subjective assessment
• abundant (objective) data• discrete random events• gambling
• limited (subjective) data• imprecise measurements• linguistic quantification
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• experience/expert knowledge
Reliability analysis
Uncertainty modeling
objective information
f(x) µ(x)f(x) µ=01
f(x)~
µ=1
x
randomness
x
fuzziness
xfuzzy
randomnessrandomness
subjective information
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j
Reliability analysis
Fuzzy set
1
• general definition
convexity• convexity
• -level discretization • -level optimization
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Reliability analysis
Fuzzy structural analysis
fuzzy inputquantity
fuzzy inputquantity
mappingmapping
"-level optimization"-level optimization" level optimization" level optimization
fuzzy resultquantity
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Specification of lt ti d i alternative design spaces
Specification of alternative design spaces
General scheme
constraints identificationof partition
alternative design spaces
generation of point set
pac
ein
put
s
z=f(x) x=f-1(x)
cesu
lt s
pac
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res
Specification of alternative design spaces
Dimensionality problem
• 3D • 2D
• more than sensitive 3 input quantities
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Specification of alternative design spaces
General scheme
constraints identificationof partition
alternative design spaces
generation of point set
pac
ein
put
s
z=f(x) x=f-1(x)
cesu
lt s
pac
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res
Specification of alternative design spaces
Partition
permissible
constraint
non-permissible
le len- le n- le
per
mis
sibl
per
mis
sibl
non
per
mis
sibl
non
per
mis
sibl
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p pp p
Specification of alternative design spaces
Cluster analysis – objective
- pairwise disjoint
preconditions on clusters
- nonempty
- reproduce point set
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Specification of alternative design spaces
Cluster analysis – objective
homogeneity • homogeneitypoints in a same cluster should be as similar as possible
heterogeneity
• heterogeneityg ypoints of different clusters should be as dissimilar as possible
determination of an appropriate cluster configuration ; optimization task
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predefined number of clusters - challenge
Specification of alternative design spaces
General scheme
constraints identificationof partition
alternative design spaces
generation of point set
pac
ein
put
s
z=f(x) x=f-1(x)
cesu
lt s
pac
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res
Specification of alternative design spaces
Alternative design space(s)
h ll h b id l convex hull vs.hypercuboid
hypercuboids per cluster vs.maximal possible hypercuboids
interacted design variables hypercuboid
bases on available
ambitiousand expensive
available point set
interaction-free detection design variables of number of
non-connected input spaces
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Examples
Rosenbrock function
Rosenbrock function z=f(x,y)
xy
permissibility condition
x x
yy y
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z z
Metal forming example I
Model
crack sensitive area
computational model FLD
results
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Metal forming example I
Reliability assessment – Fuzzy Analysis
Input parameters Delivery tolerances Fuzzy quantitiesp p
yield stress
tensile
Rp02
Rm
y
180 … 230
340 … 420
y q
<180, 205, 230>
<340, 380, 420>strength
hardeningexponent
n 0.20 … 0.30 <0.20, 0.22, 0.30>
anisotropy R90 1.80 … 4.00 <1.80, 2.40, 4.00>
1.0
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Metal forming example I
Reliability assessment – fuzzy analysis
• evaluated results
cracking
(Grossenbacher 2008)
cracking
thinning
f lt tit• fuzzy result quantity
number of -levels: 5
rain
t
determined intervalbounds of -level: co
nstr
simulations runs: 150
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Metal forming example I
Constraints
cross-plot: n – R90cross-plot: Rp02 – Rm
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permissible non-permissible
Metal forming example I
Partitioning – cluster analysis
cross-plot: n – R90cross-plot: Rp02 – Rm
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not assigned non-permissibleCluster Cluster
Metal forming example I
Partitioning – cluster analysis
3 cl ste 4 cl ste 5 cl ste3 cluster 4 cluster 5 cluster
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Metal forming example I
Alternative design space
cross-plot: n – R90cross-plot: Rp02 – Rm
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permissible non-permissiblealternative design space
Metal forming example II
Model
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Metal forming example II
Input quantities
1.0
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Metal forming example II
Reliability assessment – fuzzy analysis
• evaluated results
− geometry
− cracking (FLC)
− manufacturing
aint
• fuzzy result quantity
b f l l 2
cons
tra number of -levels: 2
determined intervalbounds of -level: bounds of level:
simulations runs: 232
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Metal forming example II
Demonstrator
Determination of Determination of alternative design spaces
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Conclusions
Conclusions
• assessment of reliability in an early design stages reasonable
• determination of alternative design spacesinstead of an optimal design
• detection of non-connected point sets with cluster analysis
li bilit i d li d
• assignment of hypercuboids to clusters − only permissible points
• applicability is underlined by means of an industry-relevant example
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Institute for Structural Analysis
Umformsimulation mit LS-DYNA und ETA/DYNAFORMInstitute for Structural Analysis
Beurteilung und Beeinflussung der Beurteilung und Beeinflussung der Zuverlässigkeit von Tiefziehprozessenin der frühen Entwurfsphasein der frühen Entwurfsphase
Stephan PannierWolfgang GrafMichael KaliskeMichael Kaliske
Kathrin GrossenbacherMarkus GanserMarkus GanserArnulf Lipp
Martin LiebscherMartin LiebscherHeiner Müllerschön