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Advanced Engineering Informatics 30 (2016) 713–727
Contents lists available at ScienceDirect
Advanced Engineering Informatics
journal homepage: www.elsevier .com/ locate/ae i
Full length article
Product design-optimization integration via associative
optimizationfeature modeling
http://dx.doi.org/10.1016/j.aei.2016.09.0041474-0346/� 2016
Elsevier Ltd. All rights reserved.
⇑ Corresponding author.E-mail address: [email protected]
(Y. Ma).
Jikai Liu, Zhengrong Cheng, Yongsheng Ma ⇑Department of
Mechanical Engineering, University of Alberta, Edmonton, AB,
Canada
a r t i c l e i n f o a b s t r a c t
Article history:Received 26 November 2015Received in revised
form 19 September2016Accepted 27 September 2016Available online 1
October 2016
Keywords:Associative featureAssociative optimization
featureProduct design processStructural optimizationOptimization
intent
This paper addresses an important problem of integrating
structural optimization into a traditional CAxsystem and therefore,
realizes an integrated product design-optimization system.
Specifically, structuraloptimization has been embedded as an
independent module of most commercial CAx systems. It
mainlycommunicates with CAD but can only have the STL-based CAD
geometry as input. The knowledge-levelinformation transfer is not
supported which causes the optimization intent not fully captured.
The con-sequence could be quite negative that the optimization
process generates unsatisfactory or even uselessdesign solutions
and tedious manual efforts are required to modify or even redesign
the immature solu-tions, which reduces the overall design
efficiency and quality. To fix this issue, this paper proposes
anintegrated product design-optimization system by enabling the
complete information transfer betweenCAD and structural
optimization modules. Interfacing rules have been defined to enable
the completeinformation transfer and the associative optimization
feature concept is proposed to manage the trans-ferred information
for the structural optimization module. Furthermore, knowledge
based reasoning isperformed to capture the full optimization intent
in order to create a fit-for-purpose optimization model,including
both the optimization problem formulation and the solution
strategy. For technical merits, thisintegrated product
design-optimization system robustly ensures the timely and
high-quality productdesign delivery which is superior to the
existing commercial systems. Effectiveness of this proposed sys-tem
has been proven through a few case studies.
� 2016 Elsevier Ltd. All rights reserved.
1. Introduction
Industrial products are embedded of increasingly rigorous
andcomplex design requirements which make the product design
pro-cess difficult and time-consuming. To meet the challenge,
increas-ingly more design tasks are solved through structural
optimizationalgorithms and the structural optimization tools are
gaining thepopularity. Generally speaking, structural optimization
algorithmperforms the finite element analysis to evaluate the
structural per-formance and accordingly, calculates the sensitivity
result todecide design changes. This process is repeated till
convergenceand the derived design solution is at least close to the
global opti-mum which can hardly be achieved through the
traditional trial-and-error approach.
A flow chart of the feature-based product design process
involv-ing structural optimization is demonstrated in Fig. 1. We
can seethat structural optimization plays a major role during the
embod-
iment design phase which effectively generates the design
solutionfrom a conceptual idea or an existing product model.
After introducing the background, this paragraph will
disclosethe remaining research issue that structural optimization
is notfully embedded into the feature-based product design process;
inother words, the structural optimization module is not a
well-integrated part of the CAx-based product design system. As
indi-cated in Fig. 1, structural optimization starts by extracting
geome-try from a conceptual CAD model or an existing product model.
Allthe attached semantic information is just removed and
theirimportance is ignored. The semantic information is generally
areflection of design intent which supports the product
relatedhigh-level reasoning, e.g. functionality and
manufacturability eval-uations. Conventionally, a major principle
of feature-based designis to keep the information consistency in
order to avoid designintent violations. However, the geometry
extraction procedure def-initely violates this principle, which in
fact isolates the structuraloptimization module and makes it a
standalone tool. The impactof ignoring the attached semantic
information is quite negativethat, the optimization process would
generate less optimal or even
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Fig. 1. Feature-based product design process involving
structural optimization.
714 J. Liu et al. / Advanced Engineering Informatics 30 (2016)
713–727
useless design solutions and afterwards, tedious manual efforts
arerequired to modify or even regenerate the solutions.
An example is demonstrated in Fig. 2. External profile of
thepipe gripper is generated as a conceptual idea and the internal
ribsare to be designed through structural optimization. The
semanticinformation attached indicates the injection molding
manufactur-ing method. Then, if only the geometry is imported into
the struc-tural optimization module, it will generate the solution
aspresented in Fig. 1b; in contrast, if the attached
manufacturinginformation is also received and properly interpreted,
the optimalsolution will satisfy the constant rib thickness
requirement asdemonstrated in Fig. 1c which employs much better
manufactura-bility. In summary, embedment of the structural
optimization
module into the CAx-based product design system is not well
real-ized because of the incomplete information transfer.
To fix this issue, the paper proposes an integrated
productdesign-optimization systemwhich supports the complete
informa-tion transfer between the internal modules. The framework
is pre-sented in Fig. 3.
This system consists of four main components: associative
fea-ture modeling, information transfer, associative optimization
fea-ture modeling, and optimization intent capture. The
associativefeature concept was proposed earlier by the authors (see
Fig. 4)[26,28]. It effectively supports the sematic information
creationand management, and therefore, is adopted as the core part
ofthe information management mechanism in CAD module.
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(a) Initial design domain and loading condition
(b) Optimization result without manufacturing information
(c) Optimization result with captured manufacturing
information
Fig. 2. Impact of the semantic information loss.
Fig. 3. Framework of the proposed system.
J. Liu et al. / Advanced Engineering Informatics 30 (2016)
713–727 715
Information transfer is mandatory and the main requirement is
toensure the completeness. Since both the geometry and theattached
sematic information are represented in different formsbetween the
internal modules, a set of interfacing rules has beenestablished to
support the information transformation. The asso-ciative
optimization feature is a newly proposed concept whichfollows the
associative feature concept and realizes the equivalentinformation
management in structural optimization module. Thelast but the most
important component: optimization intent cap-ture, interprets the
semantic information contained by the associa-tive optimization
feature model and serves the role of creating afit-for-purpose
optimization model. Details about these compo-nents will be
introduced in the later sections.
For the technical merits of this proposed system,
productdesign-optimization integration is realized through the
completeinformation transfer between the internal modules; more
impor-tantly, the semantic information can be properly interpreted
fromthe perspective of structural optimization through
knowledgebased reasoning to create a fit-for-purpose optimization
model.Both design efficiency and quality could be greatly
enhanced.
To highlight the technical merits, a brief survey about the
com-mercial software systems is conducted. So far, structural
optimiza-tion has been embedded as a module of most commercial
CAxsystems, e.g. the OptiStruct from Altair HyperWorks, and
theSIMULIA Tosca Structure applied in Abaqus, ANSYS, and MSC
Nas-tran. However, these systems commonly share the limitation
thatthe CAD and structural optimization modules are only
integratedat the geometry level, i.e. the structural optimization
module readsin the STL-based CAD geometry. At the knowledge level,
majorityof the design intent is lost and the optimization intent is
restored
based on the designer’s intuition which is tedious and lacks
ofcompleteness. On the other hand, the structural optimization
mod-ule supports few options about the optimization intent
restoration,such as design domain selection, symmetric and
repetitive pat-terns, and minimum length scale, which are far from
enough.Therefore, the integrated design-optimization system
proposed inthis work shows superior characteristics in optimization
intentcapture and optimization model creation.
It is also worth noticing that, scope of this paper is to
demon-strate how this proposed system works by emphasizing the
con-sisting components and their inter-relationship. A few
prototypeswill be programmed for demonstration, instead of
developing arigorously working platform based on commercial
software tools.
The following contents will be organized as: Section 2 presentsa
literature survey about the associative feature modeling and
thelevel set structural optimization. Section 3 introduces the
associa-tive optimization feature concept and the interfacing rules
forcomplete information transfer. Section 4 introduces the
optimiza-tion intent concept and its capture through the knowledge
basedreasoning. Section 5 presents two 3D design examples to
demon-strate the effectiveness of feature based product
design-optimization integration. A conclusion is given in Section
6.
2. Literature survey and motivations
2.1. Associative feature modeling
Feature technology plays a dominating role in today’s
productdesign process. Specifically, geometric feature serves as
the basisfor product modeling; functional feature associates
the
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Fig. 4. Partial relations defined in the associative
feature/associative assembly feature class [28].
716 J. Liu et al. / Advanced Engineering Informatics 30 (2016)
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functionality to the geometry; engineering features,
includingmanufacturing feature and assembly feature, etc., attach
certainengineering meanings to the geometry to address
downstreamengineering concerns during the early design stage. In
summary,feature-based design unifies the geometry and the semantic
infor-mation to build the product model, which supports the
high-levelreasoning from different engineering aspects, e.g.
functionality andmanufacturability evaluations, etc. [25,8].
Because of the diversified feature definitions, numerous
seman-tic information could be attached to a product model. It has
been along-lasting issue about how to effectively manage the design
con-sistency during the entire product design process, spanning
fromthe conceptual design, the embodiment design, to the
detaildesign. Quite a few management mechanisms have been
proposed[26,28,35,46,5], among which the associative feature
concept, pro-posed by [26,28], works effectively and shows
outstandingcharacteristics.
Associative feature was introduced in the form of
self-containeddesign object group with a set of geometric and
non-geometricdesign associations (DAs) built on the product
geometry entities[26,27,28]. Here, geometric DAs indicate the
spatial relationshipsamong the geometric entities and non-geometric
DAs mean theattributes attached to the geometric entities.
Therefore, associativefeature offers a mechanism of tightly bonding
the semantic infor-mation to the geometric entities through DAs,
and it has been pro-ven that associative feature could deal with
the intricacy of DAs
across the multiple design stages and effectively maintain
thedesign consistency subject to the numerous design
changes[26,27,28,29].
The first implementation of associative feature was found in
thearea of mold design which made extensive use of the
‘‘smartobjects” [26,27]. The cooling channels was abstracted into
smartguiding lines associated with attributes describing the
coolingchannel diameter, depth, and end type, etc. Geometrically,
thesmart guiding lines were mutually associated to form the
coolingsystem. With such well-organized DAs, designers could be
releasedfrom the tedious geometry reconstruction subject to any
designchange, which significantly shortens the mold design
process[26,27,29]. The associative feature concept later was
extended tothe assembly design domain by defining the associative
assemblyfeature, which realized the DA management between
components[28].
A few requirements of associative feature modeling have
beenidentified and summarized as below [28]:
� All DAs related to geometric entities must be collected to
form acomplete associative feature model.
� A self-validation mechanism must be defined to check the
con-sistency of the associative feature instances.
� Necessary methods for construction, storing, indexing,
editing,and destroying the associative feature instances must
beprovided.
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� The associative feature must be query-able and executable
forhigh level knowledge process.
� The associate feature must be able to interact with other
engi-neering applications.
In fact, some commercial CAx systems have implemented sim-ilar
concepts as of associative feature. CATIA has the knowledge-ware
module to capture engineering knowledge. Geometric DAscan be
established through building formulas on the geometricparameters
and there is the check function to ensure the formu-lated
relationship not violated. Basic geometric entities can begrouped
to form user defined features or part templates. Thepowercopy
function greatly facilitates the product design andknowledge reuse.
More importantly, rules can be established forhigh-level
engineering reasoning and the rules can be automati-cally checked
to prevent violation. NX has a similar module namedKnowledge
Fusion, which provides the similar functionalities.
Even though the effectiveness of the associative feature
model-ing has been proven by many research works and commercial
soft-ware tools, the concept is never extended to the
structuraloptimization domain, especially for shape and topology
optimiza-tion. As discussed earlier, the semantic information
attached tothe CAD geometry get stripped off during model transfer,
or inother words, all the attached DAs are removed. Therefore, it
is crit-ical to develop the associative optimization feature
concept toinherit and manage the complete information for the
structuraloptimization module.
2.2. Level set structural optimization
Normally, structural optimization can be classified into
threelevels: sizing optimization, shape optimization, and topology
opti-mization. For many problems, the different levels of
optimizationare concurrently involved. Therefore, structural
optimization inthis work will be based on the level set method
[36,38,1], becauseit well supports the concurrent sizing, shape,
and topology opti-mization, as well as the geometric feature
manipulations[9,10,11,30,50,4,18,23].
In addition, feature-based product design may be performedunder
different physical disciplines, e.g. solid mechanics,
fluiddynamics, thermodynamics, etc. Therefore, to be part of the
designprocess, structural optimization should be able to work under
anyof these physical disciplines, where level set method has
demon-strated the capability. In solid mechanics domain, Wang et
al.[38] and Allaire et al. [1] solved the
compliance-minimizationproblems; and later, the stress-minimization
and stress-constrained problems were also solved
[2,17,45,41,47,15]; in[39,40,43], the structural design problems
with multiple materi-als/functionally graded materials were
addressed through levelset method. About fluid mechanics, the flow
channel design prob-lems have been addressed through level set
method given differentflow types, e.g. Darcy flow, Stokes flow, and
Navier-Stokes flow[51,7,13,14]. Similarly, heat conduction problems
were also solvedthrough level set method [19,52]. For more details,
a comprehen-sive review could be found in [37].
Apart from the superior problem solving capability,
anotherreason of employing the level set method for structural
optimiza-tion is that level set itself is a powerful geometry
modelingmethod.
Osher and Sethian [33] proposed the level set function as a
nat-ural way of closed boundary representation. LetD 2 Rn ðn ¼ 2 or
3Þ be the initial design domain,X 2 Rn ðn ¼ 2 or 3Þ represent the
area filled with materials and@X be the boundary of the material
domain. UðXÞ : Rn#R; is thelevel set function that
UðXÞ > 0; X 2 X=@XUðXÞ ¼ 0; X 2 @XUðXÞ < 0; X 2 D=X
8><>: ð1Þ
Because of the implicit nature, level set function could
triviallydefine any freeform geometry, as well as the form
features[9,10,30]. For instance, a circle can be represented by
UðXÞ ¼ R� sqrtðX2 þ Y2Þ ð2Þand a square by
UðXÞ ¼ min L2� ðx� x0Þ; L2þ ðx� x0Þ;
L2� ðx� x0Þ; L2þ ðx� x0Þ
� �
ð3ÞThen, complex geometry can be formed by Boolean
operations
on the individual level set functions [9,10,30] as,
U1 [U2 ¼ maxðU1;U2ÞU1 \U2 ¼ minðU1;U2ÞU1 nU2 ¼ minðU1;�U2Þ
ð4Þ
Therefore, level set geometry modeling conforms to the
conven-tional CSG (constructive solid geometry) format. The
geometrytransfer from CAD into structural optimization module is
simpli-fied into the format transformation from B-rep to CSG. This
is asuperior advantage compared to other structural
optimizationmethods.
For the high-level attempts to embedding structural
optimiza-tion into feature-based product design process, Cugini et
al. [12]used the PROSIT approach to integrate CAI (Computer-Aided
Inno-vation) and PLM (Product Lifecycle Management) via the
topologyoptimization method. Later, Cardillo et al. [6] expresses a
similaridea of using topology optimization as the main body of
embodi-ment design, to connect CAI and PLM. Muzzupappa et al.
[31]defined the roles, activities, data to be exchanged, and
softwaretools to be used to integrate topology optimization into
productdevelopment process; special attentions have been paid to
knowl-edge transfer. However, these attempts are all based on
densitybased topology optimization method. It employs the
voxel-basedgeometry representation, with which the geometric
constraintsand the other semantic information are nearly impossible
to bemaintained. Additionally, sizing optimization cannot be
supportedwhich severely limits the optimization flexibility.
Therefore, weconclude that level set method is the most appropriate
for struc-tural optimization for the integration purpose.
Hence, in this work, level set structural optimization is
adoptedas the core method by the structural optimization
module.
3. Associative optimization feature modeling
3.1. Definition of the associative optimization feature
Associative optimization feature is an extension of the
associa-tive feature concept into the structural optimization
domain. Asshown in Fig. 5, it groups form and freeform features
representedby implicit level set functions, and manages the
in-group DAs,which has the similar definition as compared to
associative featureconcept. On the other hand, clear distinctions
exist between thesetwo concepts: (1) They are both domain-specific
concepts, as asso-ciative feature functions in the CAD module and
associative opti-mization feature is adopted by the structural
optimizationmodule. They express the feature group and in-group DAs
in differ-ent formats, and information communication and
inheritance asso-ciates these two concepts to collaboratively
support the featurebased product design. (2) From the perspective
of design flow,
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Fig. 5. Partial relations defined in the associative
optimization feature class.
718 J. Liu et al. / Advanced Engineering Informatics 30 (2016)
713–727
associative feature modeling and associative optimization
featuremodeling employ the sequential relationship. As illustrated
inFig. 1, associative feature functions at the conceptual and
detaildesign phases to manage the conceptual design and refine the
opti-mized solution; instead, associative optimization feature
plays therole in the embodiment design phase which calculates the
materialdistribution to form the embodied shape and topology.
3.2. Information transfer
To generate the associative optimization feature model,
itrequires the complete information transfer, including both
thegeometry and the attached DAs. Clear interfacing rules have
beendefined to support the transfer, as follows:
(1) Geometry transfer
In CAD systems, B-rep (Boundary representation) is the
widelyused geometry representation, which stores the explicit
boundaryentities and the in-between topological relationship;
however, CSG(Constructive solid geometry) is more appropriate to be
used byoptimization activities [9,10], because CSG employs the
implicitrepresentation which is not sensitive to topological
changes.Therefore, the primary step of the information transfer is
to trans-form the geometry representation from B-rep to CSG.
(2) DA transfer
DAs widely exist in the feature based product model, which canbe
both geometric and non-geometric, including ‘‘constraints,
dependencies, equations, memberships, part-whole relations,
cou-pling, patterns, etc.” [28]. A specific categorization is
plotted inFig. 6. It is worth noticing that, Fig. 6 covers some
frequentlyapplied DA types; however, it cannot cover all in a
single image.This categorization is extendable according to the
specific needs,i.e. there could be more manufacturing methods
involved otherthan the listed three.
About details of the DA transfer, non-geometric DAs remain tobe
semantically stored, while the imposed objects switch fromexplicit
boundary/body entities to implicit level set contours/-fields;
geometric DAs would be directly written into constraints,which
later will form part of the optimization problem formulationif
necessary.
An instance is presented in Fig. 7. The B-rep model is com-posed
of two explicitly represented block features, as well as agroup of
geometric and non-geometric DAs. When transformedinto the
optimization model, the block features are switched intolevel set
descriptions and combined by union operations as:U1 [U2. The
geometric DA: d1 > 5 is transformed into z1+ d2/2-(z2 +
d3/2)>5, where (x1, y1, z1) and (x2, y2, z2) are thecenter
points of feature 1 and feature 2, respectively. For non-geometric
DA, we assume a coating layer is designed to facesf1, f2, f3, f4,
and f5, and after transformation, it is re-attached tothe surface:
(@XU1[U2 \ @XU2).
So far, all required information transfer has been
completed,including both the geometry and the attached DAs. In
other words,the associative feature model has been switched into
the associa-tive optimization feature model. Again, it reveals that
these twoconcepts are equivalent in information representation
while theyserve for different engineering modules.
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Fig. 6. A specific categorization of DAs.
Fig. 7. Model transformation.
J. Liu et al. / Advanced Engineering Informatics 30 (2016)
713–727 719
4. Optimization intent
4.1. Introduction to optimization intent
In [49], design knowledge is subdivided into three
categories:process history, design intent, and domain specific
knowledge.For product modeling, modeling history and design intent
supportthe associative feature modeling, and assembly specific
knowledgesupports the associative assembly feature modeling. For
simula-tion, Nolan et al. [32] proposed the concept of simulation
intent,which was defined to ‘‘include all of the analysis, modeling
andidealization decisions, and all the parameters required to
createan efficient and fit-for-purpose analysis model from an
input
CAD geometry”. In fact, simulation intent is the simulation
specificknowledge captured from both the designer’s input and the
inter-pretation of the CAD geometry. For instance, loading and
boundaryconditions are defined by designer input, and detail and
dimensionreduction is performed by the system by analyzing the
geometry.
In this paper, we proposed the new concept, named optimiza-tion
intent. As indicted by the name, optimization intent belongsto the
structural optimization specific knowledge and it includesall
decisions in formulating and solving the optimization problem.It is
obtained by reasoning the associative optimization featuremodel and
also receiving some supplemental user input. Properlyand completely
capturing the optimization intent is extremelyimportant because it
will facilitate the effective and efficient
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720 J. Liu et al. / Advanced Engineering Informatics 30 (2016)
713–727
optimization model creation. To fulfill this job, knowledge
basedreasoning is mandatory and a list of possible optimization
intentattributes should be summarized; see Table 1.
It is worth noticing that this table covers majority of the
attri-butes within the authors’ knowledge scope. It is general in
applica-tion and could cover a large variety of optimization
problems.However, this table may be extended in the near future as
thestructural optimization technique is currently under rapid
devel-opment and accordingly, new optimization intent attributes
mayappear.
4.2. Optimization intent capture
4.2.1. Define the optimization variables/optimization
domainsAfter model transformation, the feature based CSG model
con-
tains numerous implicitly-represented feature primitives, as
wellas their parameter sets. Generally, they would not all be
employedas designable optimization variables/domains and user input
isrequired to make the selection.
One situation is that the feature primitive is only allowed
withparametric changes, which means design freedoms of scaling,
rota-tion and movement. The designer needs to pick up the active
sizingand mounting parameters to be the designable optimization
vari-ables. For the other situation, the feature primitive is
allowed ofshape and topological changes and this type of feature
primitivewould be defined as designable optimization domain of the
levelset structural optimization. However, because of the shape
andtopological changes, parameters related to the feature
primitivewill disappear and so will the related geometric DAs. To
fix thisproblem, a bounding feature is virtually added which is
geometri-cally identical to the initial feature primitive. It
inherits the sizingand mounting parameters; see Fig. 8, and the
main function is tomaintain the related geometric DAs.
Structural optimization is a simulation based reverse
process.Therefore, the simulation intent should be manually defined
aswell. It specifically includes the attributes of
dimensionality,boundary condition, mesh type, model clean-up, and
solution type,etc.
4.2.2. Define the basic optimization intentThe basic
optimization intent includes the objective function,
physical constraints, solution method, sensitivity analysis
tech-nique, and design update. Definition of the basic
optimizationintent relies on user input, and it is already
commercialized inmost structural optimization tools.
Table 1Optimization intent attributes.
Optimization intentattribute
Potential decisions
Objective function Compliance minimization/Stress
minimization/Energydissipation minimization/. . . . . .
Extra controlfunctional
Thickness control/Boundary smoothing/Graduatechange of material
mixture. . . . . .
Physical constraint Stress constraint/Material volume
constraint/Component/void size constraints/Boundary
curvatureconstraint/. . . . . .
Geometricconstraint
Angle/Parallel/Perpendicular/Distance/. . . . . .
Optimizationvariable
Level set function/Geometric parameters/Localmaterial
parameter/. . . . . .
Optimizationdomain
Optimization domain/Multi-material
optimizationdomain/Non-optimization domain
Solution method Lagrange multiplier method/. . . . .
.Sensitivity analysis
techniqueRegular sensitivity analysis on the level set function
orother parameters/Repetitive or symmetric sensitivityanalysis/. .
. . . .
Design update Solving the Hamilton-Jacobian
equation/Parametricupdate/Adjustment of boundary velocities
The general level set structural optimization formulation
is,
min Jðu;UÞ ¼ZDFðuÞHðUÞdX ðobjective functionÞ
s:t: aðu;v;UÞ ¼ lðv ;UÞ ðweak form of the governing
equationÞVðUÞ ¼
ZDHðUÞdX 6 Vmax ðmaterial volume constraintÞ
ð5ÞThrough adjoint sensitivity analysis, the sensitivity result
can be
derived as,
L0ðu;w;UÞ ¼ZDbðu;w;UÞdðUÞdX ð6Þ
where Lðu;w;UÞ is the Lagrange function and bðu;w;UÞ is the
shapesensitivity density; u is the status variable such as
deformation ortemperature and v is the test variable; w is the
adjoint variable. Itshould be emphasized that the sensitivity
result has to be in theboundary integration form because of the
boundary velocity baseddesign update, and the shape sensitivity
density determines the rateof local boundary evolvement.
Based on the sensitivity result, the regular approach for
designupdate is to solve the Hamilton-Jacobi equation through
upwinddifference. For more details, interested readers can refer to
[34].
4.2.3. Analysis of the associative optimization feature
modelOther than the basic optimization intent, the main
contribution
of this paper is to capture the optimization intent through
reason-ing the DAs managed by the associative optimization
featuremodel.
As mentioned earlier, knowledge based reasoning is mandatoryand
a list of rules should be established. These rules support
thedecision making in mapping the DAs contained by the
associativeoptimization feature model into specific optimization
intent attri-bute selections. Specifically in implementation, an
inference agentgoes through the DA list and creates the related
mappings. Therecould be different situations that: some DAs are
clearly mappedinto optimization intent attribute selections; some
DAs are irrele-vant to any optimization intent, e.g. geometric DA
defined onnon-designable parameters; some DAs would lead to
conflictingoptions of an optimization intent attribute which
requires userintervention to resolve the conflict; and some DAs
lead to incom-plete optimization intent attribute which requires
additional userinput to supplement information, e.g. targeted
thickness value ofthe uniform thickness requirement. All these
situations should bepredicted in advance and resolvable by the
inference agent.
So far, we have accumulated the following rules to support
theknowledge based reasoning.
(1) Geometric DAs: The geometric DAs are already in the form
ofequivalent or inequivalent equations, and therefore, theycan be
directly applied as geometric constraints in the opti-mization
problem formulation.
(2) Non-geometric DAs: It is non-trivial to deal with the
non-geometric DAs, because of the diversity as shown in Fig. 6.Each
of the sub-categories may be mapped to quite differentoptimization
intent attributes.(2.1) Material: Homogeneous material is the most
common
case in structural optimization and the underlyingoptimization
intent is just the fixed material proper-ties. Comparatively, it is
worth a deep investigationabout the heterogeneous material,
especially for itscomplexity and the increasing popularity.
� Multi-material: Multi-material means that the com-ponent is
composed of multiple materials and thereis a macro
material/material interface. Concerning
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(a) A block feature (b) Bounding feature (the transparent
frame) after topology optimization
Fig. 8. Virtual bounding feature.
J. Liu et al. / Advanced Engineering Informatics 30 (2016)
713–727 721
the underlying optimization intent, the optimizationdomain
should be defined by the multi-material levelset model. Currently,
there are mainly two multi-material level set models: the ‘‘color”
level set[39,40] and the ‘‘multi-material” level set [42].
Theycould achieve equivalent optimization effects.
� Functionally graded material (FGM): FGM means thematerial
mixture gradually varies within the compo-nent following linear or
other low-order profiles.About the underlying optimization intent,
the localmaterial parameter is needed to reflect the local
mate-rial mixture. A material mixture function is required[21] or
an extra control functional is adopted to real-ize the
gradually-varying material mixture in the opti-mization result
[43].
� Highly nonlinear: Highly nonlinear means the mate-rial mixture
varies arbitrarily in highly nonlinear pat-tern. The underlying
optimization intent is simplethat, only local material parameter is
required toreflect the local material mixture and there is
notgradual-change requirement. Besides, there could belocal
micro-geometry involved other than the simplematerial mixture, for
which extra effort is requiredto calculate the local material
properties, e.g. byapplying homogenization and/or surrogate
modeling[16].
A mold insert design case study is presented below todemonstrate
the structural optimization with heterogeneousmaterials. About the
basic optimization intent, the objective isto maximize the thermal
compliance under the material volumeratio constraints of 0.35 for
the copper and 0.65 for the steel.Heat conductivity of the cooper
is 380 W=ðm �� CÞ and that ofthe steel is 20 W=ðm �� CÞ. Concerning
the simulation intent,boundary conditions attached to the
optimization domain arepresented in Fig. 9a and the static heat
conduction simulationis employed.
For multi-material scheme, the optimization result is shown
inFig. 9b, in which the yellow color represents copper and the
greycolor represents steel. For highly nonlinear scheme, the
localmicro-geometry as presented in Fig. 9c is applied and the
opti-mization results are shown in Fig. 9d and e. We can see that
both
parameter a and the orientation of the local micro-geometry can
beeffectively optimized.
(2.2) Manufacture: The adopted manufacture method has a
majorinfluence in configuring and solving the optimization
prob-lem. The underlying optimization intent is separately
sum-marized below for the different manufacture methods [24].
� Machining: There are several special requirements in
structural optimization because of the employment ofthe
machining method. First, very small hole featuresshould be avoided
because they are non-manufacturable [53] and this can be satisfied
by addingcomponent/void size constraints [18,24]. Second,
themaximum local curvature of the boundary contour isdetermined by
the minimum cutting tool radius and thiscan be satisfied by adding
boundary curvature con-straints. Third, no undercut and interior
holes shouldappear, also because they are non-manufacturable[44,3].
This requirement can be satisfied by adjustingthe boundary velocity
directions.
� Injection molding: An important rule for injection mold-ing
parts is the uniform rib thickness distribution,because it could
improve the cooling balance and there-fore reduce the defects. To
satisfy this rule, both addingcomponent size constraints [18,4] and
using extra thick-ness control functional [11,22] are feasible
solutions. Inaddition, the third requirement of no undercut and
inte-rior holes, as mentioned in the last paragraph, should alsobe
satisfied, because they are also non-manufacturablefeatures for
injection molding.
Here, we present a case study to demonstrate the
structuraloptimization of injection molding parts. About the basic
optimiza-tion intent, the objective is to minimize the structural
complianceand different solid material volume constraints will be
imposed.The solid material employs Young’s modulus of 1.3 and the
Poissonratio of 0.4. Concerning the simulation intent, boundary
conditionattached to the optimization domain is presented in Fig.
10a andthe static elastic simulation is employed.
The optimization results with different targeted rib
thicknessvalues are demonstrated in Fig. 10b–d. This case is cited
from[22] in which the uniform rib thickness is realized through
addingextra thickness control functional.
-
(a) Optimization (b) Multi-material optimization
result
(c) Local micro-geometry
(d) The a value distribution (e) The orientation
distribution
0:
=230℃
0: = 0℃
Mold insert
Coo
ling
chan
nel
Fig. 9. Heterogeneous mold insert design.
722 J. Liu et al. / Advanced Engineering Informatics 30 (2016)
713–727
(2.3) Special pattern: In mechanical design, special patterns
suchas symmetry or repetition are very common, and it is alsonot
difficult to derive these patterns through the optimiza-tion
process. A typical way is to post-treat the sensitivityresult into
symmetric or repetitive pattern [48,20].
A case study is presented below to demonstrate the
repetitivestructural optimization. About the basic optimization
intent, theobjective is to minimize the structural compliance under
the solidmaterial volume constraint of 50%. The solid material
employsYoung’s modulus of 1.3 and the Poisson ratio of 0.4.
Concerningthe simulation intent, boundary condition attached to the
opti-mization domain is presented in Fig. 11a, and the static
elastic sim-ulation is employed.
5. 3D Examples
In this section, the authors intend to study two 3Dexamples to
demonstrate the effectiveness of the proposedmethod.
5.1. A wheel structure problem
First, internal structure of a plastic wheel of size100 mm ⁄ 15
mm is to be innovatively designed. The conceptualCAD model is
presented in Fig. 12a and the attached semanticinformation
indicates the injection molding manufacturingmethod and the 4 ⁄ 1
circular repetition and symmetry require-ment for the spoke
area.
-
(a) Optimization domain and
boundary condition
(b) = 6 (c) = 9 (d) = 12
Fig. 10. Structural optimization with uniform rib thickness
[22].
(a) the cantilever problem (b) the basic solution
(c) the double-repetitive solution (d) the triple-repetitive
solution
Fig. 11. Repetitive cantilever design.
J. Liu et al. / Advanced Engineering Informatics 30 (2016)
713–727 723
After model transformation, the simulation intent is attached
tothe optimization model as shown in Fig. 12b.
Clearly, the spoke area is adopted as the optimization
domain,and no optimization variable is employed in this case. The
basicoptimization intent is to minimize the structural compliance
underthe material volume constraint of 50%.
Conventionally, the optimization process would start
immedi-ately once the simulation intent and the basic optimization
intenthave been defined. Consequently, the optimization result is
shownin Fig. 13a. It’s clear that the design quality is poor
because the
semantically attached design requirements are not
addressed.Warpage will appear in the large plane because of the
injectionmolding manufacturing method, and the wheel can only bear
tan-gential load located at certain points of the outer frame
because ofthe non-repetitive internal structure.
In contrast, if the associative optimization feature model is
con-structed through complete information transfer and
properlyinterpreted through the knowledge based reasoning, the full
opti-mization intent could be captured and a very different
optimiza-tion result could be derived as presented in Fig. 13b. All
the
-
(a) CAD geometry (b) Optimization geometry with simulation
intent
Fig. 12. Conceptual models.
(a) Optimization result without full optimization intent (b)
Optimization result with full optimization intent
(c) Output CAD geometry
Fig. 13. Optimization results for an example wheel
component.
724 J. Liu et al. / Advanced Engineering Informatics 30 (2016)
713–727
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J. Liu et al. / Advanced Engineering Informatics 30 (2016)
713–727 725
semantically defined design requirements have been
addressedincluding the closely-satisfied uniform rib thickness and
thetightly-satisfied circular repetition and symmetry. So far, only
aminor post-treatment is required to derive the final CAD
model.Owing to the employed level set method, the skeletons of the
inter-nal rib structure can be trivially extracted. The skeletons
areapproximated into piecewise straight lines and a double-sided
off-set is performed to derive the strictly satisfied constant rib
thick-ness. These are trivial CAD operations to quickly derive the
finalCAD model; see Fig. 13c.
5.2. Rib-enhanced thin plate design
For this case, the milk tray design is retrieved from the
databaseas shown in Fig. 14a, and is intentionally to be enhanced
about itsworking stiffness.
During the conceptual design phase, the wall structure(400 mm ⁄
300 mm) is recognized into four design regions asshown in Fig. 14b
which will be separately enhanced. A few man-ual modifications have
been made that, region 1 and 3 aredeployed of two groups of
symmetric ribs and the geometric DAsof repetition and symmetry are
created; region 4 is filled of solidmaterials which is intended to
be topologically optimized in theembodiment design phase; the
non-geometric DA of injectionmolding manufacturing is attached to
the whole structure.
After model transformation, user input is required to define
theoptimization variables and optimization domains. In region 1
and3, the rib orientations are employed as optimization
variableswithin the allowable range [�60�, 60�]. In region 2,
vertical dis-tance of the handle x2 is to be optimized within the
range of[27 mm, 37 mm]. More importantly, region 4 is employed as
theoptimization domain for the structural topology
optimization.
In addition, two groups of boundary conditions are attached
tothe optimization model as shown in Fig. 15. The basic
optimizationintent is to maximize the structural stiffness.
Then, by reasoning the included DAs, the repetitive and
sym-metric pattern of the ribs in region 1 and 3 makes all the ribs
sharea unified optimization variable x1, and the related injection
mold-ing manufacturing leads to the uniform rib thickness
requirementfor the structural topology optimization in region 4.
Once the opti-mization intent is fully captured, two separate
optimization pro-cesses are conducted which derives two distinctive
optimizationresults as demonstrated in Fig. 16. It can be seen that
both results
(a) Conceptual design
Fig. 14. Conceptual
have been effectively enhanced by adding ribs; more
importantly,the optimization intent is well reflected in the
optimization results.
6. Conclusion
This paper proposed an integrated product
design-optimizationsystem by making structural optimization tools
seamlessly inte-grated into the traditional CAx system. A few
prototypes have beendeveloped and implemented. It has been observed
from the imple-mentations that the fit-for-purpose optimization
model could beeffectively and efficiently created and the optimized
design solu-tions well conform to the original design intent; in
other words,design quality is greatly improved while little
post-treatment isrequired. Therefore, the effectiveness of the
proposed system hasbeen proven.
Characteristics of the proposed system are summarized below:
(1) Design intent included in the original CAD model is well
sus-tained and reflected in the optimization result; See Figs.
13and 16 for the satisfied uniform thickness distribution andthe
repetitive and symmetric structural patterns. This againconfirms
that an important motivation of realizing the pro-duct
design-optimization integration is to maintain thedesign
consistency throughout the entire product designprocess. The
proposed associative optimization feature mod-eling and
optimization intent capture serve the purpose ofsustaining the
design intent throughout the structural opti-mization process.
(2) Design intent violation is no longer a major problem
associ-ated with structural optimization. The benefit would be
thegreatly saved post-treatment effort. In practice, it has
alwaysbeen a headache to designers to manually post-treat
thestructural optimization result.
(3) The concurrent sizing, shape, and topology optimization
isrealized in a single structural optimization process; seeFig. 16,
while in existing structural optimization tools, theseprocesses are
generally conducted procedurally which sacri-fices of the overall
optimality.
About limitations of the proposed system, the fully
capturedoptimization intent complicates the optimization model and
manycontrol parameters are involved. This reduces the stability of
theoptimization model and a fine tuning process is required to
findthe fit values of the control parameters. This issue reduces
the
(b) Modified conceptual design
design models.
-
(a) Boundary condition 1 (b) Boundary condition 2
Fig. 15. Two sets of boundary conditions.
(a) Optimization result with boundary condition 1 (b)
Optimization result with boundary condition 2
Fig. 16. Optimization results for a typical box component.
726 J. Liu et al. / Advanced Engineering Informatics 30 (2016)
713–727
implementation efficiency and is currently under
activeexploration.
Acknowledgement
The authors would like to acknowledge China ScholarshipCouncil
(CSC) for their PhD student grant, NSERC (Canada) for itsDiscovery
grants, and the accelerate cluster internship supportfrom MITACS
and Canada Pump and Power Pte. All the researchworks were carried
out at University of Alberta.
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Product design-optimization integration via associative
optimization feature modeling1 Introduction2 Literature survey and
motivations2.1 Associative feature modeling2.2 Level set structural
optimization
3 Associative optimization feature modeling3.1 Definition of the
associative optimization feature3.2 Information transfer
4 Optimization intent4.1 Introduction to optimization intent4.2
Optimization intent capture4.2.1 Define the optimization
variables/optimization domains4.2.2 Define the basic optimization
intent4.2.3 Analysis of the associative optimization feature
model
5 3D Examples5.1 A wheel structure problem5.2 Rib-enhanced thin
plate design
6 ConclusionAcknowledgementReferences