Advanced Engineering Informaticsyongshen/index_files/Product...J. Liu et al./Advanced Engineering Informatics 30 (2016) 713–727 715 functionality to the geometry; engineering features,

Advanced Engineering Informatics 30 (2016) 713–727

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Advanced Engineering Informatics

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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.

(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

Fig. 4. Partial relations defined in the associative feature/associative assembly feature class [28].


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.


� 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,

Fig. 5. Partial relations defined in the associative optimization feature class.


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.

Fig. 6. A specific categorization of DAs.

Fig. 7. Model transformation.


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


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

(a) A block feature (b) Bounding feature (the transparent

frame) after topology optimization

Fig. 8. Virtual bounding feature.


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.


(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.


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.



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.


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

Documents

Advanced Engineering Informaticsyongshen/index_files/Product...J. Liu et al./Advanced Engineering Informatics 30 (2016) 713–727 715 functionality to the geometry; engineering features,