ABSTRACTTitle of thesis: DEVELOPMENT OF A CAD MODELSIMPLIFICATION FRAMEWORK FORFINITE ELEMENT ANALYSISBrian Henry Russ, Master of Science, 2012Thesis directed by: Professor Satyandra K. GuptaDepartment of Mechanical Engineering,Institute for Systems ResearchAnalyzing complex 3D models using finite element analysis software requiressuppressing features/parts that are not likely to influence the analysis results, butmay significantly improve the computational performance both in terms of meshsize and mesh quality. The suppression step often depends on the context andapplication. Currently, most analysts perform this step manually. This step cantake a long time to perform on a complex model and can be tedious in nature. Thegoal of this thesis was to generate a simplification framework for both part andassembly CAD models for finite element analysis model preparation. At the partlevel, a rule-based approach for suppressing holes, rounds, and chamfers is presented.Then a tool for suppressing multiple specified part models at once is described atthe assembly level. Upon discussion of the frameworks, the tools are demonstratedon several different models to show the complete approach and the computationalperformances.The work presented in this thesis is expected to significantly reduce the man-ual time consuming activities within the model simplification stage. This is accom-plished through multiple feature/part suppression compared to the industry stan-dard of suppressing one feature/part at a time. A simplified model speeds up theoverall analysis, reducing the meshing time and calculation of the analysis values,while maintaining and on occassion inproving the quality of the analysis.DEVELOPMENT OF A CAD MODELSIMPLIFICATION FRAMEWORK FORFINITE ELEMENT ANALYSISbyBrian Henry RussThesis submitted to the Faculty of the Graduate School of theUniversity of Maryland, College Park in partial fulfillmentof the requirements for the degree ofMaster of Science2012Advisory Committee:Professor Satyandra K. Gupta, Chair/AdvisorProfessor Hugh A. BruckProfessor Santiago D. Solaresc⃝ Copyright byBrian Henry Russ2011AcknowledgmentsI would first like to express my deepest gratitude to my advisor, Dr. Gupta,who provided invaluable guidance during my tenure as his student. This guidancenot only provided critical insight for the completion of the thesis, which otherwisewould not have been possible, but also helped me develop as a person and anengineer. I would, also, like to thank Dr. Bruck and Dr. Solares for their supportas committee members of my defense.I am grateful for the support provided by Andrew Chorney. His expertisein model preparation and model analysis has proven to be most useful within myresearch, allowing me to generate practical solutions. I appreciate all the time hetook out of his busy schedule to meet and answer any questions I had.I owe a special thanks and acknowledgment to Madan Dabbeeru for his assis-tance and contribution to this work. Madan helped me extend my coding languageand was always willing to help when a problem arose. Madan and my other labmates also provided moral support and an entertaining work environment.This research was funded by and done in collaboration with Patuxent RiverNaval Air Warfare Center and I would like to thank them for providing the financialsupport and the opportunities that arose from it.Finally, I would like to thank my family, who have supported and believed inme from the beginning. Without you I would not have become the person I am noreven had the possibility to be given this opportunity.iiTable of ContentsList of Tables vList of Figures viList of Abbreviations viii1 Introduction 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Thesis Goals and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.1 Part Simplification . . . . . . . . . . . . . . . . . . . . . . . . 41.2.2 Assembly Simplification . . . . . . . . . . . . . . . . . . . . . 51.3 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Related Work 82.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Techniques Based on Surface Entities . . . . . . . . . . . . . . . . . . 82.2.1 Boundary Loop Decomposition . . . . . . . . . . . . . . . . . 82.2.2 Low Pass Filtering . . . . . . . . . . . . . . . . . . . . . . . . 102.2.3 Face Cluster Based Simplification . . . . . . . . . . . . . . . . 102.3 Techniques Based on Volumetric Entities . . . . . . . . . . . . . . . . 122.3.1 Voxel Based Simplification . . . . . . . . . . . . . . . . . . . . 132.3.2 Effective Volume Based Simplification . . . . . . . . . . . . . . 142.4 Techniques Based on Explicit Features . . . . . . . . . . . . . . . . . 172.4.1 Prismatic Feature Simplification . . . . . . . . . . . . . . . . . 182.4.2 Blend Simplification . . . . . . . . . . . . . . . . . . . . . . . 202.4.3 Arbitrary Shaped Feature Simplification . . . . . . . . . . . . 222.5 Techniques based on Dimension Reduction . . . . . . . . . . . . . . . 232.5.1 Medial Axis Transform . . . . . . . . . . . . . . . . . . . . . . 242.5.2 Mid-Surface Abstraction . . . . . . . . . . . . . . . . . . . . . 262.6 Sumamry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273 Part Model Simplification for Finite Element Analysis 293.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Using Inductive Decision Tree to Generate Suppression Rules . . . . . 343.2.1 Training Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.2 Algorithm for Generating Rules . . . . . . . . . . . . . . . . . 413.3 Applying Learned-Rules for Simplification . . . . . . . . . . . . . . . 463.3.1 Extracting CAD Model Information . . . . . . . . . . . . . . . 463.3.2 Utilizing CAD Model Information within Rules . . . . . . . . 483.3.3 Accounting for Parent-Child Relationships during Feature Sup-pression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503.4 Results & Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70iii4 Assembly Model Simplification for Finite Element Analysis 724.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.2 Part Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.2.1 Part Utilization . . . . . . . . . . . . . . . . . . . . . . . . . . 744.2.2 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.2.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.3 Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 844.4.1 Modal Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 844.4.2 Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . 914.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985 Conclusion 995.1 Intellectual Contributions . . . . . . . . . . . . . . . . . . . . . . . . 995.2 Anticipated Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015.3.1 Improvement to the Part Simplification Framework . . . . . . 1015.3.2 Advancements in Assembly Simplification Approach . . . . . . 102Bibliography 104ivList of Tables3.1 Training data collected from the examples shown in Fig. 3.4. . . . . . 403.2 Rules for computing the suppressibility state of holes . . . . . . . . . 423.3 Rules for computing the suppressibility state of holes . . . . . . . . . 433.4 Rules for computing the suppressibility state of chamfers . . . . . . . 443.5 Rules for computing the suppressibility state of rounds . . . . . . . . 453.6 Errors and error types within the rule learning application: Conser-vative errors can be allowed as they will not affect the analysis resultsbut Non-Conservative errors can generate erroneous results. . . . . . 493.7 Analysis of learned rules on the five test parts (A)-(E). . . . . . . . . 623.8 Analysis of models before and after simplification . . . . . . . . . . . 634.1 Mesh improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.2 Modes calculated within the modal analysis . . . . . . . . . . . . . . 864.3 Mesh improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.4 Mesh improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97vList of Figures1.1 Napier Sabre 24 cylinder aicraft engine [1] . . . . . . . . . . . . . . . 21.2 Suppressibility of a feature: The decision to suppress or preserve afeature strongly depends upon the analysis context and the applica-tion. For a given loading and boundary conditions, “Insuppressiblefeatures” would affect the FEA analysis whereas the “suppressiblefeatures” would not. . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1 Face clustering [18] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Original model construction [28] . . . . . . . . . . . . . . . . . . . . . 172.3 Reconstruction of the model by rearranging the features and usingthe effective volumes [28] . . . . . . . . . . . . . . . . . . . . . . . . . 173.1 Overview of the approach: Acquire knowledge through expert demon-strations, learn suppression rules from the acquired knowledge data,then apply the learned rules for feature suppression . . . . . . . . . . 303.2 A Simple decision tree: An example of a representative decision treefor suppressing a hole feature considering attributes diameter, min-imum distance to the boundary condition feature, and the geomet-ric type. Rectangular boxes and elliptical boxes represent the non-terminal nodes and the leaf nodes respectively. . . . . . . . . . . . . . 353.3 Example of suppression based on inter-feature distances . . . . . . . . 383.4 Training examples used to collect attributes of holes, rounds, andchamfers. Synthetic parts are generated from these examples to tunethe transition boundaries of the decision trees for better classification. 393.5 Suppression based on chamfer geometric types: (a) D × D (b) D1 ×D2 (c) ANG × D (d) 45 × D (e) O × O and (f) O1 × O2 . . . . . . 473.6 Dependency graph showing an example of finding features to be sup-pressed based on the parent-child relationships. Dependent relation-ships among the features should be considered before suppression; thesuppression of one feature may suppress the dependent critical feature. 533.7 Part A: boundary condition features and feature suppression afterrule implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563.8 Part B: boundary condition features and feature suppression afterrule implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.9 Part C: boundary condition features and feature suppression afterrule implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.10 Part D: boundary condition features and feature suppression afterrule implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.11 Part E: boundary condition features and feature suppression afterrule implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.12 Stress analysis results for the unsimplified and simplified models forpart A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64vi3.13 Stress analyses results for the unsimplified and simplified models forpart B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.14 Stress analyses results for the unsimplified and simplified models forpart C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.15 Stress analyses results for the unsimplified and simplified models forpart D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.16 Stress analyses results for the unsimplified and simplified models forpart E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.17 Example of suppression based on parent-child relationships . . . . . . 694.1 Overview of the assembly approach . . . . . . . . . . . . . . . . . . . 724.2 Example assembly model . . . . . . . . . . . . . . . . . . . . . . . . . 774.3 Stresses within the model when the two parts are made of the materialsteel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.4 Stresses within the model when the two parts are made of the materialnylon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.5 Simple four-legged table for illustration of the parent-child relation-ship within a model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.6 Example of the generated parent-child relationship graph . . . . . . . 824.7 Unsimplified boom model for a modal analysis . . . . . . . . . . . . . 844.8 Simplified boom model for a modal analysis . . . . . . . . . . . . . . 854.9 (a) Mode 1 of the unsimplified boom assembly (b) Mode 1 of thesimplified boom assembly . . . . . . . . . . . . . . . . . . . . . . . . 874.10 (a) Mode 2 of the unsimplified boom assembly (b) Mode 2 of thesimplified boom assembly . . . . . . . . . . . . . . . . . . . . . . . . 884.11 (a) Mode 3 of the unsimplified boom assembly (b) Mode 3 of thesimplified boom assembly . . . . . . . . . . . . . . . . . . . . . . . . 894.12 (a) Mode 4 of the unsimplified boom assembly (b) Mode 4 of thesimplified boom assembly . . . . . . . . . . . . . . . . . . . . . . . . 904.13 Unsimplified weight bench assembly model for a structural analysis . 914.14 Simplified weight bench assembly model for a structural analysis . . . 924.15 Von Mises Stress distribution on the unsimplified weight bench assembly 944.16 Von Mises Stress distribution on the simplified weight bench assembly 944.17 Unsimplified boom assembly model for a structural analysis . . . . . 954.18 Simplified boom assembly model for a structural analysis . . . . . . . 954.19 Von Mises Stress distribution on the unsimplified boom assembly . . 974.20 Von Mises Stress distribution on the unsimplified boom assembly . . 97viiList of AbbreviationsCAD Computer Aided DesignFEA Finite Element AnalysisFE Finite ElementProE Pro/Engineer2D Two Dimensional3D Three DimensionalSR Simplified RegionLPF Low Pass FilteredTDPS Trihedral Discretized Polyhedra SimplificationMDCO Maximal Division Classical OctreeBTG Border Terminal GreyLOD Level of DetailB-Rep Boundary RepresentationNMT Non-Mainfold TopologicalCSG Constructive Solid GeometryFCT Feature Constructing TrianglesRAG Region Adjacency GraphMAT Medial Axis TransformAPI Application Programming InterfaceXML Extensible Markup LanguageAVMI Air Vehicle Modification and InstrumentationCG Center of GravityFEA Finite Element AnalysisviiiChapter 1Introduction1.1 MotivationEngineering models today are mainly developed within a 3D computer aideddesign (CAD) software, for the reasons that the CAD models are unambiguous,visualization and manufacturing-planning is easier within the environment, and 3Dmodel data exchange is well established. The 3D models created using these CADsystems often contain an abundant amount of features. Fig. 1.1 illustrates an air-craft engine with thousands of features. These features are necessary for a widevariety of life cycle needs including safety, functionality, aesthetics, and manufac-turability.The generated 3D CAD models are used for downstream applications withinthe design and manufacturing process. Finite element analysis (FEA), is one of thedownstream applications, has emerged as an important engineering analysis tooland is extensively used for structural, thermal, and modal analyses to ensure thatthe design of the model will meet the specifications required from the operationof the model. FEA is a numerical technique for calculating approximate solutionsof complicated equations used to calculate the analysis results. It does this bygenerating a mesh, grid of nodes, over the entire model. The density of the gripvaries throughout the model, using having a higher density at fillets, corners, and1high stress areas. The mesh contains the structural and material properties, whichdefine how the structure reacts to the conditions implemented within the analysis.At each node an equilibrium equation is generated and the equations are solved toobtain the results in the analysis.Importing the detailed 3D models, such as the one shown in Fig. 1.1, intothe FEA software often presents several challenges. First, the meshing time rapidlyincreases with the complexity of the model. Second, it may take a long time toanalyze the large FEA mesh that results from the detailed CAD models. Third, thepresence of a small feature may lead to a poor quality mesh and hence may leadto erroneous analysis results. In extreme cases, the automated meshing may failon very complex models, requiring manual meshing of the model. Utilizing a morepowerful computer can not solve all the issues associated with analyzing complexCAD models. Meshless methods have been proposed as an alternative to FEA,which use the geometry of the object directly for the calculations. These methodsare not as widely used within the community.Figure 1.1: Napier Sabre 24 cylinder aicraft engine [1]2To circumvent the above described problems, experienced engineering analystsrarely perform meshing on the original complex models containing all the designfeatures. In most situations, the model is simplified before proceeding with meshing.Simplification carefully examines the model and suppresses the features/parts thatare not likely to influence the analysis results, but may significantly improve thecomputational performance both in terms of mesh size and mesh quality. Currently,the simplification of models is mainly performed manually, which can take a longtime to perform on a complex model and can be tedious in nature. Also, most of thestate-of-the-art mesh generation algorithms fail to generate meshes for those featuresthat are smaller than the FE size. In these situations, CAD model simplification isessential to producing FE models adaptable to analysis. Certainly, automation inthis task can improve analysts’ productivity. Hence, automated feature suppressionhas been acknowledged as a useful tool in CAD-FEA integration [26].Automated optimization of a CAD model for analysis can be a highly beneficialtool within the industry. As mentioned previously, the models are currently simpli-fied manually for finite element analysis. Automating this process can potentiallydecrease the amount of time required for simplification, suppress all non-critical fea-tures/parts, and retain all critical fetaures/parts; ultimately speeding up the processand reducing the amount of errors involved within the process. For automation ofthis simplification process, numerous factors will have to be accounted for to cor-rectly classify a feature/part as critical or non-critical to the analysis. A few of thesefactures include dimensions, material, and purpose.Two different types of approaches can be taken to perform automated model3simplification for FEA. The first approach is geometry based and utilizes the geo-metric operators to simplify the parts [40]. Unfortunately, encoding the preferencesof an analyst in this approach is very difficult and can lead to erroneous and in-consistent results [30]. The second approach is knowledge based. In this case, thepreferences and knowledge used by the analyst are explicitly encoded as simplifica-tion rules. This approach captures analysts’ knowledge in terms of rules that expressthe characteristics of features/parts that should be considered for suppression.1.2 Thesis Goals and ScopeThe goals and scope of this thesis revolve around developing a simplificationtool for complex CAD models in preparation for FEA. The FEA types that arefocused on within the framework are structural and modal. This tool is dividedinto two primary parts: part model simplification through feature suppression andassembly model simplification through part suppression and part simplification. Fordevelopment of these tools a knowledge based approach has been utilized.1.2.1 Part SimplificationPart model simplification consists of suppressing non-critical features withina CAD model. The determination of the non-critical (suppressible) features relieson the different attributes of not only the features themselves, but also of the entirepart model and analysis. Some of these attributes include the feature type, featuredimensions, feature distances to boundary conditions, analysis type, and part di-4mensions. The dimensions of the part is required, so that the relative size of thefeature to the overall part can be calculated. This is crucial, since part sizes arenot limited and a feature that is seen as dimensionally small within one part maybe quite large within another. Fig. 1.2 illustrates an example of a CAD model withfeatures capable of being suppressed and those features that cannot be suppressed.(a) Boundary conditions (b) Suppressibility of featuresFigure 1.2: Suppressibility of a feature: The decision to suppress or preserve a featurestrongly depends upon the analysis context and the application. For a given loadingand boundary conditions, “Insuppressible features” would affect the FEA analysiswhereas the “suppressible features” would not.1.2.2 Assembly SimplificationAssembly model simplification consists of suppressing or simplifying part mod-els within a CAD model. Similarly to that of the part approach, parts can be labeled5as either non-critical (suppressible) or critical (non-suppressible); although unlikethe part appproach, there can also be semi-critical parts within the assembly model.Semi-critical are the parts that must remain in the model for analysis, but the over-all complexity of the part is not required; this can either consist of suppressing thenon-critical features or simplifying the overall geometry of the part.1.3 OrganizationChapter 2 is a survey of the current literature within the field of modelsimplification, which is not only limited to the simplification techniques specifiedfor FEA model preparation. This chapter is arranegd into four collective sections;model simplification based upon surface operators, volume operators, dimensionreduction operators, andexplicit feature operators. Each section is then furthersplit up into the specific methods types of the simplification.Chapter 3 presents a model simplification framework for CAD part models,by suppressing non-critical features. In this framework a decision-tree based rep-resentation has been developed for implementing the suppression rules on features;such as holes, rounds, and chamfers. Feature suppression demonstrations from anexpert analysts provide a useful way of acquiring application dependent featuresuppression rules. This method does not burden the human expert with explicitlycataloging feature suppression rules. Instead, feature suppression rules are extractedthrough demonstrations, in an unobtrusive fashion. These application dependentrules can be learned by using decision tree learning algorithms. We have developed6utilities in the Pro/Engineer CAD system to identify features that meet the learnedrules and suppress them.Chapter 4 presents a model simplification framework for CAD assembly mod-els, by suppressing/simplifying non-critical parts. In this framework utilities havebeen developed within the Pro/Engineer CAD system to identify and suppress partswith a specified material or PART NAME value.Chapter 5 discusses the intellectual contributions of the research and possibleareas of future research to further extend the frameworks discussed within the thesis.7Chapter 2Related Work2.1 OverviewModel simplification has been a focus within the modeling area for a whilenow, consequently there is a rich body of literature within this field. As not allof the literature can be reviewed within this thesis, I will focus on some of themore prevalent proposed techniques. For organization purposes the section followsthe classification within a survey paper by Thakuer et al. [40], specifically: surfacebased operators, volume based operators, dimension reduction based operators, andexplicit feature based operators.2.2 Techniques Based on Surface EntitiesThis section reviews the techniques for which the simplification is based uponthe surface entities and are organized into three classifications; boundary loop de-composition, low pass filtering, and face cluster based simplification.2.2.1 Boundary Loop DecompositionSun et al. [39] presents a simplification method for B-rep models using regionsuppression. First, the simplified region (SR) and its boundary loop must be deter-8mined and classified. A hybrid method, both automated and manual, was adoptedfor determination of the SR and the faces which are to simplified are identified us-ing their area ratio. After identifying the SR, the boundary loops are formed fromthe edges of the region. Each SR is classified according to whether it has singleor multiple boundary loops. Multiple loop boundaries must be reduced to a singleloop, either by dealing with the loops separately or constructing a bridge betweenthe two separate loops to combine the loops into one.A divide and conquer strategy is then used to decompose the loops. Thisrecursively divides the boundary loops into multiple sub-loops by connecting twonon-adjacent vertices with an edge, if there are either critical edges or boundaryedges lying on the same underlying curve. The iteration process continues untilthe no co-defined edge pairs can be identified. The sub-loops are then furtherdecomposed into co-surface loops.Upon the decomposition of the boundary loops, the SRs are deleted from themodel. The hole is fixed by REPAIR and PATCH operators. The REPAIR operatormodifies the neighboring faces boundary and the PATCH operator constructs a newface and stitches the faces to the model. Both operations are possible through theuse of a co-surface loop. To validate the B-rep model duplicate edges, vertices,and faces are merged. Advantages of the technique described is that it does notrequire Boolean operators and the REPAIR operator is insensitive to different typesof features.92.2.2 Low Pass FilteringLee and Lee et al. [29] proposed a semi-automatic low pass filtering techniqueusing Discrete Fourier Transform. For implementation of the method the CADmodel must first be digitized, converted into a 2D digital image of resolution 512X 512. A surface can then be plotted from the pixels, having a value of -1.0, 0, or1.0. Upon application of the Fourier transform to the surface function, the surface isexpressed in the frequency domain. Within the frequency domain the low frequencyterms represent the overall shape, whereas the high frequency terms represent thedetailed features. Removal of the high frequency components generates a low passfiltered (LPF) model of the original model. The adverse result of the LPF model isthat all sharp corners were rounded. Removal of the sharp edges is unfavorable in theanalysis model, since sharp edges tend to acquire a higher stress concentration. Toretain the sharp edges within the simplified model, the boundary elements averagedistance between the original model and LPF model is evaluated as a metric ofcomplexity. If the metric is below a given threshold the entity is considered to bedetailed and if the metric is below the given threshold the entity is considered to beto belong to the overall shape. The method is only developed for 2D images and ifextended to a 3D image it is limited in terms reconstructing the removed faces.2.2.3 Face Cluster Based SimplificationInoue et al. [18] proposed a face clustering technique for CAD model simplifi-cation. The first step within the process is to decompose the model into faces. From10this decomposition a planar adjacency graph can be constructed; the graph nodesrepresent the faces, which are connected by arcs representing the adjacency of theface pairs. To determine the nodes to be clustered, a weight for each arc is calculatedbased on several geometric indices. The geometric indices attempt to take the areasize, boundary smoothness, and region flatness into consideration. The equationsfor these indices are presented within the paper for reference.Upon calculation of the arc weights, the arcs are prioritized for node clusteringby ranking the weight values highest to lowest. After prioritizing the arcs, a merge-ability test is completed using the geometric indices. The top weighted arc thatpasses the mergeability test is then contracted, merging the two connected nodes. Ifthe two nodes both had an connected with a similar node, the two arcs are combinedinto one. This process is then completed for the entire adjacency graph, simplifyingthe original model. Fig. 2.1 display the process of removing the arcs and mergingthe nodes. For the example discussed within the paper, a model containing 1742individual faces was simplified to a final model containing only 34 faces.Figure 2.1: Face clustering [18]Sheffer et al. [2] expanded upon this technique proposed by Inuoe. The clus-tering algorithm is maintained within the new process, although different geometric11indices are calculated. The new geometric indices quantify the boundary preser-vation, region size, region smoothness, and simplicity of the boundary shape. Themain advantage of these indices is that they can also account for non-planar regions.In addition to the new indices, Sheffer introduced a collapsibility test to de-termine faces that can be symetrically divided between adjacent clusters, after theclustering process. This division is completed using virtual topology operators tomerge and collapse the faces. In this process the face cluster found to be divisiblefrom the collapsibility test is then split into a number of faces equal to the numberof adjacent neighboring faces. The new faces are then merged to the respectiveneighboring face from which an edge is shared. This further reduces the numberfaces within the model.In a similar technique to the cluster division by virtual topology operators,Dey et al. [10] introduced a framework to eliminate the feature effects at meshlevel. This technique identifies mesh entities with per quality metrics, based uponthe dihedral angle measurement and aspect ratio of the mesh. After identification,the suppression of these entities is ensured to maintain geometric validity of themodified mesh and the entities are suppressed accordingly.2.3 Techniques Based on Volumetric EntitiesThis section reviews the techniques for which the simplification is based uponthe surface entities and are organized into two classifications; voxel based simplifi-cation and effective volume simplification.122.3.1 Voxel Based SimplificationAndujar et al. [3] proposed a topology-reducing simplification algorithm calledTrihedral Discretized Polyhedra Simplification (TDPS). This algorithm containsthree steps: discretization, reconstruction, and face reduction. Maximal divisionclassical octree (MDCO) is used to discretize the model. MDCO arranges eightoctants, obtained by recursively subdividing the cubic universe into an 8-ary tree.The leaves of the tree falling completely in or out of the model volume are labeled aseither black or white, respectively, and the leaves containing part of the boundary,partially in or out of the model, are labeled as grey. The grey leaves are then furthersubdivided until the parts are either black or white or the tree reaches a certain level.Reconstruction step involves converting the MDCO octree representation intoa 3D digital picture, set of points arranged in a regular grid, and extracting anisosurface from the digital picture. To compute the digital picture the MDCO istraversed to find the BTG nodes, boundary nodes. Each BTG node is subdividedinto eight octants and the color at each octant corner is then labeled as either whiteor black, depending on the color of the node in contact with the corner. From thisdigital picture a surface, R, is extracted based upon an error bound in terms of thesolid-Hausdorff distance, satisfying the condition that all white nodes are completelyout of R and all black nodes are completely inside the R. The face reduction stepfurther reduces the geometric complexity of R, using an edge collapse technique.The authors report that TDPS has several advantages over other model simpli-fication techniques; suitable for both parts and assemblies, it is not affected by input13surface degeneracies, and produces a two-manifold solids even with non-manifold in-puts. Although there is a limitation of TDPS in that it is not intended for smallerror thresholds.2.3.2 Effective Volume Based SimplificationFrameworks for multiresolution representations of solid models producing sim-plified models at various levels of detail (LODs) have been extensively researched.[26, 28, 6, 25] The focus of the research can be split into two separate approaches.The first approach uses conventional solid boundary representations (B-rep) [6] andthe second approach uses non-manifold B-reps [28]. Conventional solid B-reps is ad-vantageous since it can be implemented into commercial 3D CAD systems, due tothe same data structures; although the computational cost of the boundary evalua-tion is very high, causing the method to be time consuming. Unlike the conventionalB-reps, non-manifold B-reps are less time consuming and therefore will be exploredfurther.The non-manifold model is capable of representing any combination of wire-frame, surface, solid, and cellular models in a unified data structure. It consistsof three key modules: a feature-based modeling module, a feature-based idealiza-tion module, and a non-manifold topological (NMT) modeling kernel. The modulesmanage the database of the features, perform the detail removal and dimensionreduction, and manipulate the geometric models, respectively. The detail removalwithin the idealization module consists of three steps to simplify the model. First all14idealization features with a design application domain are extracted from the mastermodel. Then according to the given LOD criterion, most often the feature volume,the extracted idealization features are rearranged. If the criterion is based upondecreasing volume, features with a volume below the given threshold are consideredfor simplification. Finally, the LOD is selected manually to obtain the appropriatesimplified model.[26]Both the conventional and non-manifold B-rep approaches have a feature ar-rangement issue. Rearrangement of the features to generate the various LODs ofthe model will possibly result in a shape different from that of the original modelshape, since the additive and subtractive Boolean operations are not commutative.Lee et al. [25] and Choi et al. [6] introduce a delta volume, redefined volume, ifrequired, of the subtractive feature operations to ensure model similarity. The rear-rangement algorithm applied within these approaches combines all additive featuresto generate the lowest resolution model and the delta volumes are subtracted fromthe model in descending order of volumes to generate the higher resolution models.This method is only applicable for the specified feature rearrangement, not for anyarbitrary rearrangement.Lee [28] expanded upon technique by introducing the concept of the effectivevolume of a feature, fractional or entire volume of the feature to provide the sameresult in spite of Boolean arrangement. This volume is calculated using Booleanalgebra. Let Vi denote the volume of the solid primitive of a feature Fi, Xi denotea Boolean operation, and Mn denote the resulting model obtained by applying nBoolean operations between n+1 solid models:15Mn =n∏i=0⊗iVi, wℎere⊗0V0 = ⊗0V0 (2.1)If the jtℎ Boolean operation XjVj is moved to the mth position Mn can berepresented as follows:Mn =⎛⎝ m∏i=0,i ∕=j⊗iVi⎞⎠⎛⎝⊗j⎛⎝Vj − m−j∑l=1'⎛⎝⊗j,⊗j+1⎞⎠Vj+1⎞⎠⎞⎠×( n∏i=m+1⊗iVi)(2.2)where,' (a, b) =⎧⎨⎩0 ifa = b1 ifa ∕= b(2.3)Figs. 2.2-2.3 illustrate the use of Eqns. 2.1-2.3 on a model generated by ap-plying five form features [27]. The original model is shown in Fig. 2.2. If we alterthe order of features from F0 → F1 → F2 → F3 → F4 to F0 → F2 → F3 → F4 → F1by moving F1 to the last position, the Boolean operation sequence changes fromV0−V1UV2−V3UV4 to V0UV2−V3UV4−V1, where Vi is the respective volume of Fi.When just reorganizing the form features V1 will just remove the volume for whichit encompasses, i.e. removing V2 and the connection of V2 to V0. Although, if weapply Eqns. 2.1-2.3 the effective volumes of F0, F1, F2, F3, and F4 are calculated tobe V0, V1−V2−V4, V2, V3, and V4, respectively. Fig. 2.3 displays the rearranged fea-ture model using the effective volumes of the features, which is identical the overalloriginal model. This technique can allow for arbitrary rearrangement of the featuresand generate the same final shape as the original model.16Figure 2.2: Original model construction [28]Figure 2.3: Reconstruction of the model by rearranging the features and using theeffective volumes [28]2.4 Techniques Based on Explicit FeaturesThis section reviews the techniques for which the simplification is based uponthe explicit features and are organized into three classifications; prismatic feature17simplification, blend simplification, arbitrary shaped feature simplification.2.4.1 Prismatic Feature SimplificationDabke et al. [8] implemented DESIDE-X, a rule-based software package forsuppressing features, which relies upon a constructive solid geometry (CSG) treeand is specifically for modal analysis. Through the use of a feature by featurelooping mechanism, each feature in the tree is analyzed and determined to be eithersignificant or non-significant. The significance of the feature is evaluated based upona rule base that takes into account different criteria; such as, mass and stiffnesscontributions, proximity to high stress areas, and the design functionality role. Thenodes of the features found to be non-significant are removed from the tree alongwith the associated links. One drawback to this approach is that modern CADsystems rarely have the features readily available by means of a CSG tree.Date and Nishigaki [9] present a alternative mesh simplification method throughfeature recognition and removal of blind holes, through holes, and bosses. The meshis segmented into regions enclosed by the edges of the features. The edges areextracted using the dihedral angles between common edge faces. Upon mesh seg-mentation, the regions having an area larger than the given threshold are classifiedas base surfaces. The triangles not within the base surfaces are extracted as featureconstructing triangles (FCTs). For each FCT the feature type and parameters aredetermined. the feature type is identified by the number of boundary loops and itsconcavity, while the dimensions are calculated using a least squares fit. Recognized18features are removed by deleting the FCTs and then filling the boundary loops bytriangulation. An advantage to the proposed method is that the removed featuresare capable of being recovered later on in the process, which is extremely useful fora design model within the industry.Gao et al. [14] proposed another framework for feature suppression basedCAD mesh model simplification. There are three overall steps; segmentation of themesh model, recognition of form features, and feature suppression.Segmentation of the mesh model is achieved through an improved watershedmethod. The first step within the improved method is to refine the mesh by addingnew vertices to the model, which allow for the model curvature to be calculated.Adding new vertices must not change the model geometry, so a different manner isused to add the vertices for all the triangle edges as feature edges and for triangleedges which are not all feature edges. Upon refining the mesh, the mesh is thensegmented using a multi-descent strategy. The refined mesh of the segmented re-gions is then replaced with the original mesh of the model, so the original trianglesrepresent the segmentation results. These segmentation results are over segmenteddue to the added vertices, therefore iterative region merging is used to generate thefinal segmentation.After segmentation of the model is complete, a graph-based method recognizesthe features within the model. Initially the region adjacency graph (RAG) is set up,where each node refers to a region and each arc represents the relationship betweenthe regions. All base regions are then determined from the regions which have eitheran inner loop or concave vertex and deleted from the RAG. The remaining sub-19graphs of the RAG may then correspond to a form feature capable of suppression.To determine which ones are capable of suppression, the adjacency of the regionswith the base features on inner loop edges or concave edges are checked and thesub-graphs that are adjacent is taken a s a candidate. Each feature graph candidateis compared to the RAG of the pre-defined features and a feature is recognized, if amatch is found.To generate the simplified model the features recognized in the previous stepmust then deleted and the hole filled. [14] proposed three different hole filling tech-niques planar Delaunay triangulation method for planar features, poisson equationmethod for curved features, and a blend feature method.2.4.2 Blend SimplificationJoshi and Dutta [21] propose an algorithm to suppress blends with a circularcross-section. Recognition of the blend is determined from the curvature variationacross the faces, calculated along the two directions, (U,V), of the parameterizedNURBS surface, X(U,V).The curvatures at any point are given by Eqns. 2.4 and2.5.KU =∣∣∣∣∂X∂U × ∂2X∂U2∣∣∣∣∣∣∣∣∂X∂U∣∣∣∣2 (2.4)KV =∣∣∣∣∂X∂V × ∂2X∂V 2∣∣∣∣∣∣∣∣∂X∂V∣∣∣∣2 (2.5)20The face is marked as a potential blend, if Ku remains constant in the Vdirection and is greater than the calculated threshold and vice versa. The thresholdis calculated based upon the object boundary box, causing the recognition to beindependent of the model scale. For the potential blends to be classified as blends,the curves in the direction of the blend must be opposite an angle between 0 and180 at the spine curve.Blends are then suppressed in the reverse order of creation, to maintain a validmodel. The blend order is determined by visiting each blend and then analyzingthe adjoining faces to determine whether or not these faces are also blends. If theadjoining face is determined to be a blend, an evaluation is done to whether thetwo blends were created within the same operation or if the adjoining faces blendpreceded/followed the initial blend operation. Suppression of the blend involvesremoving the blend face and then extrapolating the adjacent faces to a point ofintersection, generating a simplified model.Venkataraman And Sohoni [41] presented a similar algorithm for blend detec-tion and order arrangement; although rather than considering the curvatures overthe entire face along the parametric direction, [41] compares the curvatures of ad-joining faces at the common edge midpoints. Then the suppression algorithm deletesthe blend faces and collapses the cross edges, mutual edges of the blend face andadjacent edges, into vertices and the spring edges, the edges between the blend faceand adjoin faces, into a single edge.Zhu and Menq et al. [42] also present a method to suppress constant radiusrounds and fillets, but within a B-rep model focusing on the repairing the suppressed21features. Initially, trace faces, faces generated from edge blending, are identified bythe convexity of their topological entities. These trace faces are then removed fromthe model, suppressing the rounds and fillets. This suppression leaves gaps betweenthe adjacent neighboring faces in the model. To close this gap a knitting process isimplemented, which generates new edges and vertices. The overall knitting processis determined on the basis of on two factors of the H.E of the trace face, is the H.E.a disk or ring and is the H.E. a closed loop or open loop. This process has a coupleadvantages; the new B-rep model maintains geometric and topological consistency,along with being a reversible process.2.4.3 Arbitrary Shaped Feature SimplificationJoshi and Dutta [21] proposed algorithms for the identification and suppressionof different features in B-rep models. The first algorithm described is for ”hole”features, which are described as any loop of edges without a surface on the inside.Initially, the edges having a surface on one side and no surface on the other arelabeled as free edges. Upon labeling the free edges, all the free edges are formedinto closed loops; starting at one vertex and following the edge until the startingvertex is reached again. All these closed loops are considered to be holes, eventhe boundary of the model. The boundary must be eliminated as a hole, so todo this, the perimeters of all the closed loops are calculated and the hole with thelargest perimeter value is designated as the model boundary; thus, removing theconsideration for suppression. All loops with a perimeter value below the given22threshold are deleted and replaced by a surface patch with the same underlyingsurface equations as the loop.Boss features, compound feature formed by a planar surface and two filletrings, have also been implemented within the framework designed by [21]. For eachplanar face within the model, the adjacent faces on the outermost loop are visitedto determine if they are a blend (defined within the blend section). If the adjacentfaces are found to be blends and the blends are all part of the same loop, thenthe algorithm analyzes the adjacent faces of the opposing side of the blends. Ifthe opposing faces are found to either have another blend loop on its other side orbe a blend loop itself, then the faces are grouped together and labeled as a boss.Suppression of the boss entails removal of all the components and patching thesurface, similar to the suppression of the holes.These algorithms, in combination with the algorithm proposed for blends, canbe extended to recognize and suppress any feature type in a model.2.5 Techniques based on Dimension ReductionThis section reviews the techniques for which the simplification is based uponthe dimension reduction and are organized into two classifications; medial axis trans-form and mid-surface abstraction. Dimensional reduction can be very beneficial forFEA. In some cases it is possible to reduce the dimension of the model withoutcritically affecting the results of the model. This dramatically reduces the computa-tional time of the model. For example, a long round slender bar of uniform diameter23can be reduced to a 1D beam [40]. Other methods have led to significant advancesin thin structure model simplification, but may not be applicable to generic struc-tures; such as an algebraic reduction for beams [19], nonlinear algebraic reductionfor snap-fit simulation [20], and an algebraic reduction of 3D plates [31], a surfaceintegration approach for 3D beams [36] and a method to decompose a model intoparts and then apply the mid-surface abstraction technique by [7].2.5.1 Medial Axis TransformThe medial axis transform, initially proposed by Blum [16], provides a skeleton-like representation of a geometric shape, which is comprised of a set of geometricentities. The geometric entities are generated by tracing out the centroid of themaximal inscribed disk/sphere as it rolls around the interior of the object. Thisconcept provides both geometrical and topological proximity information, enablinga dimension reduction of the model, i.e. a 2D model can be reduced to a 1D modeland a 3D model can be reduced to a 2D model.Robinson et al. [35] discusses a medial axis transform method for both 2D and3D models. Only the 3D reduction will be touched on within, but the paper can bereferenced for the 2D or mixed dimension reduction. The first step in the processis to identify the thin regions within the model. In this step medial flaps, medialedge or face that terminates with a value of zero; medial faces not defined by twoobjects; and medial faces are with a large variation in 3D medial radius or thicknessare all eliminated from the possibility of reduction. The remaining medial faces are24analyzed to determine if their lateral face dimensions are sufficiently large relativeto their thickness. For this a conservative aspect ratio, since the smallest distanceis divided by the largest thickness, is calculated from a 2D MAT on the 3D medialface. A medial face with an aspect ratio less than the critical aspect ratio is alsoeliminated from the possibility of dimension reduction. Not all medial faces thatare left are capable of reduction, so only the capable regions should be reduced.After determining the capable faces for reduction, mid-faces are created. Mid-faces are generated by an insetting of the interface by a distance equal to a variableOS multiplied by the region thickness, achieved by reusing the 2D MAT on each 3Dmedial face, and introducing rounding splines at convex corners of the inset. Upongeneration of the mid-faces, the model is partitioned into thin sheet and complexregions. The bounding edges of the mid-face is project onto the medial faces andthe projected area is deleted and replaced by a thin sheet. The thin sheet is thenextended to the boundary of the component. Mixed dimensional coupling is requiredto at the interface of the detailed section and reduced section to join the elements.The has been extensive research done for the MAT and only one of the pro-cesses has been discussed within this thesis. Other algorithms that have been pre-sented are a method for the reduction of 2D planar or 3D shell models by a Donaghyet al. [11], polyhedral model homotopy preserving medial axis transform by Sud etal. [38], and an extension on the common MAT method known as Θ-MAT for poly-hedral mesh models by Foskey et al. [13]. MAT has been extensively researched andthe survey paper by Attali et al. [5] can be reviewed for a more complete review ofMAT.252.5.2 Mid-Surface AbstractionRezayat [34] introduced a mid-surface abstraction technique. Abstraction ofthe mid-surface involves four steps; pairing surfaces, surface topology and size basedadjacency graphs, mid-surface patch generation by geometric interpolation and 2DBoolean operations, and adjacency based patch sewing. Within the surface pairingstep, all the faces of the model are paired excluding the end-caps (faces on theedges of the solid model) and orphans (faces that are not on the thin-wall section).The excluded faces are determined by whether or not the ratio of the minimum faceheight and length divided by the thickness measure is greater than a given parameterX. A ratio less than X distinguishes a face as either an end face or orphan. To pairthe faces an arbitrary face is selected as a seed face and a ray is cast into the materialside in the normal direction of the face. The face upon which the ray hits is identifiedalong with the common edge faces as processed. This is then repeated until all thefaces have been processed.Upon pairing the faces, an adjacency graph is then generated. The nodes of thegraph are the faces and the connecting arcs are the relationship between the faces,either paired or stitched (common edge faces). The cyclic pattern of the adjacencygraph references the geometric configuration of the model. A geometric interpolationof the paired faces is used to generate a mid-surface patch, where a 2x2 grid anda 15x15 grid are utilized to create the interpolation points of planar and free-formsurfaces, respectively. The patches are sewn together at their intersecting edges,trimming the patch area beyond the intersection. If no intersection is possible, then26a new surface is created between the patches by a mesh of curves approximation.The part thickness, T, at a point, P, on the mid-surface of the parent surfaces, S1and S2, is given byT = dist (P, S2) + dist (P, S1) (2.6)The authors have reported several benefits of this method in comparison tothe medial axis transform methods. These benefits include volume preserving, ef-ficient feature suppression and detail removal, shape definition through geometricreasoning, and part form reflection.2.6 SumamryThe techniques described above are present many methods for which a modelcan be simplified for different applications. For the work discussed within this the-sis, the techniques based on explicit features and dimension reduction are mostuseful; since our main focus is to suppress non-critical features for finite elementanalysis purposes. Within the category of explicit features we explain techniquesfor suppressing and modifying different features, such as: blind holes, through holes,chamfers, and rounds of any given geometric model. Although these methods dis-cuss ways in which a model can be simplified, the literature does not provide errorestimations between the analyses of the original and simplified models. For this[17] developed a formal theory for computing the defeaturing-induced engineeringanalysis errors, which would help to identify the suppressible features. [23] presents27an algorithm or computing the sensitivity of the design to finite feature suppression,thereby identifying the features that would affect the FEA. The approach discussedwithin this thesis has compared the analysis values, to ensure the technique is withinan error range of 5% between the models.28Chapter 3Part Model Simplification for Finite Element Analysis3.1 OverviewThe main focus of the approach is to design an automated tool that assistsa user in identifying the features capable of suppression. The overall approachtowards generating a CAD simplification tool, shown in Fig. 3.1, can be brokendown into stages. First, the experts’ knowledge is captured through demonstrationand then suppression rules are generated with the use of a statistical inductionlearning technique [22]. In order to encode the experts’ knowledge a representationis needed with the adequate expressivity. A representation was developed thatallows the suppression rules to be expressed in a neutral format and these rules areexpressed as a binary decision tree. The developed language has a very rich library,which allows the user to edit the rules if necessary. Upon learning the rules, theyare applied for identification of suppressible features within the test parts. Featuresthat are found to be suppressible are further examined based on their parent childrelationships. Lastly, the expert verifies the suppressibility of the features and theCAD model is simplified accordingly.The decision to suppress or preserve a feature strongly depends upon theanalysis context and the application. For developing a rule language the followingfour attributes that play a major role in determining whether or not the feature is29Figure 3.1: Overview of the approach: Acquire knowledge through expert demon-strations, learn suppression rules from the acquired knowledge data, then apply thelearned rules for feature suppressionsuppressed were considered:1. Feature types play a major role in determining what features should be sup-pressed and what features should be preserved. Certain feature types are oftenmore likely to be suppressed. For example, holes, fillets, and chamfers oftendo not significantly affect the analysis results. However, the presence of asingle small hole in the model can significantly increase the size of mesh andalso lower the quality of mesh element. So, such cosmetic features are primecandidates for suppression.302. Feature dimensions play a major role in determining whether they should besuppressed or not. Often features with small sizes are prime candidates forsuppression. However, in many cases it is not the absolute dimensions, butthe relative dimensions of the features that determine whether they should beconsidered for suppression or not.3. Another important consideration when selecting features for suppression istheir topological proximity to the features on the part on which boundary andload conditions are applied. Features that lie close to either the point of loadapplication or the displacement constraints should not be eliminated.4. In CAD models, feature references can be used to define placement of otherfeatures. Such dependency among features may cause problems during featuresuppression. For example, let us assume that a feature is eligible for suppres-sion. However, if a large number of features use this feature as a reference,then suppressing this feature may require redefining features using other fea-tures as references. Not doing so may lead to deletion of those features aswell.Rules that describe which features are possible candidates for suppression canbe quite complex in nature. As more complex parts are simplified, the rule library isexpanded upon in the decision tree. Conditions in the decision tree can be expressedusing the values returned by the following functions supported by our representationframework:Feature Type (feature id): This function returns the type of the feature identified31by variable feature id.Feature Parameter Value (feature id, parameter name): This function returns thevalue of the feature parameter specified by variable parameter name. For example,parameter name can be set to DIAMETER to get the diameter of a hole feature.Find Features (expression): This function returns the list of features that meetthe criteria specified by the variable expression. Expressions used as an input forthis function can be composed by referring to features types, feature labels, andkeywords. We also support all standard logical constructs. For example, expression((Feature Type(this feature) == HOLE) ∧ (¬ (Label == BOUNDARY CONDITION)∧ (DIAMETER < 10)))returns all features in the model that are of type HOLE, donot have label as BOUNDARY CONDITION, and have DIAMETER values smaller then 10.Values used in the expression are assumed to have the same units as the units beingused in the CAD model.Feature Bounding Box (feature id): This function returns the bounding box of thefeature.Model Bounding Box():This function returns the bounding box of the CAD model.Max Distance Between A Feature And Feature List (feature id, feature list): Thisfunction returns the maximum distance of the feature defined by variable feature idwith the features in the feature list.Min Distance Between A Feature And Feature List (feature id, feature list): Thisfunction returns the minimum distance of the feature defined by variable feature idwith the features in the feature list.32Parent Features (feature id): This function returns the list of features that areused as a reference for constructing the feature defined by variable feature id.Child Features (feature id): This function returns the list of features that use thefeature defined by variable feature id as a reference.The variable this feature refers to the feature being currently evaluated. Therule language was generated based upon the four attributes discussed earlier; featuretype, feature dimensions, topological distance, and feature references. The featuredimensions and topological distance are values that are relative to the overall sizeof the 3D model. To acquire a representative rule base for 3D models, these valuesmust be normalized to eliminate the correlation between the overall model size andthe feature values. To accomplish this task the feature values were divided by theaverage of the sides of the overall models bounding box. This normalizes the dataand removes the dimensional bias of the of the feature value with respect to theoverall model size.The representation allows a wide variety of knowledge associated with featuresuppression in a wide variety of contexts to be easily captured. A decision tree inthe context of brackets and mounts to illustrate how the approach works has beendeveloped. Section 3.2 describes the framework to learn the rules for suppressionbased on the knowledge/data collected during the expert demonstrations. Section3.3 presents an algorithm for applying these learned rules and Section 3.4 presentstest results of the simplification process.333.2 Using Inductive Decision Tree to Generate Suppression RulesMachine learning mechanizes the acquisition of knowledge from experiencethrough the use of computational methods [24]. It aims to improve performanceby automating manual time-consuming activity within the knowledge process andincrease accuracy by discovering and exploiting regularities in training data [24]. Apopular technique in robotics is learning from demonstration [4]. Inductive decisiontrees have proven to be a successful tool within the numerous fields and these areproven to be advantageous in improving the accuracy or efficiency of the system.Many real world problems have implemented the technique and their experimentshave shown that the learned rules are more accurate than the handcrafted onespreviously used [15, 12].The framework implemented here requires the rules to classify the features assuppressible or non-suppressible. The feature attributes used for the rule learningprocess are both discrete, having a predefined set of options, or continuous, realnumbers. Regression and other model-fitting methods require discrete attributes tobe encoded as numbers, in which the transformation introduce spatial connotationsthat may affect the outcome. On the other hand Bayesian methods require allattributes to be discrete, so continuous attributes must be divided into sub-ranges[32]. For these reasons decision trees were used, since it can cope with both discreteand continuous attributes. Trees are also very clear and concise in style; along ascontext sensitive, allowing for the relevance of different attributes to be conditionalon the outcomes of previous tests [32].34SuppressibleSuppressible Non−suppressible< 0.03 >= 0.03>= 0.05 < 0.05TypeTHROUGHBoundaryMinDis.Non−suppressibleBLINDDiameterFeature TypeROUND HOLE CHAMFERD1 D2Figure 3.2: A Simple decision tree: An example of a representative decision treefor suppressing a hole feature considering attributes diameter, minimum distanceto the boundary condition feature, and the geometric type. Rectangular boxes andelliptical boxes represent the non-terminal nodes and the leaf nodes respectively.The decision tree is used to classify the suppressibility of the features in thefollowing manner. Given a feature to classify, the decision tree is traversed fromthe root node to a leaf node along a path. All non-terminal nodes in the decisiontree only define test conditions. These nodes in the decision tree point to exactlytwo children nodes. The left node is the node that should be executed if the con-dition is true. The right node is the node that should be executed if the conditionis false. Terminal nodes, leaf node, in the decision tree assign the variable sup-pressibility state for the feature. If the feature is suppressible, then the variablesuppressibility state is set to TRUE. Otherwise, this label is set to FALSE. For a35given set of rules as shown below, a simple decision tree can be formed (Fig. 3.2)by using various split conditions. The decision to suppress or not to suppress canbe made based on the attribute values. Features that are found to be suitable forsuppression are further examined based on their parent-child relationship.∙ If((Feature Type(this feature)==HOLE) ∧ (Feature Parameter Value(this feature,DIAMETER) < 0.03) ∧((Min Distnace Between A Feature And Feature List(this feature,Find Features (Label==BOUNDARY CONDITION)))>= 0.05) then (Suppressibility State = TRUE))∙ If((Feature Type(this feature)==HOLE) ∧ (Feature Parameter Value(this feature,DIAMETER)>=0.03) ∧ (Feature Parameter Value(this feature,TYPE)¬ BLIND) ∧(Feature Parameter Value(this feature,TYPE)¬ THROUGH) then(Suppressibility State = TRUE))The set of attributes used for the learning process will be dependent upon thefeature type. Holes have the feature parameters of diameter, type (through/blind),and minimum distance to the boundary conditions. The diameter and minimumdistance to the boundary condition attributes are both continuous in nature, whereasthe type attribute is discrete in nature. Rounds have the attribute types of radius,conic value and minimum distance to the boundary conditions. Chamfers have theattribute types of D1, D2, and minimum distance to the boundary conditions. Eventhough the attributes for rounds and chamfers are all considered to be continuous36in nature, a decision tree is still used for analysis consistency with the hole features.These attributes were selected to convey the key aspects of the features; featuretype, feature size, and minimum geometric distance to the boundary conditions.These aspects have a effect on whether the feature is critical or not. A couplemodels have been analyzed to demonstrate the effects of the different aspects onthe analysis results. The importance of knowing the minimum distance to theboundary conditions is illustrated in Figs.3.3(a)and(b). There is a round, meetingthe dimensional requirements for suppression, but it is within a critical distanceto the boundary condition. Suppression of this round feature is detrimental to theaccuracy of the results. Upon suppressing this round feature the critical stress valuechanges from a value of 42.27 MPa within the original model illustrated in 3.3(a) toa value of 32.87 MPa shown in 3.3(b). When the round is maintained the criticalstress value is comparable to the original model at a value of 43.61 MPa. Not onlyis value of the critical stress erroneous, but the location of the critical stress valuehas changed and can also be seen in the following figures.To learn the decision trees the analysts experiential knowledge was obtainedby conducting numerous simplification demonstrations on various training parts,where the information about the features and their associated suppressibility statesassigned by the analyst was collected. Collecting the data of the non-suppressedfeatures along with the suppressible features allows for a more expansive rule basefor easy classification.37(a) Original model(b) Simplified model with critical round suppressedFigure 3.3: Example of suppression based on inter-feature distances3.2.1 Training PartsFormation of reasonably good decision trees can be possible by generating alarge number of training parts for demonstration purposes; although this can bemanually time consuming for the expert to conduct demonstrations for such a largedata set. However, with the most informative training examples the decision treecan classify the features correctly without a need of as many examples, through38Figure 3.4: Training examples used to collect attributes of holes, rounds, and cham-fers. Synthetic parts are generated from these examples to tune the transitionboundaries of the decision trees for better classification.the use of synthetic parts to refine the transition point values at the classificationboundaries. For this, some heuristics were used for choosing places where the deci-sion tree performs poorly and generate an additional set of training data at thoseplaces for refining the boundaries.Initially, 10 training parts were started with that offer diversity in terms offeature types and feature parameters. A decision tree is formed from these initialparts. This decision tree failed to give the correct answer for those places where thetransition region between the suppressible and non-suppressible class is very largeand hence locating the correct transition boundary separating these two classes is adifficult task. To overcome this issue the divide-and-conquer strategy (binary search)39Feature Type No. of No. of No. ofof Features Suppressible Seatures Non-Suppressible FeaturesHoles 169 60 109Chamfers 57 23 34Rounds 118 75 43Table 3.1: Training data collected from the examples shown in Fig. 3.4.was used to locate this region and then tune the decision tree with the synthetictest cases generated in the vicinity of the boundary. To determine the transitionregion another 37 synthetic parts were generated to refine the transition points ofthe rule base. From these 37 synthetic parts the only recorded features were thosefeatures used for the transition region or features that required alteration whendesigning the transition feature of the synthetic part. Only recording these featureswithin the synthetic parts eliminated the chance of biasing the data, through theintroduction of the same features numerous times within the data. Since the datais being recorded in this fashion, there will be a relatively low total feature countfor the number of total training parts. The training parts can be seen in Figs. 3.4.Numerous hole, round, and chamfer features were obtained from these examples forrule learning. There was a total of 344 features within the training parts, 158 weresuppressible and 186 were non-suppressible. Table 3.1 displays the statistics of thesefeatures within the training parts.403.2.2 Algorithm for Generating RulesIn this work, a decision trees was built from the geometric feature attributesand the associated suppressibility values. From the set of training parts a decisiontree [22] can be formed to generate a classification model that can generalize beyondthe training samples so that new samples can also be classified with a high accuracy.In order to do this, the decision tree must capture some meaningful relationshipsbetween the output class (C = C1, C2, ..., Ck) and its input data space consists ofvalues from independent parameters (A = A1, A2, ...Ak). Within the data there arethree independent parameters; for instance a hole feature utilizes the diameter, type,and minimum distance to a boundary condition feature. The dependent parameter,Ci, represents the class, whether suppressible or non-suppressible.Development of the tree from the training cases begins at a test node, knownas the root node, of the tree. The tree builds from the root node, splitting thedataset of one particular attribute at each sub-node. The division of the attributesis determined based on the information gain, which is maximized at each node; theattribute with the highest information gain is placed at the node. The informationgain is the entropy relationship of the node before and after the split based on thespecified attribute [22]. This process is continued until the node contains only oneclass; then the node is no longer a test node, but considered to be a leaf node. Thetree is now considered to be fully grown. Fully grown trees tend to over-fit the data,meaning that the tree characterizes too much detail or noise from within the trainingset. To reduce the error of over-fitting the data, the tree was pruned. Pruning the41tree involves calculating the error rates of the branches of the tree. Comparison ofthe error rates determines whether the branch is left unchanged, changed to a leafnode, or replaced by an alternate sub-tree.The generated decision trees for the different feature types are then written inthe framework rule language. Tables 3.2-3.5 display the actual rules produced fromthe decision trees of the hole, round, and chamfer features.Rule Suppressibility State∙ If((Feature Type(this feature) == HOLE) ∧ (Min Distnace Between A Feature And Feature List(this feature,Find Features (Label == BOUNDARY CONDITION))) <= 0.02368)FALSE∙ If((Feature Type(this feature) == HOLE) ∧ (Min Distnace Between A Feature And Feature List(this feature,Find Features(Label == BOUNDARY CONDITION))) > 0.02368)∧ (Feature Parameter Value (this feature,DIAMETER) <= 0.08451) ∧(Feature Parameter Value (this feature,TYPE) == THROUGH)TRUE∙ If((Feature Type(this feature) == HOLE) ∧ (Min Distnace Between A Feature And Feature List(this feature,Find Features (Label == BOUNDARY CONDITION))) > 0.02368)∧ (Feature Parameter Value(this feature,DIAMETER) <= 0.08451) ∧(Feature Parameter Value(this feature,TYPE) == BLIND) ∧ (Feature Parameter Value(this feature,DIAMETER) <= 0.018626)TRUETable 3.2: Rules for computing the suppressibility state of holes42Rule Suppressibility State∙ If((Feature Type(this feature)== HOLE) ∧ (Min Distnace Between A Feature And Feature List(this feature,Find Features(Label==BOUNDARY CONDITION))) > 0.02368)∧ (Feature Parameter Value (this feature,DIAMETER) <= 0.08451) ∧(Feature Parameter Value (this feature,TYPE)==BLIND) ∧ (Feature Parameter Value(this feature,DIAMETER) > 0.018626) ∧ (Feature Parameter Value(this feature,DIAMETER) <= 0.02314)FALSE∙ If((Feature Type(this feature) == HOLE) ∧ (Min Distnace Between A Feature And Feature List(this feature,Find Features(Label == BOUNDARY CONDITION))) > 0.02368)∧ (Feature Parameter Value (this feature,DIAMETER) <= 0.08451) ∧(Feature Parameter Value (this feature,TYPE) == BLIND) ∧ (Feature Parameter Value(this feature,DIAMETER) > 0.018626) ∧ (Feature Parameter Value(this feature,DIAMETER) > 0.02314)TRUE∙ If((Feature Type(this feature) == HOLE) ∧ (Min Distnace Between A Feature And Feature List(this feature,Find Features(Label == BOUNDARY CONDITION))) > 0.02368)∧ (Feature Parameter Value (this feature,DIAMETER) > 0.08451) ∧(Feature Parameter Value (this feature,TYPE) == THROUGH)FALSE∙ If((Feature Type(this feature) == HOLE) ∧ (Min Distnace Between A Feature And Feature List(this feature,Find Features(Label == BOUNDARY CONDITION))) > 0.02368)∧ (Feature Parameter Value (this feature,DIAMETER) > 0.08451) ∧(Feature Parameter Value (this feature,TYPE) == BLIND)TRUETable 3.3: Rules for computing the suppressibility state of holes43Rule Suppressibility State∙ If((Feature Type(this feature) == CHAMFER) ∧(Min Distnace Between A Feature And Feature List (this feature,Find Features(Label== BOUNDARY CONDITION))) <= 0.004121)FALSE∙ If((Feature Type(this feature) == CHAMFER) ∧(Min Distnace Between A Feature And Feature List (this feature,Find Features(Label== BOUNDARY CONDITION))) > 0.004121) ∧ (Feature Parameter Value (this feature,D1)<= 0.01714)TRUE∙ If((Feature Type(this feature) == CHAMFER) ∧(Min Distnace Between A Feature And Feature List (this feature,Find Features(Label== BOUNDARY CONDITION))) > 0.004121) ∧ (Feature Parameter Value (this feature,D1) >0.01714)FALSETable 3.4: Rules for computing the suppressibility state of chamfers44Rule Suppressibility State∙ If((Feature Type(this feature) == ROUND) ∧ (Feature Parameter Value(this feature,RADIUS) <= 0.02623) ∧ (Min Distnace Between A Feature And Feature List(this feature,Find Features(Label==BOUNDARY CONDITION))) <= 0.013545)FALSE∙ If((Feature Type(this feature) == ROUND) ∧ (Feature Parameter Value(this feature,RADIUS) <= 0.02623) ∧ (Min Distnace Between A Feature And Feature List(this feature,Find Features(Label==BOUNDARY CONDITION))) > 0.013545)TRUE∙ ((Feature Type(this feature) == ROUND) ∧ (Feature Parameter Value(this feature,RADIUS) > 0.02623))FALSETable 3.5: Rules for computing the suppressibility state of rounds453.3 Applying Learned-Rules for SimplificationThe rules have been learned from training parts, now the next step withinthe approach, as seen in Fig. 3.1, is to apply the rules to new models. To do this,a utility was needed to extract the attribute information and classify the featureswithin the model, for this ProE was used.3.3.1 Extracting CAD Model InformationProE has a Pro/Toolkit API, which allows customization within the frame-work. In this API, the design model is stored by ProMdl, a data handle to retrievethe complete information of the model such as features, their dependencies, etc. Byutilizing the ProMdl the framework traverses through all the features, where eachfeature can contain a large amount of information. In ProE, the complete designmodel is stored as a feature element tree that contains all information about thefeature, including, for example: all attributes, such as the material, placements ofholes; all references to the existing geometries such as placement references; and alldimension values. For example, a “hole” feature contains information as to whetherthe hole is straight, standard, or sketched; whether the hole is a clearance hole ora threaded hole; parameters of the hole, etc; all this information can be obtainedthrough the element tree.To implement the part of the rule Feature Type(feature id), the element tree ofthe complete design model was traversed and determined the feature f correspondingto the feature id. Now, the element tree of this feature f was traversed to extract46(a) (D × D) (b) (D1 × D2) (c) (ANG × D)(d) (45 × D) (e) (O × O) (f) (O1 × O2)Figure 3.5: Suppression based on chamfer geometric types: (a) D × D (b) D1 × D2(c) ANG × D (d) 45 × D (e) O × O and (f) O1 × O2the internal structure of the feature information, such as the diameter value for ahole or the D1 value for a chamfer. There are many types of features that can bepresent within a CAD model, including holes, rounds, chamfers, fillets, steps, andslots. Currently, the framework implemented considers (a) chamfers (b) holes and(c) rounds. In the case of chamfers there is an option of six different geometricrepresentations; described by one distance (D × D) (Fig. 3.5)(a); by two distances(D1 × D2) (Fig. 3.5)(b); by an angle and a distance (ANG × D) (Fig. 3.5)(c); bya 45o angle and a distance (45 × D) (Figure 3.5)(d); by an off-set distance (O ×O) (Fig. 3.5)(e); or by two off-set distances (O1 × O2) (Fig. 3.5)(f). In a similarmanner the suppressibility state of holes is described by two types; blind holes andthrough holes; and rounds are described as either conical or circular.In addition to the size and type, feature locations must also be calculated47for the rule implementation. Feature locations play an important role in determin-ing the extent of the feature criticality, since often features that are very close tothe boundary conditions are very critical and should not be eliminated irrespec-tive of their size. In most situations, closeness in terms of the topological distanceis more important than the geometric distances. Features that are far away fromthe boundary conditions can also become critical if they are located within thestress flow path from the load application to the displacement constraints. Utilizingthe available ProE API functions each and every feature of the design model wasvisited, computing the inter-feature distances among all the relevant feature pairsavailable in the model. Then the feature pairs are retrieved associated with load ordisplacement constraints locations. In the framework, features associated with loador displacement constraint locations are labeled as BOUNDARY CONDITION features.This labeling needs to be done manually.3.3.2 Utilizing CAD Model Information within RulesThe collected attribute data for each feature in the model from section 3.3.1was normalized just like the training data, to remove the dimensional bias of theparts. The normalized data was then evaluated utilizing the machine learned rules,generated from the training data. For instance, the attribute values of a hole, con-sisting of the diameter, type, and minimum distance to the boundary condition,collected in section 3.3.1 were compared to the rule values in Table 3.2. Referringto Table 3.2 a hole with a calculated normalized minimum distance to the boundary48condition features of 0 would be classified as non-suppressible without any otherattribute analysis, where as a normalized distance of .03 would then cause the di-ameter attribute to be analyzed. Upon analyzing the diameter, the type would thenbe used for comparison and depending on the diameter and type values the analysiscould potentially stop there or continue. After the feature’s attribute values wereanalyzed using the generated rule set, the features were then labeled as suppressibleor non-suppressible determined by the classification obtained from the rule base.Actual Rule Classification Error TypeSuppressibility State Suppressibility StateTrue True Correct NoneFalse False Correct NoneTrue False Incorrect ConservativeFalse True Incorrect Non-ConservativeTable 3.6: Errors and error types within the rule learning application: Conserva-tive errors can be allowed as they will not affect the analysis results but Non-Conservative errors can generate erroneous results.Implementation of the learned rules from the training data may sometimesbe flawed, which can generate two different error types, shown in Table 3.6 whencompared with the actual suppressibility states of the features. The first type is aconservative error, which is an error that will not affect the analysis results of thesimplified model. This occurs when the rule states not to suppress a feature that hasan actual suppressibility state of TRUE, or non-critical feature. The other type is a49non-conservative error, which will likely affect the analysis results of the simplifiedmodel. This error occurs when the rule states to suppress a feature that has anactual suppressibility status of FALSE, or critical feature. For the reason that non-conservative errors can generate erroneous results, the error has been limited withinthe inductive learning process to allow for only conservatives errors. This was donethrough the use of the synthetic parts to refine the transition points.3.3.3 Accounting for Parent-Child Relationships during Feature Sup-pressionDesign model generation using a feature-based approach allows flexibility tocompile a set of information about the product at higher levels of abstractions. Thisinformation can be represented in the form of data structures that maintain the asso-ciations between the geometric entities, further aiding in making any changes to thedesign. All major parametric CAD modeling systems have adopted the feature-baseddesign approach by representing the final design model with features dependent onone another. This is called the design feature history tree [33, 37]. The same designmodel may be designed in several different ways, depending on the designer, whobuilds the design feature history. For the finite element analysis the order in whichone simplifies the features is immaterial. However, it is necessary to understandthe dependent relationships among the features, as the suppression of one featuremay suppress another feature that may be very critical to the analysis. Hence, it isimperative to understand features’ parent-child relationships for suppressions. For50example, on a block a hole was first created and then a round operation was per-formed on it. The round is defined as the child of the parent hole, which in turn isthe child of the parent block. In this case, suppressing the hole would also suppressthe round. Extracting these parent-child dependencies is crucial in order to avoidsuppressing any non-critical features.In the approach, the feature dependencies were initially extracted from themodel using the available API functions and represented as a feature dependencygraph, as illustrated in Figure 3.6. Let G(V,E) represent the parent-child relation-ship graph. Each v in V represents a feature in the feature tree. Each element ein E is a directed edge (v, v) that represents the fact that node v is a parent ofnode v. Since features are inserted one by one in the feature tree and can onlyuse the already defined features as references, by the property of the feature treeconstruction, G is a directed acyclic graph.Within the graph the nodes represent the various features of the model. Eachdependency is represented by an arrow, which is directed from the parent featureto the child feature. The tree illustrates the dependencies for easy analysis. Af-ter obtaining the G value, we follow an algorithm for identifying different cases ofsuppression possibilities, as a feature should not be suppressed just because it issuppressible. It may have child features indicating that it is not suppressible. Onthe other hand, it can be suppressed if all of its direct children can be suppressed.Hence, we needed to use a special sequence to determine which features can besuppressed by accounting for their parent-child relationships.The algorithm for suppressing features is as follow:511. Construct G by inserting a node in V corresponding to every feature in thefeature tree. If feature f ′ uses a feature f as a reference, then insert an edge(v, f ′) in G. Here vertex v corresponds to feature f and vertex v′ correspondsto feature f ′.2. Find nodes X in V that do not have parents and have label suppressibil-ity state = TRUE. If X is empty, then reset suppressibility state for all nodesto be FALSE and stop. Otherwise do the following:(a) Remove every node in X from G by deleting associated vertex and edges.(b) Go to Step 2.Figure 3.6(a) shows a parent-child relationship graph. Figures 3.6(b) through (e)show how executing the above algorithm correctly identifies the features to be sup-pressed. This algorithm discovers at least one feature to suppress; otherwise itterminates in Step 2. Hence, it takes at most V iterations to complete its task. Inthis way, what our tool is capable of suppressing the features based on the feasibilitydependencies.52(a) Initial tree (b) First pass for suppression(c) Second pass for suppression (d) Third pass for suppression(e) Fourth pass for suppressionFigure 3.6: Dependency graph showing an example of finding features to be sup-pressed based on the parent-child relationships. Dependent relationships among thefeatures should be considered before suppression; the suppression of one feature maysuppress the dependent critical feature.533.4 Results & DiscussionTo demonstrate the simplification tool five parts were considered Fig.3.7-Fig.3.11. The simplified models were obtained by using the learned rules from thetraining models. Now a comparison was done of the analysis results of the originaland simplified models (Fig. 3.7(b) - Fig.3.11(b). In terms of analysis we initiallyadd displacement constraints and applied forces were added to each part and a fi-nite element analysis was conducted with the help of Pro/Mechanica (available inProE). Pro/Mechanica requires every model to contain a constraint and a force foranalysis.The location of the displacement constraints along with the applied forcesis explained below. Figs. 3.7(a) - Fig.3.11(a) illustrate the boundary conditions(constraints and forces) applied to the to the five complex models.1. Part-A: The constraints were placed at the eight outside holes on the baseof the part, where it is bolted into place. The forces were applied in thedownward vertical direction located at the two center holes of the extensionat the top of the part (Fig. 3.7(a)).2. Part-B: The constraints are located at the vertical slots. A downward forcewas applied on the pin holes shown in Fig. 3.8(a).3. Part-C: The constraints are located at the rectangular slots in the model thatare connection points to a vertical piece. A distributed vertical load was placedon the plane of the face perpendicular to the vertical plane (Fig. 3.9(a)).544. Part-D: The constraint was applied at the location of the hole, where this partwill be bolted into place. Multiple forces were applied at different locationsof the model, (1) tensile forces were applied at the hole on the free end and(2) another force was applied on the other end of the part in the oppositedirection at the middle pin shown in Fig. 3.10(a).5. Part-E: The part slides into grooves on a wall support and then pinned intoplace. The top curve latches on a lip and acts as the constraint of the model. Aforce was applied in the vertical direction on the horizontal face (Fig. 3.11(a))55(a) Boundary conditions(b) Suppression of featuresFigure 3.7: Part A: boundary condition features and feature suppression after ruleimplementation56(a) Boundary conditions(b) Suppression of featuresFigure 3.8: Part B: boundary condition features and feature suppression after ruleimplementation57(a) Boundary conditions(b) Suppression of featuresFigure 3.9: Part C: boundary condition features and feature suppression after ruleimplementation58(a) Boundary conditions(b) Suppression of featuresFigure 3.10: Part D: boundary condition features and feature suppression after ruleimplementation59(a) Boundary conditions(b) Suppression of featuresFigure 3.11: Part E: boundary condition features and feature suppression after ruleimplementation60Now, an analysis was conducted independently for both the original and sim-plified models of these parts after applying the boundary conditions described above.First the learned rules were applied to the five test parts. After applying the learnedrules, the suppressibility state of the features by the learned rules were comparedto the suppressibility states of the features given by an expert analyst. The learnedrules proved to be highly accurate for the five test parts compared to the expertanalysis of the parts. For the five parts there were a total of two feature classificationerrors of the total 154 features in the models, both arising within the round features.The errors were caused due to rare suppression occurrences within the simplificationmethod, but found to be conservative in nature. One round was relatively largerand the other was relatively closer to a boundary condition when compared to thestandard values for round suppression. Table 3.7 displays the results of the rules tothe actual suppression analysis.Meshes were then generated for these parts in Pro/Mechanica to allow for acomparison of analysis results in terms of mesh quality, mesh generation time, andmaximum Von Mises stress between the original and simplified models. The resultsshown in Table 3.8 demonstrate a significant reduction in the amount of elementsby more than a factor of two, with the largest being a factor of over eight. Therewas also a decrease in the maximum aspect ratio, signifying a higher quality mesh.Due to the simplification, the time to mesh was also greatly reduced by at least 27seconds; this could be significant when analyzing numerous parts.To evaluate the effectiveness of the simplification process, the maximum VonMises stresses were compared between the original and simplified models. In each61Feature Type No. of Features No. of Errors Error TypeHole 93 0 NoneRound 44 2 ConservativeChamfer 17 0 NoneTable 3.7: Analysis of learned rules on the five test parts (A)-(E).case there is a difference of less than five percent, indicating that the simplificationprocess did not significantly alter the accuracy of the results. The stress analysesresults for both the unsimplified and simplified models can be seen in Figs. 3.13-3.16. In the results of part C, the critical stress values are displayed to show thatthis location is constant between the original and simplified models.62Tetra Max. Meshing Time Max. VonElements Aspect Ratio (sec) Mises Stress (MPa)Part-A original 19500 11.39 81 33.97Part-A simplified 4511 11.20 7.2 33.15Part-B original 6848 20.09 22.2 372.39Part-B simplified 2462 11.20 7.8 373.01Part-C original 20643 20.34 165 30.06Part-C simplified 7865 15.60 46.9 29.93Part-D original 7706 11.17 28.2 42.27Part-D simplified 1445 10.59 4.8 43.61Part-E original 9164 11.45 43.2 162.30Part-E simplified 4049 11.19 13.8 159.82Table 3.8: Analysis of models before and after simplification63(a) Unsimplified model(b) Simplified modelFigure 3.12: Stress analysis results for the unsimplified and simplified models forpart A64(a) Unsimplified model(b) Simplified modelFigure 3.13: Stress analyses results for the unsimplified and simplified models forpart B65(a) Unsimplified model(b) Simplified modelFigure 3.14: Stress analyses results for the unsimplified and simplified models forpart C66(a) Unsimplified model(b) Simplified modelFigure 3.15: Stress analyses results for the unsimplified and simplified models forpart D67(a) Unsimplified model(b) Simplified modelFigure 3.16: Stress analyses results for the unsimplified and simplified models forpart E68After conducting finite element analysis, the five simplified parts showed ac-ceptable errors within 5% and improved mesh quality when compared with theoriginal models. The learned rules proved to be highly accurate for the test parts.As mentioned earlier only conservative errors were allowed for within the analysisprocess.Examination of how the parent-child relationships affect the results was done.For that the parts A and D were considered, shown in Fig. 3.17(a)-(b). Withinthese models the parent child dependencies were accessed and there were featuresthat needed to be retained in order to preserve parent-child relationships. Thechamfers shown in red in Fig. 3.17(a) has its children shown in green. If the parentis suppressed then these children will also get suppressed. However, in this case thechildren also meet the suppression criteria, hence both the parent and child wouldbe suppressed. The holes shown in the Fig. 3.17(b) cannot be suppressed becausethe children are labeled BOUNDARY CONDITION.(a) Part-A (b) Part-DFigure 3.17: Example of suppression based on parent-child relationships693.5 SummaryIn this chapter, a framework was presented that can be utilized in any of theexisting CAD softwares for suppressing geometric features before conducting finiteelement analysis. The automated tool developed in this chapter assists users inidentifying the suppressible features for FEA and it reduces the burden on usersin identifying suppressible features manually. Towards generating this automatedtool, initially a rule language was developed that can capture experts’ suppressionknowledge. This knowledge was acquired through expert demonstrations and therules were expressed in terms of a decision tree. With the help of statistical inductionlearning techniques suppression rules were learned for suppressing holes, rounds andchamfers.The Pro/Toolkit API available in ProE was utilized to generate a model simpli-fication tool; for hole, round and chamfer features. The complete model is traversedthrough to determine the features that were capable of suppression based upon therules learned through expert demonstrations. The suppression state was determinedby the feature type, dimensions, and relation to other features, i.e. parent-child re-lationship and inter-feature distances. To demonstrate the simplification method,five different models were analyzed. Evaluation of the learned rules found two outof 154 features that should have been suppressed, but were given the suppressibil-ity state of FALSE; this error was of conservative nature. In comparison to theoriginal models, the simplified models had a decrease of at least two percent in theamount of elements within the mesh. Furthermore, the maximum Von Mises stress70was within the error range of 5%.71Chapter 4Assembly Model Simplification for Finite Element Analysis4.1 OverviewThe main focus of the assembly approach is to design a framework that as-sists the user in the simplification of complex CAD assembly models, consisting ofnumerous part models; similar to the part simplification framework. The overall ap-proach can be broken down into a process flow, displayed in Fig. 4.1. Initially, thecomplete assembly information is extracted and written in an XML format. Thisinformation is stored as an element tree that contains all information about theparts, including, for example: all attributes, such as the material, and all referencesto the existing parts, such as placement and orientation. Upon extraction of themodel information, the insignificant parts are then determined and the model issimplified, whether parts are suppressed or replaced.Figure 4.1: Overview of the assembly approach72Discussions with AVMI engineers introduced three key parameters that can beused to assist in the classification of parts as structurally significant or insignificant.These parameters include DESCRIP, PART NAME, and MATERIAL.1. The DESCRIP parameter often provides part information. This informationcan include the type of the part; e.g. nut, washer, or screw (standard hard-ware), and characteristics of the part type, e.g. thread pitch, bolt diameter,and head shape (bolt or screw).2. The generation of the PART NAME is usually standardized throughout theindustry, grouping similar parts. For instance, within AVMI a PART NAMEincluding the AN*, MS*, or NAS* string is standard hardware, whereas aPART NAME including the PE* or #####M* string is a unique part.3. The part material is dependent upon the requirements of the part within theoverall assembly. Different materials are used for different types of parts, so aspecific material can be seen as insignificant within the overall model.A search within the XML file for key words and/or numbering schemes ofthe specified parameters can indicate whether or not the part is standard hardwareor a unique component. Standard hardware is generally not advantageous withinthe FEA model, as they generate unnecessary mesh complexities within the analysisand can be suppressed; whereas a unique component is a designed part that requiresFEA, but may be capable of simplification.The framework has been implemented within the ProE CAD system. Section4.2 describes the algorithm for suppressing parts based upon the PART NAME and73MATERIAL and usefulness of this technique. Section 4.3 describes simplificationmethods pertaining to the individual parts of the assembly. Section 4.4 presentsresults of the simplification process, by using the techniques described in the previoussections.4.2 Part SuppressionIn order to assist in the simplification process of the assembly models, thePro/Toolkit API in ProE was utilized to generate a model suppression tool, justas in the part simplification framework. For recap, this tool is an add-on modulein ProE, accessible through the menu systems in the ProE environment. In theAPI, the design model is stored by ProMdl, a data handle to retrieve the completeinformation of the design model. This information is stored within ProE as anelement tree that contains all information about the parts, including, for example:all attributes, such as the material, and all references to the existing parts, such asplacement and orientation. Suppression is based upon the part MATERIAL andPART NAME parameters.4.2.1 Part UtilizationDefining the intended purpose of the part within the overall assembly model;e.g. structural stability, thermal enhancement, ergonomic aspect, or part attach-ment method; can facilitate the classification of the part’s criticality for analysis.The PART NAME and DESCRIP parameters can aid in the identification of the74part’s purpose within the assembly. Generally, the PART NAME has a commonstring, specifying the group type to which the part belongs; for example the MS*string refers to a type of fastener and then the DESCRIP parameter contains keywords to assist in specifying the intended purpose, such as bolt or screw.Although this can facilitate the classification, the intended purpose of thepart is not always clearly defined. Different aspects of the part can be intended forvarious purposes or parts unintended for the specified purpose can have an effecton different analysis results; e.g. a heat shield that is placed within an assemblyfor the thermal protection of other parts, may not only affect a thermal analysis(for which the part is intended), but could also have an effect on the modal analysisof the overall model. For these reasons, focus was geared toward a specific parttype that mainly falls into the intended purpose of attachment methods: hardware(i.e. fasteners), such as nuts and bolts. Depending on the number of parts in theassembly, a model could potentially contain a couple hundred fasteners. Even withthe large amount of fasteners, there is often only a select few of different fastenerswithin the model. Using the same fasteners throughout reduces the overall partcount of the model. There are several benefits to reducing the overall part countof an assembly; (1)decreases some of the cost because less material types need tobe purchased, (2) similar tools can be used to assemble the model and (3) reducesthe error probability during the manufacturing process of the model. Typically,these fasteners have minimal to no effect on analyses and, therefore, fasteners arefrequently suppressed before an analysis; greatly reducing the computational costof the analysis.75Currently, an engineer will have to manually transverse through the modeland/or the model tree and independently suppress each fastener. With a largemodel this could become a tedious time consuming task. To help expedite theprocess of fastener suppression, or other parts that may appear several times withinthe model, the framework can suppress the parts by the PART NAME; all parts inthe model with that part name will be quickly suppressed. For instance, a modelcontaining 25 bolts of two different types (PART NAMEs), would only require twoindependent suppressions, instead of the manual independent suppressions of 25.4.2.2 MaterialIn addition to the part’s intended purpose, material selection plays a role indetermining the extent of the part criticality, from the analysis results point ofview. The analysis response of a part is highly dependent upon its overall shapeand dimensions, but the magnitude of this response is a result of the material; i.e.the material properties. For instance, Fig. 4.2 displays an example assembly modelsection, which is the input for two static analyses. For comparison the parts in redare constucted of a similar material and only the material of these two parts is alteredbetween the two tests. The material properties of the two parts for the analyses arethat of steel and nylon. From the results shown in Figs. 4.3 and 4.4, steel and nylonmaterial attributes respectively, it can be deduced that the critical stress withinthe model is much higher in the assembly model where the parts are made of steel,than that of the assembly model where the parts are made of nylon. This stress76Figure 4.2: Example assembly modelFigure 4.3: Stresses within the model when the two parts are made of the materialsteeldifference is the result of the difference in the densities of the two materials. Theanalysis demonstrates that the part material is critical in determining the criticalityof the part for analysis purposes.The behavioral response of the material, due to its properties as discussed77Figure 4.4: Stresses within the model when the two parts are made of the materialnylonabove, has generated basic standards within the material selection phase; for in-stance, a load bearing part is generally constructed of a material with a higherstrength, such as a metal compared to a plastic. Knowledge of these standards andthe analysis type to be performed on the model can signify material types as in-significant or significant to the analysis. For example, in a structural analysis, often,plastic parts can be viewed as insignificant, since load bearing parts are usually notconstructed with this material.4.2.3 AlgorithmThe parts considered to be insignificant based upon their material or purposeare then suppressed. Either the MATERIAL or PART NAME value can be enteredto suppress all the parts containing that parameter value. Before suppression it78is necessary to understand the dependency relationships among the parts, just asdiscussed in the previous chapter. The previous chapter discusses the feature-basedapproach in model generation, where features are dependent among one anotherwithin a model; generating the feature history tree [33, 37]. Just as the features aredependent upon one another in a part model, parts are dependent upon one anotherwithin an assembly model. When constructing the assembly model, parts are intro-duced into the model one at a time referencing the previous parts within the modelfor placement. The same model can be constructed in several ways , dependentupon the order in which the parts were added to the model, generating differenthistory trees and, ultimately, different dependencies among the parts. Suppressionof a parent will ultimately suppress its children parts, hence, it is imperative tounderstand parts’ parent-child relationships for suppressions; since the child couldpotentially be a critical part for the analysis.For example, let’s look at the construction of a simple table with four legs,attached by nuts and bolts, illustrated in Fig. 4.5. Conventionally the table topwould be first inserted into the model. Then the legs would be brought in one at atime, referencing the axis of the holes within the table top for the desired location ofthe legs. Upon including the legs, the bolts would be inserted into the table top andlegs by referencing the axes once again to line up the bolts and then referencing thetable top surface and connecting surface of the bolt head. After this the nuts areadded by referencing the bolt axis and the connecting surfaces of the nut and tableleg. In this instance, suppression of the bolts would also suppress the nuts, since theyare referenced from the bolts axis. This setup would not cause any critical features79Figure 4.5: Simple four-legged table for illustration of the parent-child relationshipwithin a modelto be suppressed within the model, however, a designer could assemble the tablein a different manner within the software. Let’s say the designer unconventionallydecides to bring the bolts into the model and reference the table top and legs fromthe bolts. Then suppression of the bolts would ultimately suppress the entire model.Extracting these parent-child dependencies is crucial in order to avoid suppressingany non-critical features.An algorithm has been developed to account for the parent-child relationshipsduring the suppression process, similar to that of the algorithm presented in theprevious chapter for suppressing features based upon the parent-child relationships.Alteration of the algorithm was required, since there is not a general rule set thatassigns a suppressibility status based upon all the criteria; i.e. suppression is based80upon either the MATERIAL or PART NAME value.The algorithm for suppressing features is as follows:1. Construct G (parent-child relationship graph) by inserting a node V corre-sponding to every part in the tree, which is not suppressed. If part p’ usesa part p as a reference, then insert an edge (v, p’) in G. Here the vertex vcorresponds to part p and vertex v’ corresponds to part p’. Fig. 4.6 shows anexample of the parent-child relationship graph.2. Find nodes X in V that do not have children and have the attribute value (MA-TERIAL or PART NAME) given. If X is empty proceed to step 3, otherwisedo the following:(a) Remove every node in X from G by deleting the associated vertex andedges.(b) Go to step 2.3. Find nodes Y in V that have children and the attribute value and do thefollowing:(a) For node Yi, highlight the child/children in green and the parent nodein red, ask if the user would like to suppress the parent and associatedchild/children. If Yi is empty, then stop.i. Yes, then remove node Yi and child/children nodes of G by deletingthe associated vertex and edges. Proceed back to step 3a.81Figure 4.6: Example of the generated parent-child relationship graphii. No, then add 1 to i and proceed to step 3a.This model is only valid for assembly models generated using only parts and nominor assembly models. When minor assembly models are used within the overallassembly, the parent references of the minor assembly are not necessarily used asthe reference for inclusion into the overall model. If the parent is not used, thenit is not seen as a child to the parts from which the minor assembly is referenced.Then suppression of the part model of the overall assembly used for referencinggenerates an error because the parents of the referenced part are not suppressed,but the references for the part into the overall model are suppressed.4.3 SimplificationSuppression of parts is not the only means of simplifying an assembly model,the parts themselves can also be simplified within the model. Simplification of the82parts can be accomplished by suppressing the non-critical features, or the parts canbe replaced, either with a simpler geometry or point mass that maintains the effectsof the original part.The first method was thoroughly discussed in Chapter 2. To successfully usethis approach within ProE, the simplification of the part must be done within thepart file because modifications cannot be done to an individual part within theassembly file. Even though the modifications, such as suppression of features, aredone within the part file, they will be automatically reflected within the assemblymodel.The second method requires additional knowledge compared to that of theother method, since the features are not only suppressed, but the part geometryis altered; maintaining a similar response to that of the original part. First, theanalysis type must be identified, since a part can have a different response withinthe various types of analyses. Upon knowledge of the analysis type, the part mustbe quickly reviewed to determine the necessity and response, so a suitable approx-imation method can be developed, whether the method is point mass or simplergeometry with density match. Then the center of gravity (CG) is calculated of theoriginal part. For the point mass simplification the CG is the location of the pointmass. For the simpler geometry simplification the simpler geometry is designed tomaintain the location of the CG. Figure X illustrates a part that was simplifiedto a simpler geometry displayed in Figure Y. To automate this method an outsideprogram requiring numerous inputs will be needed to analyze and create a simplergeometry according to the model.83Figure 4.7: Unsimplified boom model for a modal analysis4.4 Results and DiscussionTo illustrate the framework described, assembly models have been simplifiedfor both a structural and a modal analysis. Simplification of the models was accom-plished by part suppression, based upon the MATERIAL or PART NAME attributevalue, and part simplification discussed in the previous chapter. Upon model sim-plification a finite element analysis is conducted for both the simplified and originalmodels, with the help of Pro/Mechanica. After conducting the FEA, the analysisresults were compared between the simplified and original models in terms of meshquality(number of tetra elements and maximum aspect ratio), mesh generation time,and either mode values or maximum Von Mises stress, depending on the analysistype.4.4.1 Modal AnalysisA modal analysis was done on a boom assembly model shown in Fig. 4.7. Thesimplification of the assembly model, displayed in Fig. 4.8, was done in the followingmanner:∙ The 15 bolts and their respective nuts were suppressed by their PART NAME.84Figure 4.8: Simplified boom model for a modal analysisTo suppress the 15 nuts it only took two different PART NAMEs, which ac-counted for the two different diameter nuts; although it required four PART NAMEsto suppress the bolts, accounting for the different lengths and diameters. Tocomplete the suppression of the 30 parts it only took 6 passes compared to themanual suppression of 30 passes. For clarification the nuts were suppressedprior to the bolts, removing the children parts before the parent parts. If thebolts were first suppressed, then the nuts would have been seen as children tothe bolts and the suppression message would have appeared. Either order ofsuppression achieves the same desired outcome.∙ The two mount attachments, the center slider, the complex attachment, andthe boom were simplified using the method discussed in the previous chapter.The first step in the FEA process is mesh generation. The comparison of themesh quality and mesh generation time between the two models can be seen in Table4.1. As illustrated below the simplified model has a 44% reduction of the numberof elements; the max aspect ratio is reduced by 7.75, which means the mesh qualityis better in the simplified model; and the time to mesh was reduced by almost 20%or 13.8 sec. In terms of the mesh, the simplified model has a better quality meshand was generated faster than the original model.85Tetra Elements Max. Aspect Ratio Meshing Time (sec)Original 15069 20.90 72Simplified 8422 13.15 58.2Table 4.1: Mesh improvementMode Original Model (Hz) Simplified Model (Hz) % Error1 25.23 25.28 0.19822 73.50 73.47 0.04083 75.32 74.75 0.75684 77.21 77.16 0.0648Table 4.2: Modes calculated within the modal analysisThe mesh quality is not the only factor required for comparison of the models,but the analysis results of the model must be similar or the simplified model cannotreplace the original model within the analysis process. A modal analysis has beenexecuted on the boom models and the first four modes of both the original andsimplified models were compared; shown in Table 4.2. The last column of the tableshows that there was an error of less than 1% between the two models for all fourof the modes.The modes of the two models can be seen in Figs. 4.9-4.12.86(a)(b)Figure 4.9: (a) Mode 1 of the unsimplified boom assembly (b) Mode 1 of the sim-plified boom assembly87(a)(b)Figure 4.10: (a) Mode 2 of the unsimplified boom assembly (b) Mode 2 of thesimplified boom assembly88(a)(b)Figure 4.11: (a) Mode 3 of the unsimplified boom assembly (b) Mode 3 of thesimplified boom assembly89(a)(b)Figure 4.12: (a) Mode 4 of the unsimplified boom assembly (b) Mode 4 of thesimplified boom assembly904.4.2 Structural AnalysisIn a similar fashion to the modal analysis, a structural analysis was completedfor two assembly models. The two models used for the structural analysis were aweight bench assembly and the same boom assembly from which the modal analysiswas done. Comparison between the simplification process for the modal analysisand structural analysis of the beam will highlight different simplification processes.First, the original and simplified models of the weight bench are shown inFigs. 4.13 and 4.14, respectively. Simplification of the assembly was done in thefollowing manner:Figure 4.13: Unsimplified weight bench assembly model for a structural analysis∙ The 12 bolts and their respective nuts were suppressed by their PART NAME.To suppress the 12 nuts it only took two different PART NAMEs, whichaccounted for the two different diameter nuts; although it required three91Figure 4.14: Simplified weight bench assembly model for a structural analysisPART NAMEs to suppress the bolts, accounting for the different lengths anddiameters. To complete the suppression of the 24 parts it only took five passescompared to the manual suppression of 24 passes. For clarification the nutswere suppressed prior to the bolts, removing the children parts before theparent parts. If the bolts were first suppressed, then the nuts would havebeen seen as children to the bolts and the suppression message would haveappeared. Either order of suppression achieves the same desired outcome.∙ The support frames were simplified using the method discussed in the previouschapter.∙ The attachments covering the ends of the pipes are all constructed of a nylonmaterial and have no bearing on the stresses generated within the model.These 9 caps were suppressed in one pass, using their MATERIAL value.92Just as in the modal analysis, the first step in the structural analysis is meshgeneration. The comparison of the mesh quality and mesh generation time betweenthe two models can be seen in Table 4.3. As illustrated below the simplified modelhas a 35% reduction of the number of elements; the max aspect ratio is reduced by2.27, which means the mesh quality is better in the simplified model; amd the time tomesh was reduced by about 38% or 150.68 sec. In terms of the mesh, the simplifiedmodel has a better quality mesh and was generated faster than the original model.Upon mesh generation the Von Mises stresses are calculated within the model andthe maximum stress is then compared between the two models, shown in Table 4.3,which has an error of 4.8% between the original and simplified weight bench models.Figs. 4.15 and 4.16 show the stresses within the two modelsTetra Maximum Meshing Time Max. VonElements Aspect Ratio (sec) Mises StressOriginal 46423 19.78 391.8 39.93Simplified 30133 17.51 241.2 41.85Table 4.3: Mesh improvement93Figure 4.15: Von Mises Stress distribution on the unsimplified weight bench assem-blyFigure 4.16: Von Mises Stress distribution on the simplified weight bench assembly94The other assembly model for which a sructural analysis was done was theboom assembly. Figs. 4.17 and 4.18 illustrate the original and simplified modelsof the boom assembly. The original model, Fig. 4.17, is the same as the originalmodal analysis model, Fig. 4.7, but the simplified models are slightly altered. Thestructural analysis simplified model has replaced the complex structure on the endof the boom with a simpler part; where in the modal analysis this complex end wasnot replaced, but just simplified, according to the previous chapter. Simplificationof the assembly was done in the following manner:Figure 4.17: Unsimplified boom assembly model for a structural analysisFigure 4.18: Simplified boom assembly model for a structural analysis∙ The 15 bolts and their respective nuts were suppressed by their PART NAME.To suppress the 15 nuts it only took two different PART NAMEs, which ac-counted for the two different diameter nuts; although it required four PART NAMEsto suppress the bolts, accounting for the different lengths and diameters. Tocomplete the suppression of the 30 parts it only took 6 passes compared to the95manual suppression of 30 passes. For clarification the nuts were suppressedprior to the bolts, removing the children parts before the parent parts. If thebolts were first suppressed, then the nuts would have been seen as children tothe bolts and the suppression message would have appeared. Either order ofsuppression achieves the same desired outcome.∙ The two mount attachments, the center slider, and the boom were simplifiedusing the method discussed in the previous chapter.∙ The complex attachment at the end was replaced by a simpler part geometry.The complexity of the part was reduced to a cylindrical geometry, maintainingthe CG of the part. This was not capable within the modal analysis becausethe as the mode number increased there was a higher emphasis on the modevalue from the complex features of the attachment.The comparison of the mesh quality and mesh generation time between thetwo models can be seen in Table 4.4. As illustrated below the simplified model hasa 35% reduction of the number of elements; the max aspect ratio is reduced by 9.23,which means the mesh quality is better in the simplified model; and the time tomesh was reduced by about 69.2% or 49.8 sec. In terms of the mesh, the simplifiedmodel has a better quality mesh and was generated faster than the original model.Upon mesh generation the Von Mises stresses are calculated within the model andthe maximum stress is then compared between the two models, shown in Table 4.4,which has an error of 4.8% between the original and simplified boom models. Figs.4.19 and 4.20 show the stresses within the two models.96Tetra Maximum Meshing Time Max. VonElements Aspect Ratio (sec) Mises StressOriginal 15069 20.90 72 101.49Simplified 5141 11.67 22.2 96.59Table 4.4: Mesh improvementFigure 4.19: Von Mises Stress distribution on the unsimplified boom assemblyFigure 4.20: Von Mises Stress distribution on the unsimplified boom assembly974.5 SummaryThis chapter has presented a tool to be used for the simplification of an assem-bly model for FEA, utilizing the Pro/Toolkit available within ProE. The user mustmanually determine the criticality of the parts within the model, whether they aresuppressible or non-suppressible and whether the non-suppressible features are ca-pable of simplification, based upon the analysis type, material, and the part feature.Simplification of the part can either be accomplished by the method proposed in theprevious chapter or by replacing the complex part with a simpler geometrical part.After the criticality of the part is determined, the suppressible parts can be sup-pressed in groups, rather than one-by-one, based upon either their PART NAME orMATERIAL value. This also takes into account the parent-child relationships devel-oped within the model. To demonstrate the process, two different assembly modelswere simplified and analyzed. In comparison to manually simplifying the parts, thenumber of passes to suppress the non-critical parts was better than halved; whilestill increasing the mesh quality, reducing the mesh generation time, and acquiringanalysis results within a given error of 5%.98Chapter 5Conclusion5.1 Intellectual ContributionsThe contributions of this work can be separated into two primary categories:1. A framework for simplifying CAD part models was developed with the utili-ties provided within ProE. The approach contains several key aspects. First,numerous features can be suppressed at one time, compared to the industry’scurrent simplification process of suppressing one feature at a time. Second, arule basis has been learned through expert demonstration with only conserva-tive error, which can evolve as more parts are simplified. Third, the parent-child relationships were extracted from the model and used in the analysis todetermine the suppressibility state of the model, thus, ensuring that a childfeature was not unintentionally suppressed within the process. Finally, in or-der to reduce the potential effect of the simplification on the FEA results, theinter-feature distance to the boundary conditions were calculated to maintainany features within a close proximity of the boundary and force constraints.2. A framework for simplifying CAD assembly models was developed with theutilities provided within ProE. The approach contains several key aspects.First, numerous parts can be suppressed at one time, compared to the indus-99try’s current simplification process of suppressing one part at a time. Second,the parent-child relationships were extracted from the model and used whensuppressing the parts, ensuring that a child part was not unintentionally sup-pressed within the process. Finally, integration of the part simplification wasintroduced within the assembly model simplification to simplify parts withinthe overall assembly model.The work presented in this thesis provides a simplification tool for both partand assembly models, which is not the case for all model simplification tools.5.2 Anticipated BenefitsThe simplification frameworks can be extremely beneficial within the industryanalysis. The overall analysis time for a model will likely be reduced, since the modelpreparation time can be reduced. In the part simplification approach discussedin Chapter 2, the process greatly reduces the users involvement in the process.Automatic identification and labeling of the non-critical features and multi-featuresuppression of the identified non-critical features, upon the user’s verification, willshow a significant time reduction from the manual technique of the user analyzingeach feature and suppressing them one at a time. In addition to reducing the modelpreparation time, errors involved in the simplifation part models may be reduced;especially in the accidental suppression of critical child features, since the the parent-child relationships are incorporated into the suppression algorithm. Reducing theerrors within the analyses has two benefits. First it reduces the chance of passing100along erroneous results and the need to rerun an analysis because it was discoveredto have suppressed a critical part.In the assembly model simplification tool, numerous parts are capable of sup-pression compared to the industry version of suppressing part by part; reducing themodel preparation time. Also, the integration of the part simplification tool intothe assembly model simplification will reduce the time to simplify the parts withinthe overall model. Initially, these tools will not create a large impact in reducingthe analysis time, but as time goes on there will be a gradual decrease in the modelpreparation time; since it will take time to gain the engineers trust.5.3 Future WorkWhile this thesis has described successful frameworks for the simplification ofboth part and assembly CAD models for the use of downstream applications, suchas FEA, there are many areas in which future work can offer further insight. Themain areas of interest for future improvement are directly related to the work thathas been complete in this thesis.5.3.1 Improvement to the Part Simplification FrameworkThe part simplification framework presented in Chapter 2, but has several lim-itations. First, the framework is limited to suppressing only three types of featureswithin the model; holes, rounds, and chamfers. Within the field, simplification of apart is not only limited to these three features. Expansion of the framework to in-101clude other features, for instance, bosses, slots, and steps, would greatly improve therobustness of the overall simplification tool. Another aspect of the framework thatcould be improved is the calculation of the feature distance to the boundary con-ditions. In the current framework the inter-feature distance calculation only takesinto account the geometric distance. Within an analysis the topological distanceand stress path can also have an effect within the criticality of the feature, so theseshould be incorporated into or included with the geometric distance calcultaion.A third aspect for expansion is to incorporate the overall volumetric changebetween the original and simplified models. The overall volumetric change is sim-ilar to the parent-child relationship, in the fact that it may require features withparameters qualifying it to be a suppressible feature to be maintained within themodel. For instance, one hole having parameters, which constitute the feature to becionsidered non-critical, will not have an impact on the analysis results; although,taking this same hole and placing it numerous times throughout the model, gen-erating a large volumetric change between the simplified and non-simplified modelmay affect the analysis results (even though the parameters of the holes constitutedit to be classified as a non-critical feature).5.3.2 Advancements in Assembly Simplification ApproachThe assembly model simplification framework was more user intensive thanthat of the part simplification framework, allowing for more areas of work to befocused on in the future. First, the parent-child relationship would need to be102extended to allow for the inclusion of minor assembly models within the overallassembly model. If the parent part of an assembly model to be included is not usedas the references for placement into the model, then they are technically a child inthe major assembly, for which they are a parent to in the minor assembly model.Although this is the case, the possibility exists for minor assembly parts to becomeunreferenced in the overall model, if its child is used as the placement reference forthe minor assembly and the suppressed for simplification in the overall model.Another possible area for extension of the framework is to automatically de-termine the criticality; non-critical, semi-critical, or critical; since in the currentframework the user must manually determine the criticality of each part. Deter-mining the criticality of parts requires a knowledge of not only the part attributes,but also of the assembly attributes and analysis type. 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