An Introduction to X-Analysis Integration (XAI) Part 2: Multi-Representation Architecture (MRA) Primer Georgia Tech Engineering Information Systems Lab eislab.gatech.edu Contact: Russell S. Peak Revision: March 15, 2001 Copyright © 1993-2001 by Georgia Tech Research Corporation, Atlanta, Georgia 30332-0415 USA. All Rights Reserved. Developed by eislab.gatech.edu. Permission to use for non-commercial purposes is hereby granted provided this notice is included. An Introduction to X-Analysis Integration (XAI) Short Course Outline Part 1: Constrained Objects (COBs) Primer – Nomenclature Part 2: Multi-Representation Architecture (MRA) Primer – Analysis Integration Challenges – Overview of COB-based XAI – Ubiquitization Methodology Part 3: Example Applications » Airframe Structural Analysis » Circuit Board Thermomechanical Analysis » Chip Package Thermal Analysis – Summary Part 4: Advanced Topics & Current Research © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 2 Analysis Integration Objectives for Simulation-based Design Analysis Module Catalogs • Highly automated • Reusable, modular, extensible • Product-specific • Leveraging generic solvers Design Product Model Selected Analysis Module (CBAM) MCAD ECAD CAE Ansys Automated Idealization/ Defeaturization Conditions Environments, Mfg. CAD/CAM, Measurements, etc. Abaqus Iterative Improvements Analysis Results Improved Design / Process © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu CBAM= context-based analysis model 3 X-Analysis Integration (X=Design, Mfg., etc.) Goal: Improve product engineering processes by integrating analysis models with other life cycle models Challenges: – Heterogeneous Transformations – Diversity: Information, Behaviors, Disciplines, Fidelity, Feature Levels, CAD/CAE Tools, etc. – Multidirectional Associativity: DesignAnalysis, Analysis Analysis One Approach: The Multi-Representation Architecture (MRA) Initial Focus: Automation of ubiquitous analysis for design © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 4 Analysis Integration Challenges: Heterogeneous Transformations Homogeneous Transformation Design Model A Design Model B STEP AP210 Mentor Graphics Cadence Heterogeneous Transformation Design Model A STEP AP210 ?? Mentor Graphics © 1993-2001 GTRC Analysis Model A STEP AP209 Engineering Information Systems Lab eislab.gatech.edu Ansys 5 Analysis Integration Challenges: Information Diversity “Manufacturable” Description STEP AP210 Environmental Conditions “Analyzable” Description STEP AP220 lamination temperature = 200oC Specification Semantics “PWB should have low bow & twist” “Warpage < 7.5% when board is cooled from lamination to 25oC” B Idealizations © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 6 Diverse Analysis Disciplines Electromagnetic Thermomechanical Electrical R101 CR101 U101 C118 T102 C112 T101 CR152 CR151 CR154 R163 C203 De C106 C146 C147 N L101 Vibration R233 R232 R231 R230 Q104 U107 Q105 U108 U104 U109 U105 U110 U106 R112 R114 R115 R111 R113 R106 R108 R107 R109 R110 Fatigue U103 CR102 C102 CR133 J101 C153 C103 C111 Thermal U102 R102 C123 Q103 Q102 Q101 y x © 1993-2001 GTRC C120 C104 PWB 96510 PWA 95145 Engineering Information Systems Lab eislab.gatech.edu 7 Multi-fidelity Models Example: Supporting age in a people information model How old are you? In years: Model content depends on: a) questions to answer b) accuracy needed – fidelity 1: age = current year - year of birth ... – fidelity 2: also consider: is today before/after birthday? In days: – fidelity 3: do not consider leap years – fidelity 4: consider leap years In hours: – fidelity 5: consider time zone – fidelity 6: consider planetary orbit adjusments In seconds: – fidelity 6: is sufficiently accurate data available? © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 8 Geometric Idealization: Dimensional Reduction Beam Example: 1D, 2D, 3D 1D Line (Curve) Same Object ... Multiple/Different Forms of Geometry Capture 2D Surface (Shell) 3D Solid (Volume) Adapted from [Gordon, 2001] © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 9 Geometric Idealization: Dimensional Reduction Beam Example: 1D, 2D, 3D (Exploded View) 1D Line (Curve) 3D Solid (Volume) 2D Surface (Shell) Adapted from [Gordon, 2001] © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 10 Geometric Idealization: Dimensional Reduction Computer-Aided Mid-Surfacing (Solids-to-Shells) Design - Solids (3D) Mid-Surfaces (2D) Trimmed and Adjusted Mid-Surfaces Issue: Matching seams in multi-part assemblies (capturing problem-dependent idealization decisions) Adapted from [Gordon, 2001] Category II © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 11 Multi-Fidelity Idealizations Behavior-dependent Idealized Geometries; Same Dimension Thermal Resistance Idealized Geometry (3D) FEA Model Common Design Model Thermal Stress © 1993-2001 GTRC Idealized Geometry (3D) Engineering Information Systems Lab eislab.gatech.edu FEA Model 12 Multi-Fidelity Idealizations Same Behavior; Idealized Geometries of Varying Dimension Design Model (MCAD) Analysis Models (MCAE) Behavior = Deformation 1D Beam/Stick Model flap support assembly inboard beam 3D Continuum/Brick Model © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 13 Reusable Multi-Fidelity Geometric Idealizations: Bounding Shapes Analysis Models Solder Joint Deformation Multiple Uses Design Model 2-D bounding box PWA Cooling Multi-Fidelity Idealizations Solder Joint Deformation Multiple Uses 3-D bounding box © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu PWA Cooling 14 Dimensions of Idealization Fidelity Idealization Dimensions Examples (Multiple Fidelities) Analytical bodies* basic extensional rod (1D): xx f (x ) solid continuum (3D): xx f ( x, y , z ) Material models linear elastic bilinear plastic Geometric simplifications total thickness; effective length bounding box Boundary conditions uniform temperature, T; T f ( x, y, z , t ) T Tavg on top surface (heuristics) *An analytical body = a combination of particular assumptions regarding kinematics (field dimensions), types of loads, and material models. Also: results idealization – How to “summarize” detailed analysis results back to product level value » Ex. Getting max. (or avg.) temperature on a surface to compute thermal resistance – Effectively a “results BC” See [Gordon, 2001] regarding categories of analysis wrt geometric idealizations and directionality – © 1993-2001 GTRC S. Gordon (Jan. 16-18, 2001) An Analyst’s View: STEP-Enabled CAD-CAE Integration. Engineering Information Systems Lab eislab.gatech.edu 15 CAE-Centric Process CAD-Centric Process Categories of Geometric Idealization for CAD-CAE Integration Category I - The CAD Geometry and the Simulation-Specific Geometry are the same (identical). This is the truly “seamless” case; there is no change in detail, no de-featuring, and no geometry gender changing required. Analysts and designers use the same (or duplicate copies of the same) geometry. Category II - Existing (available) CAD geometry has the wrong content; it is too detailed and/or of the wrong type to support the scale, scope, and purpose of the required or most appropriate type of analysis. Changes are required to add features or remove unnecessary detail from, and/or modify the gender of, the CAD geometry to create Simulation-Specific Geometry amenable to analysis. Automated and semi-automated procedures are required. Category III - Engineering analyses are performed first to define and refine a design concept using idealized geometry prior to establishment of the enterprise (CAD) product model. Simulation-Specific Geometry employed for analysis models will require modification and the addition of details and features to support drawings and manufacturing. Automated and semiautomated procedures are desirable. Adapted from [Gordon, 2001] © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 16 Recent Articles Showing Enlightened Views “Three-Dimensional CAD Design and Analyzing with Shell Elements - A Soluble Contradiction?”, by M. W. Zehn, H. M. Baumgarten, & P. Wehner, NAFEMS 7th Int’l. Conf., Newport, RI, April 1999 “Don’t Change the Model Till the Simulation Finishes”, by Paul Kurowski, Machine Design, August 19, 1999 “Rookie Mistakes - Over Reliance on CAD Geometry”, by Vince Adams, NAFEMS Benchmark, October 1999 “Common Misconceptions About FEA”, by Vince Adams, ANSYS Solutions, Fall 2000 “Eight Tips for Improving Integration Between CAD and CFD”, by Scott Gilmore, Desktop Engineering, May 2000 Adapted from [Gordon, 2001] © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 17 Vendor Status for CAD-CAE Integration Geometric Idealization COTS Vendor Report Card Category I A Mature, MCAD for solids good Category II B-,C+ Improving, recent mid-surfacing attention Category III D,F Very little for CAE-centric ‘leading design’, need shell ‘thickening’ tools, or ‘solids-on-demand’ Overall: Still too CAD-Centric Continued role for traditional FEA pre- and post-processors AP209 is ready to support / enable more CAD-CAE integration AP209 is more appropriate for CAE than AP203 Need more vendor support for AP209 Adapted from [Gordon, 2001] © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 18 Analysis at Diverse Levels of Product Structure Design Model (MCAD) Analysis Models (MCAE) Part Feature Level Model Assembly Level Model © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 19 Design Geometry - Analysis Geometry Mismatch Detailed Design Model G1 : b = cavity3.inner_width + rib8.thickness/2 + rib9.thickness/2 ... Analysis Model (with Idealized Features) G K3 f (r1,b, h) fse Idealizations P 2pr0te fbe C1 P 2 hte Channel Fitting Analysis “It is no secret that CAD models are driving more of today’s product development processes ... With the growing number of design tools on the market, however, the interoperability gap with downstream applications, such as finite element analysis, is a very real problem. As a result, CAD models are being recreated at unprecedented levels.” Ansys/ITI press Release, July 6 1999 http://www.ansys.com/webdocs/VisitAnsys/CorpInfo/PR/pr-060799.html © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 20 Missing Today: Explicit Design-Analysis Associativity CAD Model bulkhead assembly attach point detailed design geometry CAE Model channel fitting analysis material properties idealized analysis geometry analysis results © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 21 Multi-directional Relations “The Big Switch” Sizing/synthesis during early design stages – Input: Desired results - Ex. fatigue life, margin of safety – Output: Idealized design parameters – Outputs then used as targets to guide detailed design width=20 d1=6.66 G=30.00 Ac=3.33 I A thick=0.25 P=100 Analysis/req. checking during later design stages – – – – Input: Detailed design parameters Intermediate results: Idealized design parameters Output: Analysis results - Ex. fatigue life, margin of safety Outputs then compared with requirements width=20 thick=0.25 I d1=7.5 © 1993-2001 GTRC G=32.00 Ac=3.125 A P=100 Engineering Information Systems Lab eislab.gatech.edu 22 Inter-Analysis Associativity Flap Assembly FEA Model Flap Support Assembly FEA Model boundary conditions © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu Inboard Beam Bulkhead Channel Fitting Static Strength Model boundary conditions 23 An Introduction to X-Analysis Integration (XAI) Short Course Outline Part 1: Constrained Objects (COBs) Primer – Nomenclature Part 2: Multi-Representation Architecture (MRA) Primer – Analysis Integration Challenges – Overview of COB-based XAI – Ubiquitization Methodology Part 3: Example Applications » Airframe Structural Analysis » Circuit Board Thermomechanical Analysis » Chip Package Thermal Analysis – Summary Part 4: Advanced Topics & Current Research © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 24 X-Analysis Integration Techniques a. Multi-Representation Architecture (MRA) 3 Analyzable Product Model Design Model 4 Context-Based Analysis Model 2 Analysis Building Block 1 Solution Method Model CBAM ABB Solder Joint material body 1 body4 Solder Joint Solder Joint Plane Strain Model 4 CBAM C L h1 base: Alumina Epoxy ABBSMM PWB body3 APM ABB core: FR4 Plane Strain Bodies System 2 ABB G total height, h c Component Solder Joint T0 Component G linear-elastic model G primary structural SMM APM ABB Analysis Model PWA Component Occurrence 3 APM APM Printed Wiring Assembly (PWA) Component b. Explicit Design-Analysis Associativity body 1 body 4 body body 2 body 2 PWB Printed Wiring Board (PWB) Design Tools 4 CBAM Analysis Module Catalogs Analysis Procedures 3 APM Dsj solder joint shear strain range Lc total height hc primary structural material T0 linear-elastic model length 2 + total thickness Product Model 1.25 [1.1] Physical Behavior Research, Know-How, Design Handbooks, ... Commercial Design Tools pwb (Module Usage) Selected Module Solder Joint Deformation Model Commercial Analysis Tools primary structural material solder hs linear-elastic model rectangle solder joint ECAD Idealization/ Defeaturization Component Solder Joint [1.1] detailed shape [1.2] linear-elastic model [2.1] © 1993-2001 GTRC Ts average bilinear-elastoplastic model Ansys CAE a L1 h1 stress-strain model 1 T1 L2 h2 stress-strain model 2 T2 geometry model 3 stress-strain model 3 T3 xy, extreme, 3 T sj xy, extreme, sj Constrained Object-based Analysis Module PWB APM CBAM ABB SMM Tc Ls [1.2] [2.2] MCAD Plane Strain Bodies System (Module Creation) component 1 SMM deformation model Fine-Grained Associativity approximate maximum inter-solder joint distance component occurrence c ABB SMM 2 ABB Ubiquitization Ubiquitous Analysis 3 plane strain bodyi , i = 1...4 geometryi materiali (E, , ) Informal Associativity Diagram Solution Tools c. Analysis Module Creation Methodology To Constraint Schematic View Abaqus Engineering Information Systems Lab eislab.gatech.edu 25 Components of the MRA Analysis Integration Technique Conceptual architecture: MRA Methodology General purpose MRA toolkit: XaiTools – Toolkit architecture – Users guide – Tutorials (work-in-process) Product/company-specific applications – PWA/Bs (ProAM) – Aerospace structural analysis (Boeing PSI) – Chip packaging/mounting (Shinko) See http://eislab.gatech.edu/ for references © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 26 Multi-Representation Architecture for Design-Analysis Integration 3 Analyzable Product Model 4 Context-Based Analysis Model APM 2 Analysis Building Block Printed Wiring Assembly (PWA) 1 Solution Method Model CBAM ABB SMM APM ABB Component Solder Joint Component Solder Joint PWB T0 body 1 body4 ABBSMM body3 body 2 Printed Wiring Board (PWB) Design Tools Solution Tools Composed of four representations (information models) Provides flexible, modular mapping between design & analysis models Creates automated, product-specific analysis modules (CBAMs) Represents design-analysis associativity explicitly © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 27 Ubiquitous Analysis: Opportunity for Automation The regular widespread use of an established analysis models. Typical PWA Design Process Conceptual Design Develop PWA Layout 1 Potential Ubiquitous Analyses Performance EMI - Trace Spacing Variation Check Layout Acceptable Layout 2 Reliability Solder Joint Deformation - Thermomechanical [Engelmaier, 1989; Lau, et al., 1986; Kitano, et al. 1995] Solder Joint Fatigue - Component Misalignment Plated Through-Hole Fatigue [Sizemore & Sitaraman,1995] Unacceptable Layout Modify Layout 3 Manufacturability Reflow Soldering - PWA/B Warpage [Stiteler & Ume, 1996] Bed-of-Nails Test - PWA Deflection [Iannuzzelli, 1990] Solder Wave - Component Shadowing © 1993-2001 GTRC Modified Layout Engineering Information Systems Lab eislab.gatech.edu 28 Design-Analysis Integration Methodology Analysis Module Catalogs Analysis Procedures Ubiquitization (Module Creation) Physical Behavior Research, Know-How, Design Handbooks, ... Ubiquitous Analysis Commercial Design Tools Product Model (Module Usage) Selected Module Solder Joint Deformation Model MCAD ECAD Idealization/ Defeaturization © 1993-2001 GTRC Ansys Component Solder Joint CAE PWB APM CBAM ABB SMM Commercial Analysis Tools Abaqus Provides technique to bridge CAD-CAE gap Uses AI & info. technology: objects, constraint graphs, STEP, etc. Engineering Information Systems Lab eislab.gatech.edu 29 XaiTools FrameWork TM G e t D T ee e ee et X-Analysis Integration Toolkit E G E 2(1 ) Multi-Representation Architecture (MRA) Reference Implementation 3 Analyzable Product Model Template Libraries: Analysis Packages*, CBAMs, ABBs, APMs, Conditions* Instances: Usage/adaptation of templates MCAD: CATIA I-DEAS*, Pro/E*, UG *, AutoCAD*, ... ECAD: Mentor Graphics (STEP AP210) PWB Layup ADT, ChipPackage ADT Accel (PDIF, GenCAM)*, ... 4 Context-Based Analysis Model APM COB Schemas 2 Analysis Building Block Printed Wiring Assembly (PWA) CBAM ABB T0 Component body 1 body4 Solder Joint COB Mgt. Tools Navigators Editors (text & graphical*) COB/Object Manager Idealization Tools* ABBSMM SA, MCAD, ... body3 body 2 PWB * CAD Tools SMM APM ABB Solder Joint Simulation Mgt. Tools Pullable Views*, Condition Mgr*, ... Object Repositories ODBMS*, PDM* objects, x.xml* x.cos, x.exp 1 Solution Method Model Component CAD/E Integration Framework Design Tools COB Instances shear stress, shear strain, r5 shear modulus, G youngs modulus, E poissons ratio, Synthesis Tools* Printed Wiring Board (PWB) r1 cte, temperature change,DT objects, x.xml* x.coi, x.step r4 thermal strain, et elastic strain, ee r3 stress, strain, e r2 ICAD, ... Design Tools Solution Tools Libraries Material Properties Mgr. * Tool Forms (parameterized tool models/full* SMMs) MATDB*,Mvision*, ... Analysis Modules & Building Blocks Constraint Schematics shear stress, poissons ratio, r1 cte, e t DT r4 deformation model temperature change, DT thermal strain, et Thermal Bending System pwb total diagonal al1 total thickness al2 elastic strain, ee strain, e r3 ee stress,L e ee et E b DT T 3 APM warpage Dsj solder joint shear strain range 2 1 Treference r2 t coefficient of thermal bending al3 deformation model Plane Strain Bodies System T0 Lc hc total height primary structural material linear-elastic model 1.25 [1.1] length 2 + total thickness pwb primary structural material solder Tc Ls [1.2] hs linear-elastic model rectangle solder joint Mathematica FEA: Ansys, Elfini*, Abaqus*, ... Math: Mathematica, MathCAD*, Matlab*, ... Optimizers: ConMin, iSIGHT*, ModelCenter*, ... In-House Codes asterisk (*) = In-progress/envisioned extensions Airframe structural analysis PWA-B thermomechanical analysis & design XaiTools PWA-B mv1 component Solver 2 ABB approximate maximum inter-solder joint distance component occurrence c (product-specific) Constraint Product-Specific Applications shear modulus, G E G 2(1 ) Analysis Module Tools Implementations G youngs modulus, E * FASTDB*, ... shear strain, r5 Std. Parts Manager Solution Tools API / Wrapper CORBA, SOAP*, Jini* [1.1] detailed shape [1.2] linear-elastic model [2.1] Ts average bilinear-elastoplastic model [2.2] T sj a ™ L1 h1 stress-strain model 1 T1 L2 h2 stress-strain model 2 T2 geometry model 3 stress-strain model 3 T3 xy, extreme, 3 xy, extreme, sj Electronic package thermal & stress analysis XaiTools ChipPackage ™ Leveraging commercial CAD & CAE tools © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 30 COB-Enhanced XAI Interoperability Framework Company/Product-Independent View XaiTools with Envisioned Extensions Design Tools Template Libraries: Analysis Packages*, CBAMs, ABBs, APMs, Conditions* Instances: Usage/adaptation of templates MCAD: CATIA I-DEAS*, Pro/E*, UG *, AutoCAD*, ... ECAD: Mentor Graphics (STEP AP210) PWB Layup ADT, ChipPackage ADT Accel (PDIF, GenCAM)*, ... COB Schemas objects, x.xml* x.cos, x.exp CAD Tools * Object Repositories DBMS*, PDM*: Enovia, Metaphase ... COB Mgt. Tools Navigators Editors (text & graphical*) COB/Object Manager Idealization Tools* SA, MCAD, ... Simulation Mgt. Tools Pullable Views*, Condition Mgr*, ... COB Instances shear stress, shear strain, r5 G shear modulus, G youngs modulus, E Synthesis Tools* temperature change,DT objects, x.xml* x.coi, x.step Tool Forms (parameterized tool models/full* SMMs) © 1993-2001 GTRC * e t DT r4 thermal strain, et elastic strain, ee J2EE App. Server Accelis … + XaiTools * MATDB*,Mvision*, ... FASTDB*, ... r1 strain, e r3 Libraries Std. Parts Manager E 2(1 ) cte, ICAD, ... Material Properties Mgr. G poissons ratio, Solution Tools API / Wrapper CORBA, SOAP*, Jini* ee E e ee et r2 Analysis Module Tools (product-specific) Constraint Solver Mathematica FEA: Ansys, Elfini*, Abaqus*, ... Math: Mathematica, MathCAD*, Matlab*, ... Optimizers: ConMin, iSIGHT*, ModelCenter*, ... In-House Codes Engineering Information Systems Lab eislab.gatech.edu stress, asterisk (*) = In-progress/envisioned extensions 31 Using Internet/Intranet-based Analysis Solvers Thick Client Architecture Users Engineering Service Bureau Client PCs Host Machines Internet/Intranet © 1993-2001 GTRC EIS Lab CORBA Daemon Iona orbixdj - Regular internal use U-Engineer.com CORBA Servers XaiToolsAnsys Ansys XaiTools XaiTools Math. XaiTools SolverAnsys Server Solver Server Solver Server Solver Server FEA Solvers Ansys Math Solvers - Demo usage: - US - Japan Nov.’00-Present: Electronics Co. - Began production usage (dept. Intranet) Future: ... XaiTools CORBA IIOP Internet Thick Client June’99-Present: Mathematica Engineering Information Systems Lab eislab.gatech.edu Company Intranet and/or U-Engineer.com (commercial) - Other solvers 32 XaiTools CORBA Servers Installation at GIT EIS Lab as of March, 2000 Host Machines golden.marc.gatech.edu Sun UltraSPARC 1 Client PCs XaiTools Regular Users CORBA IIOP Internet Thick Client • EIS Lab • Phoenix AZ • Huntsville AL • Japan • etc. © 1993-2001 GTRC Internet/Intranet Pilot Users hoogly.marc.gatech.edu Sun UltraSPARC 10 CORBA Daemon Iona orbixdj CORBA Daemon Iona orbixdj CORBA Servers CORBA Servers XaiTools Math. Solver Server XaiTools Ansys XaiTools Ansys Solver Server Solver Server FEA Solvers Ansys Math Solvers Math Solvers Mathematica Mathematica Engineering Information Systems Lab eislab.gatech.edu 33 Lo “XAI Panorama” Flexible High Diversity Design-Analysis Integration Tutorial Examples: Flap Link (Mechanical/Structural Analysis) Design Tools y mv6 E reference temperature, To smv1 r4 force, F e DL L MCAD Tools CATIA, I-DEAS* Pro/E* , UG *, ... DL mv4 F E, A, DT, e, x One D Linear Elastic Model (no shear) mv5 sr1 temperature, T Template Libraries (ABBs, CBAMs, …) L Lo F material model youngs modulus, E cte, ee DT et e mv2 elastic strain, ee mv3 thermal strain, et mv1 strain,e stress, area, A temperature change,DT deformation model Torsional Rod linkage effective length, Leff start, x1 r1 mode: shaft torsion polar moment of inertia, J outer radius, ro material linear elastic model reaction allowable stress twist mos model Margin of Safety (> case) allowable Lo total elongation,DL cross section: effective ring end, x2 condition al1 r3 r2 undeformed length, Lo al2a length, al2bL shear modulus, G 1 2 J r G al3 T stress mos model allowable twist Margin of Safety (> case) allowable actual actual MS MS Analysis Modules of Diverse Behavior & Fidelity (CBAMs) Flap Link XaiTools Extensional Model y Extension Analyzable Product Model (APM) 1D L Leff P DL P e, E, A Analysis Tools (via SMMs) x Flap Link Plane Strain Model XaiTools 2D, 3D* General Math Mathematica Matlab* MathCAD* ... L B ts2 ts1 s sleeve1 sleeve2 shaft rib1 rib2 ds1 Materials Libraries In-House, ... Parts Libraries In-House*, ... ds2 B 1D Leff y Lo Torsion T G, r, , ,J Flap Link Torsional Model * = Item not yet available in toolkit (all others have working examples) © 1993-2001 GTRC T Engineering Information Systems Lab eislab.gatech.edu x FEA Ansys Abaqus* CATIA Elfini* MSC Nastran* MSC Patran* ... 34 Multi-Representation Architecture for Design-Analysis Integration 3 Analyzable Product Model 4 Context-Based Analysis Model APM 2 Analysis Building Block Printed Wiring Assembly (PWA) 1 Solution Method Model CBAM ABB SMM APM ABB Component Solder Joint Component Solder Joint PWB T0 body 1 body4 ABBSMM body3 body 2 Printed Wiring Board (PWB) Design Tools © 1993-2001 GTRC Solution Tools Engineering Information Systems Lab eislab.gatech.edu 35 Analysis Building Blocks (ABBs) Object representation of product-independent analytical engineering concepts Analysis Primitives Analysis Systems - Primitive building blocks Material Models e LinearElastic Continua De e Bilinear Plastic N Low Cycle Fatigue Discrete Elements q(x) Distributed Load Plate Interconnections body 2 body 1 Rigid Support x Beam Cantilever Beam System No-Slip Analysis Variables q(x) Temperature,T General - User-defined systems Stress, Damper Distributed Load © 1993-2001 GTRC - Predefined templates y Plane Strain Body Rigid Support Spring Specialized Beam Geometry Mass - Containers of ABB "assemblies" Strain, e Engineering Information Systems Lab eislab.gatech.edu 36 COB-based Libraries of Analysis Building Blocks (ABBs) Continuum ABBs Extensional Rod Material Model ABB reference temperature, To force, F 1D Linear Elastic Model shear stress, poissons ratio, r1 cte, temperature change,DT e t DT r4 thermal strain, et elastic strain, ee r3 stress, ee start, x1 shear modulus, G E G 2(1 ) E r4 F A modular re-usage end, x2 r1 ee DT et e Trr J undeformed length, Lo theta end, 2 total elongation,DL length, L y Lo T T G, r, , ,J x G radius, r theta start, 1 DT, e, x r3 DL e L DL L Lo E torque, Tr © 1993-2001 GTRC One D Linear Elastic Model r2 polar moment of inertia, J F E, A, material model Torsional Rod DL F L x2 x1 strain, e e ee et L Lo E r2 undeformed length, Lo G youngs modulus, E e area, A DT T To One D Linear Elastic Model (no shear) shear strain, r5 edb.r1 temperature, T y material model ee DT et e r1 2 1 Engineering Information Systems Lab eislab.gatech.edu r3 r L0 twist, 37 Extensional Rod Constraint Graph Mat_sc.r1 mat.r5 0 G 1D Linear Elastic Model (COB re-usage) y G F F E, A, e e e ee et E mat.r2 et L r4 r2 A L x2 x1 r1 Lo T © 1993-2001 GTRC DL L Lo DT T To edb.r1 F r3 e t DT DT F A DL L DT, e, x DL mat.r4 DL Lo E 2(1 ) mat.r3 L G ee ee e mat.r1 E x1 x2 To Engineering Information Systems Lab eislab.gatech.edu 38 Multi-Representation Architecture for Design-Analysis Integration 3 Analyzable Product Model 4 Context-Based Analysis Model APM 2 Analysis Building Block Printed Wiring Assembly (PWA) 1 Solution Method Model CBAM ABB SMM APM ABB Component Solder Joint Component Solder Joint PWB T0 body 1 body4 ABBSMM body3 body 2 Printed Wiring Board (PWB) Design Tools © 1993-2001 GTRC Solution Tools Engineering Information Systems Lab eislab.gatech.edu 39 Analyzable Product Models (APMs) Provide advanced access to design data needed by diverse analyses. Design Applications Solid Modeler Combine information Add reusable multifidelity idealizations Analysis Applications FEA-Based Analysis ... Materials Database Fasteners Database © 1993-2001 GTRC Analyzable Product Model (APM) Support multidirectionality Engineering Information Systems Lab eislab.gatech.edu FormulaBased Analysis 40 Flap Link Geometric Model (with idealizations) L B ts2 ts1 s sleeve1 sleeve2 shaft rib1 rib2 ds1 ds2 B red = idealized parameter Leff A, I, J f f tft tft htotal tfb tf tw wf hw rf Section B-B (at critical_cross_section) Detailed Design © 1993-2001 GTRC A, I, J A, I, J htotal tfb hw tw htotal tf wf tw hw wf tapered I Multifidelity Idealizations Engineering Information Systems Lab eislab.gatech.edu basic I 28b 41 Flap Linkage Example Manufacturable Product Model (MPM) = Design Description flap_link Extended Constraint Graph L w sleeve_1 A ts ts1 2 t Sleeve 1 r Sleeve 2 Shaft ds1 x A ds2 w sleeve_2 R1 t r x Product Attribute shaft Ri cross_section Product Relation tw t1f t2f rib_1 b h t rib_2 R2 b h t material © 1993-2001 GTRC R3 COB Structure (COS) wf COB flap_link SUBTYPE_OF part; part_number : STRING; inter_axis_length, L : REAL; sleeve1 : sleeve; sleeve2 : sleeve; shaft : tapered_beam; rib1 : rib; rib2 : rib; RELATIONS PRODUCT_RELATIONS pr2 : "<inter_axis_length> == <sleeve2.origin.y> <sleeve1.origin.y>"; pr3 : "<rib1.height> == (<sleeve1.width> <shaft.cross_section.design.web_thickness>)/2"; pr4 : "<rib2.height> == (<sleeve2.width> <shaft.cross_section.design.web_thickness>)/2"; ... END_COB; name Engineering Information Systems Lab eislab.gatech.edu 42 Flap Linkage Example Analyzable Product Model (APM) = MPM Subset + Idealizations flap_link Extended Constraint Graph effective_length L A ts ts1 w sleeve_1 t 2 s Sleeve 1 Sleeve 2 Shaft ds1 r ds2 A x Leff w sleeve_2 R1 t R1 r R2 x Product Attribute shaft Ri cross_section Product Relation wf R3 tw R4 t1f Idealized Attribute Ri effective_length, Leff == inter_axis_length (sleeve1.hole.cross_section.radius + sleeve2.hole.cross_section.radius) Partial COB Structure (COS) R6 R5 t2f critical_section critical_detailed Idealization Relation wf tw rib_1 R11 hw b R7 t1f h t rib_2 t2f R2 b critical_simple wf h t material tw R3 name stress_strain_model © 1993-2001 GTRC R8 area linear_elastic E hw tf cte area Engineering Information Systems Lab eislab.gatech.edu R9 R10 R12 43 Concurrent Multi-Fidelity Cross-Section Representations A, I, J f tft tft htotal tfb tf A, I, J A, I, J f hw tw rf wf Section B-B (at critical_cross_section) Detailed Design htotal tfb hw tw htotal tf wf tw hw wf tapered I basic I Multifidelity Idealizations MULTI_LEVEL_COB cross_section; design : filleted_tapered_I_section; Detailed Design Cross-Section tapered : tapered_I_section; Idealized Cross-Sections basic : basic_I_section; Associativity Relations between RELATIONS Cross-Section Fidelities PRODUCT_IDEALIZATION_RELATIONS pir8 : "<basic.total_height> == <design.total_height>"; pir9 : "<basic.flange_width> == <design.flange_width>"; pir10 : "<basic.flange_thickness> == <design.flange_base_thickness>"; pir11 : "<basic.web_thickness> == <design.web_thickness>"; pir12 : "<tapered.total_height> == <design.total_height>"; pir13 : "<tapered.flange_width> == <design.flange_width>"; pir14 : "<tapered.flange_base_thickness> == <design.flange_base_thickness>"; pir15 : "<tapered.flange_taper_thickness> == <design.flange_taper_thickness>"; pir16 : "<tapered.flange_taper_angle> == <design.flange_taper_angle>"; pir17 : "<tapered.web_thickness> == <design.web_thickness>"; END_MULTI_LEVEL_COB; © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 44 APM Interface with Tagged CAD Models (in CATIA v4) 1) APM COB Tool 7) Solve idealizations 8) Use in analysis 5) 2) request part_number : “9162”; hole1.radius : ?; hole2.radius : ?; length1 : ?; COB instance format 3) 4) GIT tk/tcl Interface CATGEO program wrapper CATIA v4 (CAD tool) 6) response part_number : “9162”; hole1.radius : 2.5; hole2.radius : 4.0; length1 : 20.0; © 1993-2001 GTRC 3 and 4 similar to other CAD APIs Engineering Information Systems Lab eislab.gatech.edu 0) Designer - Creates design geometry - Defines APM-compatible parameters/tags 45 Flap Link Tagging Dimension Entity Approach - CATIA v4 sleeve2.inner_diameter sleeve2.width inter_axis_length © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 46 Flap Link Tagging Parametric Entity Approach - CATIA v4 sleeve2.inner_diameter sleeve2.width inter_axis_length © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 47 Design Model - Idealized Model Assoc. inside CATIA v5 (work in process) Design Idealizations (PI^0.5)0.5*D D= A 2D h= B h/2 © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 48 Target Situation: CAD Model w/ associated idealized features Design Model (in CATIA v5) Idealized Features (to scale in CATIA v5) Idealized bulkhead attach point fitting Idealized rear spar attach point fitting Idealized diagonal brace lug joint b c R axial direction D = f( c , b , R ) W = f( R , D , ) e © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 49 Multi-Representation Architecture for Design-Analysis Integration 3 Analyzable Product Model 4 Context-Based Analysis Model APM 2 Analysis Building Block Printed Wiring Assembly (PWA) 1 Solution Method Model CBAM ABB SMM APM ABB Component Solder Joint Component Solder Joint PWB T0 body 1 body4 ABBSMM body3 body 2 Printed Wiring Board (PWB) Design Tools © 1993-2001 GTRC Solution Tools Engineering Information Systems Lab eislab.gatech.edu 50 COB-based Constraint Schematic for Multi-Fidelity CAD-CAE Interoperability Design Tools Analysis Building Blocks (ABBs) MCAD Tools CATIA, I-DEAS* Pro/E* , UG *, ... Analysis Modules of Diverse Behavior & Fidelity (CBAMs) Continuum ABBs: y Extensional Rod Material Model ABB: shear stress, cte, e t DT E 2(1 ) ee DT et e r4 area, A DT, e, x Extension r3 r2 undeformed length, Lo G F E, A, shear strain, r5 DL Lo F E force, F G youngs modulus, E poissons ratio, One D Linear Elastic Model (no shear) reference temperature, To 1D Linear Elastic Model L material model edb.r1 temperature, T total elongation,DL r1 start, x1 shear modulus, G linkage y temperature change,DT e r4 thermal strain, et ee stress, E Torsional Rod T One D Linear Elastic Model strain, e r3 effective length, Leff mode: shaft tension Lo material model elastic strain, ee Flap Link Extensional Model Extensional Rod (isothermal) al1 length, L end, x2 r1 r2 E material T G, r, , ,J x area, A cross section L A youngs modulus, E al3 reaction condition DL x2 al2 linear elastic model Lo x1 E F e G stress mos model torque, Tr polar moment of inertia, J ee radius, r DT et e Analysis Tools (via SMMs) Margin of Safety (> case) 1D allowable stress allowable General Math Mathematica Matlab* MathCAD* ... actual MS r3 undeformed length, Lo r1 theta start, 1 theta end, 2 twist, inter_axis_length linkage Flap Link Plane Strain Model deformation model Parameterized FEA Model sleeve_1 w r L ws1 sleeve_2 w ts1 t Legend Tool Associativity Object Re-use t 2D mode: tension r rs2 ws2 ux,max ts2 x,max rs2 shaft cross_section:basic wf wf tw tw tf tf material E name E linear_elastic_model F condition reaction flap_link allowable stress effective_length allowable inter axis length change L w sleeve_1 B ts2 ts1 t r s w sleeve_2 sleeve1 sleeve2 shaft rib1 stress mos model Margin of Safety (> case) allowable allowable actual actual MS MS R1 t rib2 R1 r ds1 R2 x ds2 B ux mos model Margin of Safety (> case) x shaft cross_section R3 wf R4 tw Leff t1f R6 R5 deformation model t2f Torsional Rod critical_section critical_detailed wf linkage effective length, Leff al1 Lo tw Materials Libraries In-House, ... Parts Libraries In-House*, ... rib_1 R7 t1f h t rib_2 t2f R2 critical_simple wf h t material R8 tw R3 E name stress_strain_model linear_elastic hw tf cte area R9 R10 cross section: effective ring material condition polar moment of inertia, J al2a outer radius, ro al2b linear elastic model reaction allowable stress R12 Analyzable Product Model (APM) * = Item not yet available in toolkit (all others have working examples) © 1993-2001 GTRC mode: shaft torsion Torsion area b 1 R11 hw b twist mos model Margin of Safety (> case) 1D allowable al3 J r G T stress mos model allowable twist Margin of Safety (> case) allowable actual actual MS MS Engineering Information Systems Lab eislab.gatech.edu shear modulus, G 2 FEA Ansys Abaqus* CATIA Elfini* MSC Nastran* MSC Patran* ... Flap Link Torsional Model 51 Tutorial Example: Flap Link Analysis Template (CBAM) (1a) Analysis Template: Flap Link Extensional Model CBAM Flap Link Analysis Documentation (2) Torsion Analysis (1) Extension Analysis a. 1D Extensional Rod 1. Behavior: Shaft Tension L A ts2 ts1 s Sleeve 1 Shaft ds1 2. Conditions: 10000 lbs linkage 3. Part Features: (idealized) in effective length, Leff APM 1020 HR Steel Geometry mode: shaft tension cross section material A = 1.125 in2 E= 30e6 allowable 18000 4. Analysis Calculations: F DL Leff A E 5. Conclusion: MS E, A allowable 1 1.025 b. 2D Plane Stress FEA ... psi psi condition area, A al1 P e, x Extensional Rod (isothermal) DL Lo x1 al2 youngs modulus, E al3 reaction DL deformation model Material Models linear elastic model L Leff P Leff Flaps down : F = 5.0 y (idealization usage) ds2 A Leff = Sleeve 2 CAD-CAE Associativity ABB L x2 A E F e SMM stress mos model Margin of Safety (> case) allowable ABB allowable stress actual MS Boundary Condition Objects Pullable Views* (links to other analyses)* Solution Tool Interaction * Boundary condition objects & pullable views are WIP concepts* © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 52 Test Case Flap Linkage: Analysis Template Reuse of APM Linkage Extensional Model (CBAM) L A ts1 L ts2 s Sleeve 1 Sleeve 2 Shaft ds1 F ds2 A DL Lo F E, A, Leff DT, e, x deformation model linkage mode: shaft tension Flap link (APM) flap_link material condition effective_length al1 area, A al2 linear elastic model reaction youngs modulus, E al3 Extensional Rod (isothermal) Lo x1 x2 A E F DL L e w sleeve_1 stress mos model t r Margin of Safety (> case) x w sleeve_2 allowable actual MS R1 t R1 r allowable stress R2 x shaft cross section effective length, Leff cross_section wf R3 tw R4 t1f R6 R5 t2f critical_section critical_detailed wf tw rib_1 R11 hw b R7 t1f h t rib_2 t2f R2 b critical_simple t wf tw R3 E name stress_strain_model © 1993-2001 GTRC R8 area h material reusable idealizations linear_elastic hw tf cte area R9 R10 R12 Engineering Information Systems Lab eislab.gatech.edu 53 Test Case Flap Linkage: Analysis Template Reuse of ABBs Linkage Extensional Model (CBAM) L A ts1 L ts2 s Sleeve 1 Sleeve 2 Shaft ds1 F ds2 A DL Lo F E, A, Leff DT, e, x deformation model linkage mode: shaft tension cross section material condition effective length, Leff al1 area, A al2 linear elastic model reaction youngs modulus, E al3 Extensional Rod (isothermal) Lo x1 x2 A E F DL L e stress mos model Margin of Safety (> case) Extensional Rod (generic ABB) y L DL Lo F material model E youngsmodulus, mv6 cte, mv5 T temperature, sr1 area,A r4 F A E start,x1 r1 end,x2 L x2 x1 © 1993-2001 GTRC smv1 ee DT mv4 et e F E, A, DT, e, x mv2 ee elastic strain, mv3 et thermal strain, e strain, mv1 stress, modular reusage DT temperature change, r2 undeformed length,Lo allowable stress One D Linear Elastic Model (no shear) To DT T To reference temperature, force,F allowable actual MS DL L Lo e DL L r3 DL total elongation, length,L Engineering Information Systems Lab eislab.gatech.edu 54 Flap Linkage Extensional Model: Lexical COB Structure COB link_extensional_model SUBTYPE_OF link_analysis_model; DESCRIPTION Represents 1D formula-based extensional model.; y L L ANALYSIS_CONTEXT P E, A e, PART_FEATURE deformation model link : flap_link Extensional Rod (isothermal) linkage al1 effective length, L BOUNDARY_CONDITION_OBJECTS L DL associated_condition : condition; x L x MODE mode: shaft tension area, A cross section al2 A material linear elastic model youngs modulus, E al3 tension; E reaction condition F e OBJECTIVES stress mos model stress_mos_model : margin_of_safety_model; Margin of Safety ANALYSIS_SUBSYSTEMS (> case) allowable stress allowable deformation_model : extensional_rod_isothermal; actual RELATIONS MS PART_FEATURE_ASSOCIATIVITIES al1 : "<deformation_model.undeformed_length> == <link.effective_length>"; al2 : "<deformation_model.area> == <link.shaft.critical_cross_section.basic.area>"; al3 : "<deformation_model.material_model.youngs_modulus> == <link.material.stress_strain_model.linear_elastic.youngs_modulus>"; al4 : "<deformation_model.material_model.name> == <link.material.name>"; BOUNDARY_CONDITION_ASSOCIATIVITIES al5 : "<deformation_model.force> == <associated_condition.reaction>"; OBJECTIVE_ASSOCIATIVITIES al6 : "<stress_mos_model.allowable> == <link.material.yield_stress>"; al7 : "<stress_mos_model.determined> == <deformation_model.material_model.stress>"; END_COB; L A ts2 ts1 eff s Sleeve 1 DL P Sleeve 2 Shaft x ds1 ds2 A Leff eff o 1 2 © 1993-2001 GTRC Desired categorization of attributes is shown above (as manually inserted) to support pullable views. Categorization capabilities is a planned XaiTools extension. Engineering Information Systems Lab eislab.gatech.edu 55 Flap Linkage Instance with Multi-Directional I/O States deformation model linkage Flap Link #3 Leff effective length, 5.0 in mode: shaft tension critical_cross _section shaft material condition reaction basic 2 1.125 in area, A al2 linear elastic model youngs modulus,E al3 steel 30e6 psi 10000 lbs Extensional Rod (isothermal) al1 Lo DL x1 L Design Verification 1.43e-3 in - Input: design details - Output: i) idealized design parameters ii) physical response criteria x2 A 8888 psi E F e description flaps mid position stress mos model Margin of Safety 18000 psi (> case) allowable stress allowable actual MS example 1, state 1 1.025 deformation model Design Synthesis - Input: desired physical response criteria - Output: i) idealized design parameters (e.g., for sizing), or ii) detailed design parameters © 1993-2001 GTRC 5.0 in effective length, Leff linkage Flap Link #3 al1 0.555 in2 mode: shaft tension condition 1.125 in2 shaft critical_cross _section material linear elastic model reaction 10000 lbs steel basic area, A al2 X youngs modulus, E al3 30e6 psi Extensional Rod (isothermal) Lo DL x1 L 3.00e-3 in x2 A E F e 18000 psi description flaps mid position stress mos model Margin of Safety (> case) 18000psi allowable stress allowable actual MS 0.0 Engineering Information Systems Lab eislab.gatech.edu example 1, state 3 56 COB-based Constraint Schematic for Multi-Fidelity CAD-CAE Interoperability Design Tools Analysis Building Blocks (ABBs) MCAD Tools CATIA, I-DEAS* Pro/E* , UG *, ... Analysis Modules of Diverse Behavior & Fidelity (CBAMs) Continuum ABBs: y Extensional Rod Material Model ABB: shear stress, cte, e t DT E 2(1 ) ee DT et e r4 area, A DT, e, x Extension r3 r2 undeformed length, Lo G F E, A, shear strain, r5 DL Lo F E force, F G youngs modulus, E poissons ratio, One D Linear Elastic Model (no shear) reference temperature, To 1D Linear Elastic Model L material model edb.r1 temperature, T total elongation,DL r1 start, x1 shear modulus, G linkage y temperature change,DT e r4 thermal strain, et ee stress, E Torsional Rod T One D Linear Elastic Model strain, e r3 effective length, Leff mode: shaft tension Lo material model elastic strain, ee Flap Link Extensional Model Extensional Rod (isothermal) al1 length, L end, x2 r1 r2 E material T G, r, , ,J x area, A cross section L A youngs modulus, E al3 reaction condition DL x2 al2 linear elastic model Lo x1 E F e G stress mos model torque, Tr polar moment of inertia, J ee radius, r DT et e Analysis Tools (via SMMs) Margin of Safety (> case) 1D allowable stress allowable General Math Mathematica Matlab* MathCAD* ... actual MS r3 undeformed length, Lo r1 theta start, 1 theta end, 2 twist, inter_axis_length linkage Flap Link Plane Strain Model deformation model Parameterized FEA Model sleeve_1 w r L ws1 sleeve_2 w ts1 t Legend Tool Associativity Object Re-use t 2D mode: tension r rs2 ws2 ux,max ts2 x,max rs2 shaft cross_section:basic wf wf tw tw tf tf material E name E linear_elastic_model F condition reaction flap_link allowable stress effective_length allowable inter axis length change L w sleeve_1 B ts2 ts1 t r s w sleeve_2 sleeve1 sleeve2 shaft rib1 stress mos model Margin of Safety (> case) allowable allowable actual actual MS MS R1 t rib2 R1 r ds1 R2 x ds2 B ux mos model Margin of Safety (> case) x shaft cross_section R3 wf R4 tw Leff t1f R6 R5 deformation model t2f Torsional Rod critical_section critical_detailed wf linkage effective length, Leff al1 Lo tw Materials Libraries In-House, ... Parts Libraries In-House*, ... rib_1 R7 t1f h t rib_2 t2f R2 critical_simple wf h t material R8 tw R3 E name stress_strain_model linear_elastic hw tf cte area R9 R10 cross section: effective ring material condition polar moment of inertia, J al2a outer radius, ro al2b linear elastic model reaction allowable stress R12 Analyzable Product Model (APM) * = Item not yet available in toolkit (all others have working examples) © 1993-2001 GTRC mode: shaft torsion Torsion area b 1 R11 hw b twist mos model Margin of Safety (> case) 1D allowable al3 J r G T stress mos model allowable twist Margin of Safety (> case) allowable actual actual MS MS Engineering Information Systems Lab eislab.gatech.edu shear modulus, G 2 FEA Ansys Abaqus* CATIA Elfini* MSC Nastran* MSC Patran* ... Flap Link Torsional Model 57 FEA-based Analysis Subsystem Used in Linkage Plane Stress Model (2D Analysis Problem) Plane Stress Bodies y Higher fidelity version vs. Linkage Extensional Model ts2 tf wf ts1 ws1 tw rs1 ws2 F rs2 C L x L inter_axis_length linkage sleeve_1 deformation model Parameterized FEA Model L w t sleeve_2 mode: tension r ws1 w ts1 t rs2 ws2 ux,max ts2 x,max r ABBSMM SMM Template rs2 shaft cross_section:basic wf tw tf wf tw tf material E name linear_elastic_model condition reaction allowable stress E F allowable inter axis length change ux mos model stress mos model Margin of Safety (> case) Margin of Safety (> case) allowable allowable actual actual MS MS © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 58 COB-based Constraint Schematic for Multi-Fidelity CAD-CAE Interoperability Design Tools Analysis Building Blocks (ABBs) MCAD Tools CATIA, I-DEAS* Pro/E* , UG *, ... Analysis Modules of Diverse Behavior & Fidelity (CBAMs) Continuum ABBs: y Extensional Rod Material Model ABB: shear stress, cte, e t DT E 2(1 ) ee DT et e r4 area, A DT, e, x Extension r3 r2 undeformed length, Lo G F E, A, shear strain, r5 DL Lo F E force, F G youngs modulus, E poissons ratio, One D Linear Elastic Model (no shear) reference temperature, To 1D Linear Elastic Model L material model edb.r1 temperature, T total elongation,DL r1 start, x1 shear modulus, G linkage y temperature change,DT e r4 thermal strain, et ee stress, E Torsional Rod T One D Linear Elastic Model strain, e r3 effective length, Leff mode: shaft tension Lo material model elastic strain, ee Flap Link Extensional Model Extensional Rod (isothermal) al1 length, L end, x2 r1 r2 E material T G, r, , ,J x area, A cross section L A youngs modulus, E al3 reaction condition DL x2 al2 linear elastic model Lo x1 E F e G stress mos model torque, Tr polar moment of inertia, J ee radius, r DT et e Analysis Tools (via SMMs) Margin of Safety (> case) 1D allowable stress allowable General Math Mathematica Matlab* MathCAD* ... actual MS r3 undeformed length, Lo r1 theta start, 1 theta end, 2 twist, inter_axis_length linkage Flap Link Plane Strain Model deformation model Parameterized FEA Model sleeve_1 w r L ws1 sleeve_2 w ts1 t Legend Tool Associativity Object Re-use t 2D mode: tension r rs2 ws2 ux,max ts2 x,max rs2 shaft cross_section:basic wf wf tw tw tf tf material E name E linear_elastic_model F condition reaction flap_link allowable stress effective_length allowable inter axis length change L w sleeve_1 B ts2 ts1 t r s w sleeve_2 sleeve1 sleeve2 shaft rib1 stress mos model Margin of Safety (> case) allowable allowable actual actual MS MS R1 t rib2 R1 r ds1 R2 x ds2 B ux mos model Margin of Safety (> case) x shaft cross_section R3 wf R4 tw Leff t1f R6 R5 deformation model t2f Torsional Rod critical_section critical_detailed wf linkage effective length, Leff al1 Lo tw Materials Libraries In-House, ... Parts Libraries In-House*, ... rib_1 R7 t1f h t rib_2 t2f R2 critical_simple wf h t material R8 tw R3 E name stress_strain_model linear_elastic hw tf cte area R9 R10 cross section: effective ring material condition polar moment of inertia, J al2a outer radius, ro al2b linear elastic model reaction allowable stress R12 Analyzable Product Model (APM) * = Item not yet available in toolkit (all others have working examples) © 1993-2001 GTRC mode: shaft torsion Torsion area b 1 R11 hw b twist mos model Margin of Safety (> case) 1D allowable al3 J r G T stress mos model allowable twist Margin of Safety (> case) allowable actual actual MS MS Engineering Information Systems Lab eislab.gatech.edu shear modulus, G 2 FEA Ansys Abaqus* CATIA Elfini* MSC Nastran* MSC Patran* ... Flap Link Torsional Model 59 Flap Linkage Torsional Model Diverse Mode (Behavior) vs. Linkage Extensional Model L A ts2 ts1 s Sleeve 1 Sleeve 2 Shaft ds1 ds2 A deformation model Leff Torsional Rod linkage effective length, Leff al1 Lo 1 mode: shaft torsion cross section: effective ring material condition polar moment of inertia, J al2a outer radius, ro al2b linear elastic model reaction allowable stress twist mos model Margin of Safety (> case) allowable al3 J r G T stress mos model allowable twist Margin of Safety (> case) allowable actual actual MS MS © 1993-2001 GTRC shear modulus, G 2 Engineering Information Systems Lab eislab.gatech.edu 60 Modular Reusable COBs Flap Link Tutorial APM Example (5,25,36) flaplink APM (1,11,10) lib\abbs lib\apm (12,34,22) lib\geometry lib\material (108,68,30) 3,9,11 3,9,11 (3,9,11) (4,11,3) (#of entities, #of attribute, # of relations) Product specific COBs General COBs © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 61 Multi-Representation Architecture for Design-Analysis Integration 3 Analyzable Product Model 4 Context-Based Analysis Model APM 2 Analysis Building Block Printed Wiring Assembly (PWA) 1 Solution Method Model CBAM ABB SMM APM ABB Component Solder Joint Component Solder Joint PWB T0 body 1 body4 ABBSMM body3 body 2 Printed Wiring Board (PWB) Design Tools © 1993-2001 GTRC Solution Tools Engineering Information Systems Lab eislab.gatech.edu 62 Typical Solution Tool Processes Tool Control Solution Tool Results Model Data Preprocessor Control Preprocessor C L Preprocessor Model 11 Postprocessor Control Solver Unsolved Mesh Model Postprocessor Solved Mesh Model 10 A1 7 8 extrema, graphics 9 A3 6 1 © 1993-2001 GTRC Processed Results 5 4 A2 3 2 Engineering Information Systems Lab eislab.gatech.edu 63 ABB-SMM- Solution Tool Interaction 2 Analysis Building Block Solution Tool 1 Solution Method Model ABB SMM ABBSMM preprocessor model body1 body4 body3 11 10 A1 7 8 6 1 5 4 A2 3 2 eu results mesh extrema model body2 outputs 1 Solution Method Model 11 8 9 6 5 4 A2 FEA Tools inputs & control 3 2 mesh model outputs Object Environment © 1993-2001 GTRC Files A3 1 eu results extrema 10 A1 7 Solution Tools Tool Agent C L preprocessor model inputs & control 9 A3 Operating System Engineering Information Systems Lab eislab.gatech.edu 64 ABB Mappings to Diverse Tool-Specific SMMs Plane Strain Model Example C L La 11 12 10 13 A1 11 body1 , material1 , T1 7 Ansys ABB 10 body 0 body 6 5 body 5 3 A2 body2 , material2 , T2 3 2 1 h2 2 L3 Lb 3 La 2 Cadas Vendor Variation Challenges • Feature set of modeling language • Region decomposition • Numbering & composition of entities • Element type designations 18 14 A25 19 10 14 11 11 A23 12 6 9 7 10 12 17 13 15 A24 16 9 13 5 8 body 1 h1 Cadas SMM h3 body 3 8 4 A20 5 A21 6 A22 7 1 1 2 2 3 3 L5 L3 body 2 h2 4 L4 Lb © 1993-2001 GTRC Ansys SMM h3 4 4 1 body 4 9 8 A3 9 body3 , material3 , T3 1 T = key point n = line n h1 = area n 7 6 Plane Strain Bodies System 8 n n An Engineering Information Systems Lab eislab.gatech.edu 65 Parameterized FEA Preprocessor Model Fixed Topology - Ansys ANSYS Prep7 Template Preprocessor Model Figure @EX1@ = Parameters populated by context ABB C L /PREP7 La 11 12 10 13 A1 11 body1 , material1 , T1 7 10 8 n n An = key point n = line n h1 = area n 9 8 A3 9 body3 , material3 , T3 h3 7 6 5 6 1 5 4 4 A2 body2 , material2 , T2 L3 Lb © 1993-2001 GTRC rectangular body 3 3 3 2 1 2 h2 ! body1 Material Properties MP,EX,1,@EX1@ ! Young's modulus MP,ALPX,@ALPX1@ ! CTE MP,NUXY,1,@NUXY1@ ! Poisson's ratio (minor) ... LA = @LA@ ! Geometric Parameters LB = @LB@ L3 = @L3@ T0 = @T0@ ! Load Parameters T1 = @T1@ T2 = @T2@ T3 = @T3@ ... K,1, 0.0, 0.0 ! Key Points K,3, LB, H2 K,5, (LA-L3), H2 ... NLB = 10 ! Mesh Density Parameters NH2 = 4 NH3 = 4 ... L,1,2,NLB ! 1 ! Lines <kp1,kp2,divisions,size ratio> L,2,3,NH2,0.5 ! 2 L,3,4,NLB/2 ! 3 ... AL, 10, 8, 11, 12, 13 ! 1 - body 1 ! Areas AL, 1, 2, 3, 4, 5, 6 ! 2 - body 2 AL, 4, 7, 8, 9 ! 3 - body 3 ... ! Assign materials, Assign loads, Automesh, etc. Engineering Information Systems Lab eislab.gatech.edu 66 Ansys SMM Implementation Plane Strain Model - Example Instance © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu solder joint deformation w/ detailed sj: case 3 67 Parameterized FEA Preprocessor Model Fixed Topology - Cadas Cadas Preprocessor Model Template Preprocessor Model Figure @EX1@ = Parameters populated by context ABB La 12 17 13 15 16 9 5 A24 13 8 18 14 A25 19 body 1 10 14 11 11 A23 12 6 9 7 10 h1 h3 body 3 8 4 A20 5 A21 6 A22 7 1 1 2 2 3 3 L5 L3 L4 Lb © 1993-2001 GTRC rectangular body 3 4 body 2 h2 addbasp 0.0 0.0 addbasp @L5@ 0.0 addbasp @L3@ 0.0 ... addlin2 1 2 addlin2 2 3 addlin2 3 15 ... addsurfp 1 2 6 5 addsurfp 2 3 7 6 addsurfp 3 15 16 7 ... matmger edit 21 @mat1_name@ matmger edit 102 @mat1_E@ ... atrsurf 30 31 group 1 atrsurf 26 27 28 32 group 2 atrsurf 29 33 34 group 3 atrgrp 1 2 3 etype s 81 atrgrp 1 material 1 atrgrp 2 material 2 atrgrp 3 material 3 divset 2601 nodiv 3 1.0 divset 2603 nodiv 3 1.0 ... mergnode all 1.000E-5 tempload group 1 v @T1@ tempload group 2 v @T2@ tempload group 3 v @T3@ fixsuprt node 40 v 23 fixsuprt line 4 15 v 1 dbsave smm.pre Engineering Information Systems Lab eislab.gatech.edu ! key points ! lines ! areas ! materials -99 close -99 close ! groups ! element type ! assign materials ! line divisions ! merge ! temperatures ! fixed origin bc ! symmetry bc 68 Other ABB-SMM Mapping Considerations ABBSMM Solution Method Variation ABB ABBSMM Vendor Variation Symbolic SMM Finite Element SMM Boundary Element SMM Finite Difference SMM Vendor-Specific Finite Element SMMs ABB Ansys SMM Cadas SMM Nastran SMM Neutral ABBSMM ABB Ansys SMM Finite Element SMM (e.g., STEP AP209) © 1993-2001 GTRC Vendor-Specific Engineering Information Systems Lab eislab.gatech.edu Cadas SMM Nastran SMM 69 SMM Status Template approach works well for fixed topology cases – Relatively simple – Leverages current parametrized FEA models Further needs: – Aid complex cases: Ex. variable toplogy multi-part/body – Enable multi-vendor / vendor-neutral representations © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 70 An Introduction to X-Analysis Integration (XAI) Short Course Outline Part 1: Constrained Objects (COBs) Primer – Nomenclature Part 2: Multi-Representation Architecture (MRA) Primer – Analysis Integration Challenges – Overview of COB-based XAI » MRA Summary – Ubiquitization Methodology Part 3: Example Applications Part 4: Advanced Topics & Current Research © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 71 Evaluation Test Case Statistics: COB Structure # of Entities, Attributes, Relations lib\geometry.cos apm.cos materials.cos pwa/b lib\apm.cos lib\materials.cos lib\abbs.cos apm.cos apm.cos cbams.cos apm.cos cbams.cos abbs.cos cbams.cos fastener.cos materials.cos airplane electrical chip package (cp) product specific lib apm.cos bikeframe cbams.cos lib pwb_board.cos apm.cos bga (ball grid array) cbams.cos apm.cos qfp(quad flat pack) cbams.cos lib\abbs.cos apm.cos lib\apm.cos lib\geometry.cos lib\apm.cos airplane\lib\abbs.cos lib\geometry.cos lib\apm.cos airplane\lib\materials.cos airplane\lib\fastener.cos airplane\lib\cbams.cos airplane\bikeframe\apm.cos lib\geometry.cos cp\lib\pwb_board.cos lib\abbs.cos cp\bga\apm.cos lib\geometry.cos cp\lib\pwb_board.cos lib\abbs.cos cp\qft\apm.cos Totals © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 4 11 3 108 68 30 12 34 22 3 9 1 1 11 10 5 25 36 77 152 5 24 21 39 23 12 2 3 1 7 7 38 16 4 23 20 8 2 Aggregate Instance Relations Total Aggregate Total COB Libraries Used abbs.cos flaplink general(lib) Structure (COS) geometry.cos Entities Attributes Aggregate Operation COB Libraries Used Oneway Test Cases 2 19 9 3 3 5 20 13 21 2 5 53 177 6 103 1 12 4 19 15 25 76 1 18 2 1 344 12 753 4 25 19 376 3 8 12 22 15 59 72 Evaluation Test Case Statistics: COB Structure Flap Link Test Case product specific general (lib) abbs.cos 4 11 3 108 68 30 geometry.cos 12 34 22 materials.cos 3 9 1 1 11 10 apm.cos lib\geometry.cos Aggregate Instance Aggregate Operation Oneway Relations Total Aggregate COB Libraries Used Total Structure (COS) Entities Attributes lib\apm.cos apm.cos lib\materials.cos lib\abbs.cos flaplink cbams.cos ….. Totals apm.cos ….. 5 25 36 2 ….. ….. ….. ….. ….. ….. 344 753 25 376 8 12 ….. 59 • Supports reusability • Supports complex large problems © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 73 Evaluation Example COB Reuse as Modular Building Blocks Structure (COS) 1D Linear Elastic Model (ABB) Margin of Safety ABB Flaplink APM BikeFrame APM PWA/B APM EBGA ChipPackage APM PBGA ChipPackage APM QFP ChipPackage APM © 1993-2001 GTRC Where used Extensional Rod ABB Torsional Rod ABB 1D Linkage Extensional Flaplink CBAM for stress 1D Torsional Extensional Flaplink CBAM for stress 1D Torsional Extensional Flaplink CBAM for twist 2D Plane Stress flaplink CBAM for stress 2D linkage extensional flaplink CBAM for deformation 1D PWB Thermal Bending for warpage 2D PWBThermal Bending for warpage 1.5D Lug CBAM for stress Linkage Extensional CBAM Linkage Plane Stress CBAM Linkage Torsional CBAM Lug Axial/Oblique; Ultimate/Shear CBAM Fitting Bending/Shear CBAM Thermal Bending CBAM 6 Layer Plain Strain CBAM N Layer Plain Strain CBAM EBGA Thermal Resistance CBAM PBGA Thermal Resistance CBAM Thermal Stress CBAM Thermal Resistance CBMA Engineering Information Systems Lab eislab.gatech.edu 74 Major Types of Analysis Objects Part Feature APM Entities Context-Based Analysis Model (CBAM) Analysis Subsystems idealizations Boundary Condition Objects Conditions & Next-Higher CBAMs Mode Analysis Context boundary variables Solution Method Models (SMMs) allowables Objectives MS Analysis Building Blocks (ABBs) Associativity Linkages allowable actual Analysis Context CBAM = why + how • Analysis specification (why vs. how) = Analysis Context • Definable during early planning stages + Analysis Subsystems (ABBs, etc.) + Associativity Linkages analysis problem a.k.a: template, context-based analysis model (CBAM), • Can be new, reused, or adapted template analysis module • Instance can contain one or more runs © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 75 MRA Summary Multiple representations required by: – Many:Many cardinality – Reusability & modularity Self-Test: Consider impact of removing a representation Similar to “software design patterns” for CAD-CAE domain – Identifies patterns between CAD and CAE (identifies new types of objects) – Other needs: conditions, requirements, next-higher analysis – Captures explicit associativity Distinctive CAD-CAE associativity needs – Multi-fidelity, multi-directional capabilities © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 76 An Introduction to X-Analysis Integration (XAI) Short Course Outline Part 1: Constrained Objects (COBs) Primer – Nomenclature Part 2: Multi-Representation Architecture (MRA) Primer – Analysis Integration Challenges – Overview of COB-based XAI – Ubiquitization Methodology Recommended Approach Skim the methodology, then review Part 3 first, then come back for a more detailed look. Part 3: Example Applications » Airframe Structural Analysis » Circuit Board Thermomechanical Analysis » Chip Package Thermal Analysis – Summary Part 4: Advanced Topics & Current Research © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 77 Classes of Analysis Aspect Inputs Design Families* Design Instances Design Variations Solution Method Develop new method Use established method Analysis Procedure Develop procedure Define analysis criteria Define idealizations, G: Boundary conditions Analytical body types Geometric simplifications Material models Validate procedure Measure samples Correlate with measurements Use established procedure Outputs Validated solution method Validated analysis procedure Sensitivity studies Example datasets Analysis results & design impact © 1993-2001 GTRC Original Analysis Class Adpative Ubiquitous Multi-layer PWBs PWB #95145 Re-order stackup Several Several - Many Several Several - Many One - Many Several New FEA element Example PWB warpage analysis Tmax = avg T of chip Uniform temperature Plane strain body Total thickness Linear elastic Shadow moire' IPC-D-279 PTH fatigue Who Senior Analyst Analyst Designer Focus Development Development Regular Usage * Design = product or process Analysis = simulation of physical behavior Engineering Information Systems Lab eislab.gatech.edu 78 Desired Characteristics of Designer* Analysis Tools Tools that are easy to use and that automate tasks as much as possible Predefined catalogs of common product-specific analysis models, along with usage guidelines Product-specific terminology for model interaction (e.g., product-specific variable names) Linkages with COTS and in-house design tools that have selective multi-directional associativity Ability to leverage COTS general purpose CAE tools, as well as in-house specialty tools Ability to utilize analysis tools without becoming a tool expert Insulation from analysis model details (e.g., node numbers), but access if needed *Note: Some organizations categorize two types of “design” product team members: a) Those who develop the product architecture and plan the design of subassemblies and piece parts (at the feature level). Commonly used names for this type of team member include engineers, physical designers, etc. b) Those who utilize CAD tools to capture these designs in detailed manufacturable form. Commonly used names include designers, CAD users, etc. In these slides the term “designer” is used loosely for both groups. Generally, Type a) team members need to use analysis modules earlier in the design process to help “size” the designs and evaluate alternatives. Then Type b) users can employ analysis modules to guide and check the detailed design. This is the typical progression of who has more training to judge the inner workings and limitations of the analysis modules (and thus an increasing class of design cases that they can be called on to analyze): Type b), Type a), and Analyst. Thus if Type b) encounters a border line case or odd analysis results, they might ask the Type a) person to take a look at it. If Type a) feels it is beyond their scope, they can then ask the Analyst to take a look. If the Analyst is also not certain about it, then physical tests and analysis module extension studies may be needed. © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 79 Increasing Design Space & Analysis Utility Ubiquitous Analysis (Template Usage) Adaptive Analysis (Procedure Creation) Needs Perform & Correlate Analyses 0.1 Analyst Applicable Design Space (Comfort Zones) Use Analyst (not automated) Use Analysis Module Examples, Sensitivity Studies, Measurement Correlation Define Applicability 0.2 Analyst Procedure Documentation, Design Guides (typical practice) Use in Design Process 2.0 Designer Improved Design Analysis Results Design Instances Ubiquitization (Template Creation) Ubiquitize Procedure Create Once Use Many Times Analysis Module Template (increased 1.0 precision & scope) All Use Design Guides © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 80 Ubiquitization Process Template Creation & Usage Phases Ubiquitization (Creation Phase) 1.0 Ubiqutize Procedure Design Needs Established Analysis Procedure Identify Ubiquitous Analysis Model 1.1 Designer & Analyst Develop CBAM & Related Entities Implement CBAM & Related Entities 1.2 Analyst & Developer 1.3 Developer Analysis Module Template (CBAM) & Applications Building Blocks Create Template Once, Use Template Many Times Ubiquitous Analysis (Usage Phase) Analysis Module Template Design Instances Use Analysis Module Automated Analysis Results 2.0 Designer Other Developer/Integrator Roles: Product Modeler, Parts Librarian, Materials Librarian, CAD & CAE Tool Specialist(s) © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 81 MRA Foundation for Product-Specific Tools product = product domain (e.g., airframes, PWBs, chip packages, …) SAS= specialized analysis system (with possibly specialized procedures - Ex. a VTMB algorithm) Product-Specific Entities j Generic MRA Foundation Specific Specific Specific SASs APMs CBAMs General SMMs Purpose Abstract Abstract APMs CBAMs ABBs 1 XaiTools FrameWork © 1993-2001 GTRC 2 3 Product-Specific Tooli i=1...n 4 Examples Engineering Information Systems Lab eislab.gatech.edu XaiTools PWA-B XaiTools ChipPackage 82 Typical Sources of Ubiquitous Analysis Models © 1993-2001 GTRC Corporate technical memos Unpublished notes & know-how Example CAD & CAE model files In-house computer programs Handbooks Journal papers Conference proceedings Textbooks Engineering Information Systems Lab eislab.gatech.edu 83 Informal Description of a Ubiquitous Analysis Model (Analysis Procedure) Model Purpose - A brief statement about the model and what design needs it fulfills. It should indicate what design stages best benefit from the model, (typically based on model accuracy versus computational cost). Major Analysis Steps and Variations - A high-level, top-down view of the major analysis steps in the form of a tree/network diagram or an IDEF0 process model. Variations such as directionality, loading conditions, and product configurations should be identified. Analyst Sketches & Idealizations - Sketches of analysis models noting types of idealizations used: bodies, loads, and material models in product-specific terms. Relations and Variables - A list of relations and variables. For models that require solution tools such as finite element analysis (FEA) programs, the list should contain a relation whose variables are the inputs and outputs for that tool. Model Limitations - Guides for the end user, including model assumptions and acceptable ranges of inputs and outputs. Model References - Background information about the model, including application to the product type at hand, as well as descriptions of product-independent analysis concepts. Representative Datasets - Example values for input, intermediate, and output variables for each major variation. These datasets should include related solution tool input and © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 84 Observations to Date Need to ensure proper usage (highly automated!) – Must capture limitations & validity criteria © 1993-2001 GTRC Knowledge capture technique Synergy of specialists; communication aid Catalyst for more analysis research Usage by designers & non-designers (e.g., mfg.) Engineering Information Systems Lab eislab.gatech.edu 85 Observations (continued) Delivery by network-based engineering service bureaus (ESBs) – Internet-based: Commercial ESB w/ self-/full-serve consulting – Intranet-based: Internal ESB (for shared corporate usage) – Extranet-based: Internal ESB, with controlled access for customers & suppliers XaiTools status: – Focus to date: » Toolkit for developers & analysts to create analysis templates (ubiquitization process, but non-interactive ) » Support automated template usage by end users (ubiquitous analysis) - fixed topology; non-field relations – Next: Aid interactive adaptive analysis (template creation / one-of-a-kind analysis) © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 86 An Introduction to X-Analysis Integration (XAI) Short Course Outline Part 1: Constrained Objects (COBs) Primer – Nomenclature Part 2: Multi-Representation Architecture (MRA) Primer – Analysis Integration Challenges – Overview of COB-based XAI – Ubiquitization Methodology Part 3: Example Applications » Airframe Structural Analysis » Circuit Board Thermomechanical Analysis » Chip Package Thermal Analysis – Summary Part 4: Advanced Topics & Current Research © 1993-2001 GTRC Engineering Information Systems Lab eislab.gatech.edu 87