elements towards next-generation knowledge representations and product modeling techniques...

Elements towards Next-Generation Knowledge Representations and Product Modeling Techniques

[email protected]://itimes.marc.gatech.edu/

http://eislab.gatech.edu/projects/

Planning Meeting for Product, Lifecycle Management, and Systems Engineering Models

May 20, 2003NIST • Gaithersburg MD (via telecon)

2

Contents

Multiple views in a knowledge representation Declarative thinking Object graph view of model interoperability

– Some factors for comparing knowledge representations Leveraging multiple standards Managing computing environments

via systems engineering methods Elevated terminology & thinking

See backup slides for other examples & references

Purpose: Help identify comparison factorsand encourage thinking about next-generation needs

3

Contents Multiple views in a knowledge representation

– Human-sensible & computer-sensible– Graphical, lexical, application-oriented

Declarative thinking – Multi-directional (non-causal)– With derivable lower-level procedural approaches

Object graph view of model interoperability Leveraging multiple standards Managing computing environments


Examples from Constrained

Objects (COBs)& CAD-CAE Integration

4

Triangle

dh

Ab

Triangle

dh

Ab

COB Structure: Graphical Forms

Tutorial: Triangle Primitive

v a r i a b l e s u b v a r i a b l es u b s y s t e m

e q u a l i t y r e l a t i o n

r e l a t i o n

s

a b

dc

a

b

d

c

e

a . das

r 1r 1 ( a , b , s . c )

e = f

s u b v a r i a b l e s . b

[ 1 . 2 ]

[ 1 . 1 ]o p t i o n 1 . 1

ff = s . d

o p t i o n 1 . 2

f = g

o p t i o n c a t e g o r y 1

gcbe

r 2

h o f c o b t y p e h

wL [ j : 1 , n ]

w j

a g g r e g a t e c . we l e m e n t w j

Basic Constraint Schematic-S Notation

c. Constraint Schematic-Sa. Shape Schematic-S

2222

1

:

21:

hbdr

bhAr

b. Relations-S

d. Subsystem-S(for reuse by other COBs)

h

b

Ad

base, br1

r2

bhA 21

height, h

222 hbd

area, A

diagonal, d

Aside: This is a “usage view” in AP210 terminology (vs. the above “design views”)

5

COB Structure (cont.): Lexical Form Tutorial: Triangle Primitive

for reference: c. Constraint Schematic-S

e. Lexical COB Structure (COS)

COB triangle SUBTYPE_OF geometric_shape; base, b : REAL; height, h : REAL; diagonal, d : REAL; area, A : REAL;RELATIONS r1 : "<area> == 0.5 * <base> * <height>"; r2 : "<diagonal>**2 == <base>**2 + <height>**2";END_COB;

base, br1

r2

bhA 21

height, h

222 hbd

area, A

diagonal, d

6

3 in22 in

3 in

base, br1

r2

bhA 21

height, h

222 hbd

area, A

diagonal, d3.60 in

200 lbs

30e6 psiResult b = 30e6 psi (output or intermediate variable)

Result c = 200 lbs (result of primary interest)

X

Relation r1 is suspended X r1

100 lbs Input a = 100 lbs

Equality relation is suspended

a

b

c

Example COB InstanceTutorial: Triangle Primitive

Constraint Schematic-I Lexical COB Instance (COI)

state 1.0 (unsolved):INSTANCE_OF triangle; base : 2.0; height : 3.0; area : ?; diagonal : ?;END_INSTANCE;

state 1.1 (solved):INSTANCE_OF triangle; base : 2.0; height : 3.0; area : 3.0; diagonal : 3.60;END_INSTANCE;Basic Constraint Schematic-I Notation

example 1, state 1.1


. . .state 2.1 (solved):INSTANCE_OF triangle; base : 2.0; height : 9.0; area : 9.0; diagonal : 9.22;END_INSTANCE;

9 in22 in

9 in

base, br1

r2

bhA 21

height, h

222 hbd

area, A

diagonal, d9.22 in

7

Multi-Directional I/O (non-causal)Tutorial: Triangle Primitive


state 2.1 (solved):INSTANCE_OF triangle; base : 2.0; height : 9.0; area : 9.0; diagonal : 9.22;END_INSTANCE;

state 3.0 (unsolved):INSTANCE_OF triangle; base : 2.0; height : ?; area : 6.0; diagonal : ?;END_INSTANCE;

state 3.1 (solved):INSTANCE_OF triangle; base : 2.0; height : 6.0; area : 6.0; diagonal : 6.32;END_INSTANCE;

6 in22 in

6 in

base, br1

r2

bhA 21

height, h

222 hbd

area, A

diagonal, d6.32 in


9 in22 in

9 in

base, br1

r2

bhA 21

height, h

222 hbd

area, A

diagonal, d9.22 in


8

TriangularPrism

Vh

b

l

COBs as Building Blocks Tutorial: Triangular Prism COB Structure

c. Constraint Schematic-Sa. Shape Schematic-S

b. Relations-S

d. Subsystem-S(for reuse by other COBs)

T ria n g le

dh

Ab

T ria n g le

dh

Ab

le n g th , l vo lu m e , Vr1

AlV

c ro s s -s e c tio nh

b

V l

AlVr :1

e. Lexical COB Structure (COS)

COB triangular_prism SUBTYPE_OF geometric_shape; length, l : REAL; cross-section : triangle; volume, V : REAL;RELATIONS r1 : "<volume> == <cross-section.area> * <length>";END_COB;

9

200 lbs

30e6 psiResult b = 30e6 psi (output or intermediate variable)

Result c = 200 lbs (result of primary interest)

X

Relation r1 is suspended X r1

100 lbs Input a = 100 lbs

Equality relation is suspended

a

b

c

Example COB InstanceTutorial: Triangular Prism


state 1.0 (unsolved):INSTANCE_OF triangular_prism; cross-section.base : 2.0; cross-section.height : 3.0; length : 5.0; volume : ?;END_INSTANCE;

state 1.1 (solved):INSTANCE_OF triangular_prism; cross-section.base : 2.0; cross-section.height : 3.0; cross-section.area : 3.0; length : 5.0; volume : 15.0;END_INSTANCE;

Basic Constraint Schematic-I Notation


Triangle

dh

Ab

Triangle

dh

Ab

length, l volume, Vr1

AlV

cross-section

3 in2

2 in

3 in

15 in35 in

10

COB Modeling Languages & Views

COB InstanceDefinition Language

(COI)

Constraint Graph-I

Constraint Schematic-I

STEPPart 21

200 lbs

30e6 psi

100 lbs 20.2 in

R101

R101

100 lbs

30e6 psi 200 lbs

20.2 in

StructureLevel(Template)

InstanceLevel

Subsystem-S

Object Relationship Diagram-S

COB StructureDefinition Language

(COS)

I/O Table-S

Constraint Graph-S

Constraint Schematic-S

STEPExpress

Express-GXML UML

Subsystem-S



(COS)

I/O Table-S

Constraint Graph-S


STEPExpress

Express-GXML UML

11

Contents Multiple views in a knowledge representation Declarative thinking Object graph view of model interoperability

– Include connections with lower-level models & COTS tools– Facilitate solution management & reasoning control– Some factors for comparing knowledge representations

Leveraging multiple standards Managing computing environments


Examples from Constrained

Objects (COBs)& CAD-CAE Integration

12

Constrained Object Panorama for Multi-Fidelity CAD-CAE Interoperability

Flap Link Benchmark Example

Material Model ABB:

Continuum ABBs:

E

One D LinearElastic Model

T

G

et

material model

polar moment of inertia, J

radius, r

undeformed length, Lo

twist,

theta start, 1

theta end, 2

r1

12

r3

0L

r

J

rTr

torque, Tr

x

TT

G, r, , ,J

Lo

y

material model

temperature, T

reference temperature, To

force, F

area, A


total elongation,L

length, L

start, x1

end, x2

E

One D LinearElastic Model

(no shear)

T

et

r1

12 xxL

r2

oLLL

r4

A

F

edb.r1

oTTT

r3

L

L

x

FF

E, A,

LLo

T, ,

yL

Torsional Rod

Extensional Rod

temperature change,T

cte,

youngs modulus, E

stress,

shear modulus, G

poissons ratio,

shear stress, shear strain,

thermal strain, t

elastic strain, estrain,

r2

r1)1(2

EG

r3

r4Tt

Ee

r5

G

te

1D Linear Elastic Model

material

effective length, Leff

linear elastic model

Lo

Extensional Rod(isothermal)

F

L

A

L

E

x2

x1

youngs modulus, E

cross section area, A

al1

al3

al2

linkage

mode: shaft tension

condition reaction

allowable stress

stress mos model

Margin of Safety(> case)

allowable

actual

MS

Analysis Modules of Diverse Behavior & Fidelity

(CBAMs) MCAD Tools

Materials LibrariesIn-House, ...

FEA Ansys

Abaqus*

CATIA Elfini*

MSC Nastran*

MSC Patran*

...

General MathMathematica

Matlab*

MathCAD*

...

Analyzable Product Model(APM)

Extension

Torsion

1D

1D

Analysis Building Blocks(ABBs)

CATIA, I-DEAS* Pro/E* , UG *, ...

Analysis Tools(via SMMs)

Design Tools

2D

flap_link

critical_section

critical_simple

t2f

wf

tw

hw

t1f

area

effective_length

critical_detailed

stress_strain_model linear_elastic

E

cte area

wf

tw

hw

tf

sleeve_1

b

h

t

b

h

t

sleeve_2

shaft

rib_1

material

rib_2

w

t

r

x

name

t2f

wf

tw

t1f

cross_section

w

t

r

x

R3

R2

R1

R8

R9

R10

6R

R7

R12

11R

1R

2

3

4

5

R

R

R

R

name

linear_elastic_model

wf

tw

tf

inter_axis_length

sleeve_2

shaft

material

linkage

sleeve_1

w

t

r

E

cross_section:basic

w

t

rL

ws1

ts1

rs2

ws2

ts2

rs2

wf

tw

tf

E

deformation model

x,max

ParameterizedFEA Model

stress mos model


allowable

actual

MS

ux mos model


allowable

actual

MS

mode: tensionux,max

Fcondition reaction

allowable inter axis length change

allowable stress

ts1

B

sleeve1

B ts2

ds2

ds1

sleeve2

L

shaft

Leff

s

rib1 rib2

material

effective length, Leff

deformation model

linear elastic model

Lo

Torsional Rod

G

J

r

2

1

shear modulus, G

cross section:effective ring polar moment of inertia, J

al1

al3

al2a

linkage

mode: shaft torsion

condition reactionT

outer radius, ro al2b

stress mos model

allowable stress

twist mos model


allowable

actual

MS


allowable

actual

MS

allowabletwist

Flap Link Extensional Model

Flap Link Plane Strain Model

Flap Link Torsional Model* = Item not yet available in toolkit (all others have working examples)

Parts LibrariesIn-House*, ...

LegendTool AssociativityObject Re-use

13

Analysis Tools

0.4375 in

0.5240 in

0.0000 in

2.440 in

1.267 in

0.307 in

0.5 in

0.310 in

2.088 in

1.770 in

67000 psi

65000 psi

57000 psi

52000 psi

39000 psi

0.067 in/in

0.030 in/in

5960 Ibs

1

10000000 psi

9.17

5.11

9.77

rear spar fitting attach point

BLE7K18

2G7T12U (Detent 0, Fairing Condition 1)

L29 -300

Outboard TE Flap, Support No 2;Inboard Beam, 123L4567

Bulkhead Fitting Joint

Program

Part

Feature

Channel FittingStatic Strength Analysis

Template

1 of 1Dataset

strength model

r1

e

b

h

tb

te

Pu

Ftu

E

r2

r0

a

FtuLT

Fty

FtyLT

epuLT

tw

MSwall

epu

jm

MSepb

MSeps


Fsu

IAS FunctionRef D6-81766

end pad

base

material

wall

analysis context

mode: (ultimate static strength)

condition:

heuristic: overall fitting factor, Jm

bolt

fitting

headradius, r1

hole radius, ro

width, b

eccentricity, e

thickness, teheight, h

radius, r2

thickness, tb

hole

thickness, twangled height, a

max allowable ultimate stress,

allowable ultimate long transverse stress,

max allowable yield stress,

max allowable long transverse stress,

max allowable shear stress,

plastic ultimate strain,

plastic ultimate strain long transverse,

young modulus of elasticity,

load, Pu

Ftu

Fty

FtyLT

Fsu

epu

epuLT

E

FtuLT

product structure (channel fitting joint)

Flexible High Diversity Design-Analysis Integration Phases 1-3 Airframe Examples:

“Bike Frame” / Flap Support Inboard Beam

Analysis Modules (CBAMs) of Diverse Feature:Mode, & Fidelity

Design Tools

Materials DBFEA

Elfini*MATDB-like

Analyzable Product Model

XaiTools

XaiTools

Fitting:Bending/Shear

3D

1.5D

Modular, ReusableTemplate Libraries

MCAD ToolsCATIA v4, v5

Lug:Axial/Oblique; Ultimate/Shear

1.5D

Assembly:Ultimate/

FailSafe/Fatigue*

* = Item not yet available in toolkit (all others have working examples)

diagonal brace lug jointj = top

0.7500 in

0.35 in

0.7500 in

1.6000 in

2

0.7433

14.686 K

2.40

4.317 K

8.633 K

k = norm

Max. torque brake settingdetent 30, 2=3.5º

7050-T7452, MS 7-214

67 Ksi

L29 -300


Diagonal Brace Lug Joint

Program

Part

Feature

Lug JointAxial Ultimate Strength Model

Template

j = top lugk = normal diameter (1 of 4)

Dataset

material

deformation model

max allowable ultimate stress, FtuL

effective width, W

analysis context

objective

mode (ultimate static strength)

condition

estimated axial ultimate strength


allowable

actual

MS

normal diameter, Dnorm

thickness, t

edge margin, e

Plug joint

size,n

lugs

lugj hole

diameters

product structure (lug joint)

r1

n

P jointlug

L [ j:1,n ]

Plug

L [ k]Dk

oversize diameter, Dover

D

PaxuW

e

t

Ftuax

Kaxu

Lug Axial UltimateStrength Model

BDM 6630

Fasteners DB

FASTDB-like

General Math Mathematica

In-HouseCodes

Image API(CATGEO);

VBScript

14

Usage of a COB-based Analysis TemplateCAD-CAE Interoperability during Lug Strength Analysis


0.7500 in

0.35 in

0.7500 in

1.6000 in

2

0.7433

14.686 K

2.40

4.317 K

8.633 K

k = norm


7050-T7452, MS 7-214

67 Ksi

L29 -300



Program

Part

Feature


Template


Dataset

material

deformation model


effective width, W

analysis context

objective


condition



allowable

actual

MS


thickness, t

edge margin, e

Plug joint

size,n

lugs

lugj hole

diameters


r1

n

P jointlug

L [ j:1,n ]

Plug

L [ k]Dk

oversize diameter, DoverD

PaxuW

e

t

Ftuax

Kaxu


DM 6630

Solution Tool Interaction

Boundary Condition Objects(links to other analyses)

CAD-CAE Associativity (idealization usage)

Material Models

Model-based Documentation

Geometry

P KW

DDtFaxu axu tuax ( )1

Requirements

15

Convergence of Representations

Database Techniques(data structure, storage …)

Software Development(algorithms …)

Artificial Intelligence& Knowledge-Based Techniques

(structure combined with algorithms/relations/behavior)

EER

STEP Express

ER

UML

Flow Charts

OMT

Objects

Rules

Constraint graphs

Constrained Object - likeRepresentations

COBs, OCL, ...

16

Contents Multiple views in a knowledge representation Declarative thinking Object graph view of model interoperability

– Include connections with lower-level models & COTS tools– Facilitate solution management & reasoning control– Some factors for comparing knowledge representations

Leveraging multiple standards Managing computing environments


17

Dimensions of AssociativitySome Knowledge Representation Comparison Factors

Operand representation: a, b– Type: numeric, logical, string, …, general object– Human-sensible vs. computer-sensible

» Computer-sensible: Flattened vs. object/feature-oriented– Other facets: security, units, uncertainty, maturity, version history,

(un)known/withheld, … Relation representation: r1, r2

– Relation type: Math formula, geometric constraint, computable algorithm, computer system (e.g., FEA tool), higher order constraint, arbitrary human process, ...

Associativity = Relations among objects

a aaYaX ..

r1System X

System Y

b).(. 2 bZraX

r2 System Z

electricalcircuitsanalogy

18

Dimensions of Associativity (cont.)

Relation representation (continued)– Explicit vs. implicit vs. unrecognized vs. unknown – Human-sensible vs. computer-sensible

» Computer-sensible: Dumb string vs. smart string vs. object/feature-oriented relation

– Level: instance, template (schema, structure), adaptable template– Other facets: priority, (in)active, plus similar facets as operands

Relation directionality– Uni-directional vs. multi-directional

vs. iteratively multi-directional Relation duration

– Continuous (“live”) vs. event-controlled Relation granularity

– Coarse vs. fine (macro vs. micro)

a aaYaX ..

r1System X

System Y

b).(. 2 bZraX

r2 System Z

Associativity graph type– Declarative vs. procedural– Cyclic vs. acyclic– Variable vs. fixed topology

19

Contents Multiple views in a knowledge representation Declarative thinking Object graph view of model interoperability Leveraging multiple standards Managing computing environments

via systems engineering methods– Including versioning & configuration mgt.

of meta-models, standards, and tools Elevated terminology & thinking

20

Tool-Product Model Schema Relationships in aStandards-Based Engineering Framework

XaiToolsPWA-B

Eagle

LKSoft, …Gap-FillingTools

XaiToolsPWA-B

EPM, LKSoft, STI, …

Traditional Tools Mentor

Graphics

STEP-Book AP210,SDAI-Edit,

STI AP210 Viewer, ...

Instance Browser/EditorPWB Stackup Tool,…

ElectricalCAD Tools

pgef

EngineeringFramework Tool

AP210

Doors

Slate

Systems EngineeringTools

Pro/E

CATIA

MechanicalCAD Tools

…

AP203, AP214 AP233

Smart Product ModelBuilding Blocks • Models & meta-models

• International standards• Industry specs• Corporate standards• Local customizations

• Modeling technologies:• Express, UML, XML, COBs, …

AP210 AP2xx

21

Primary Technologies for Schema-based Engineering Frameworks

Based on Engineering Framework Interest Group (EFWIG) emails from [email protected] (dated July 13, 2002 wrt PGPDM directions) and David Leal (dated November 26, 2002).

mailto:[email protected]





22

Contents Multiple views in a knowledge representation Declarative thinking Object graph view of model interoperability Leveraging multiple standards Managing computing environments


23

Needed Shifts in Engineering Thinking

Math-based models of physical behavior

Learn mathematics as a modeling language

Information models of physical objects

– Includes math-based models of physical behavior, but in their richer context

Learn information representation as another type of modeling language

Traditional Viewpoint

Note: Information models have their roots in modern mathematics (e.g. set theory).

Information/Knowledge-basedModeling Viewpoint

24

Needed Shifts in Engineering Thinking (cont.)

Tool usage

Data / files

Data exchange

Translators Single tools Drawings &

documents Calculations

Model creation & interaction (using tools) - knowledge capture

Information models &knowledge representations (objects)

Model connection, associativity, interoperability (often via equality relations)

Interfaces Integrated submodels Views (submodels)

connected to their richer models Usage of model operations

Traditional Computing Viewpoint

Objects (having structure and operations) that are interrelated.

Information/Knowledge-basedModeling Viewpoint

25

Summary

Multiple views in a knowledge representation Declarative thinking Object graph view of model interoperability

– Some factors for comparing knowledge representations Leveraging multiple standards Managing computing environments


See backup slides for other examples & references

Purpose: Help identify comparison factorsand encourage thinking about next-generation needs

Other Slides for Reference

27

Ar1

b

h

state 1 (relation usage)f :=: new instance of r1(b,h,A);

state 2 (value change)h := 9;status: A := 3;

A=3b=2

h=9intent

Procedural vs. Declarative Knowledge Representations

h

b

A = 1/2 bh

Procedural RepresentationTraditional programming: C, C++, Java, ...

function definition: areaarea(base,height) return (0.5 * base * height);

Declarative RepresentationMath solvers: Maple, Mathematica, ...

relation definition: r1r1(base,height,area): area :=: 0.5 * base * height;

state 3 (I/O change)A := 6;status: h := 9;

A=6b=2

h=9

intent ?

How does one compute h given A, b ?

A=3area

b=2

h=3

state 1 (function usage)b := 2, h := 3;A := area(b,h);status: A := 3;

A=9area

b=2

h=9

A := area(b,h);status’: A := 9;

A=6r1

b=2

h=6

state 3 (I/O change)h :=: ?, A :=: 6;status: h :=: 6

A=9r1

b=2

h=9

state 2 (value change)h :=: 9;status: A :=: 9

AA=3r1

b=2

h=3 b :=: 2, h :=: 3, A :=: ?;status: A :=: 3

Constrained Objects: A Knowledge Representation for Design, Analysis, and Systems Engineering Interoperability

Students: Manas Bajaj, Injoong Kim, Greg Mocko Faculty: Russell Peak

Approach and Status Approach:

Extend and apply the constrained object (COB) representation and related methodology based on positive results to date

Expand within international efforts like the OMG UML for Systems Engineering work to broaden applicability and impact

Status: Current generation capabilities have been successfully

demonstrated in diverse environments (circuit boards, electronic chip packages, airframes) with sponsors including NASA, Rockwell Collins, Shinko (a major supplier to Intel), and Boeing.

Templates for chip package thermal analysis are in production usage at Shinko with over 75% reduction in modeling effort (deformation/stress templates are soon to follow)

Objectives Develop better methods of capturing engineering knowledge that :

Are independent of vendor-specific CAD/CAE/SE tools Support both easy-to-use human-sensible views and robust computer-sensible formulations in a unified manner Handle a diversity of product domains, simulation disciplines, solution methods, and leverage disparate vendor tools

Apply these capabilities in a variety of sponsor-relevant test scenarios: Proposed candidates are templates and custom capabilities for design, analysis, and systems engineering

ContributionsTo Scholarship: Develop richer understanding of modeling

(including idealizations and multiple levels of abstraction) and representation methods

To Industry: Better designs via increased analysis intensity Increased automation and model consistency Increased modularity and reusability Increased corporate memory

via better knowledge capture

Additional Information:

1. http://eislab.gatech.edu/projects/

2. Response to OMG UML for Systems Engineering RFI:http://eislab.gatech.edu/tmp/omg-se-33e/

3. Characterizing Fine-Grained Associativity Gaps: A Preliminary Study of CAD-E Model Interoperabilityhttp://eislab.gatech.edu/pubs/conferences/2003-asme-detc-cie-peak/

Resources Needed Support for 1-3 students

depending on project scope Sponsor involvement to

provide domain knowledge and facilitate pilot usage

d i a g o n a l b r a c e l u g j o i n tj = t o p

0 . 7 5 0 0 i n

0 . 3 5 i n

0 . 7 5 0 0 i n

1 . 6 0 0 0 i n

2

0 . 7 4 3 3

1 4 . 6 8 6 K

2 . 4 0

4 . 3 1 7 K

8 . 6 3 3 K

k = n o r m

M a x . t o r q u e b r a k e s e t t i n gd e t e n t 3 0 , 2 = 3 . 5 º

7 0 5 0 - T 7 4 5 2 , M S 7 - 2 1 4

6 7 K s i

L 2 9 - 3 0 0

O u t b o a r d T E F l a p , S u p p o r t N o 2 ;I n b o a r d B e a m , 1 2 3 L 4 5 6 7

D i a g o n a l B r a c e L u g J o i n t

P r o g r a m

P a r t

F e a t u r e

L u g J o i n tA x i a l U l t i m a t e S t r e n g t h M o d e l

T e m p l a t e

j = t o p l u gk = n o r m a l d i a m e t e r ( 1 o f 4 )

D a t a s e t

m a t e r i a l

d e f o r m a t i o n m o d e l

m a x a l l o w a b l e u l t i m a t e s t r e s s , F t u L

e f f e c t i v e w i d t h , W

a n a l y s i s c o n t e x t

o b j e c t i v e

m o d e ( u l t i m a t e s t a t i c s t r e n g t h )

c o n d i t i o n

e s t i m a t e d a x i a l u l t i m a t e s t r e n g t h

M a r g i n o f S a f e t y( > c a s e )

a l l o w a b l e

a c t u a l

M S

n o r m a l d i a m e t e r , D n o r m

t h i c k n e s s , t

e d g e m a r g i n , e

P l u g j o i n t

s i z e , n

l u g s

l u g j h o l e

d i a m e t e r s

p r o d u c t s t r u c t u r e ( l u g j o i n t )

r 1

n

P jointlug

L [ j : 1 , n ]

P l u g

L [ k ]D k

o v e r s i z e d i a m e t e r , D o v e rD

P a x uW

e

t

F t u a x

K a x u

L u g A x i a l U l t i m a t eS t r e n g t h M o d e l

D M 6 6 3 0

S o l u t i o n T o o l I n t e r a c t i o n

B o u n d a r y C o n d i t i o n O b j e c t s( l i n k s t o o t h e r a n a l y s e s )

C A D - C A E A s s o c i a t i v i t y ( i d e a l i z a t i o n u s a g e )

M a t e r i a l M o d e l s

M o d e l - b a s e d D o c u m e n t a t i o n

G e o m e t r y

P KW

DD t Fa x u a x u t u a x ( )1

R e q u i r e m e n t s

Constrained Object (COB) Formulations

COB-based Airframe Analysis Template

Chip Package Stress Analysis Template

Cu(0.15)BT-Resin (0.135)

0.56

(Air)

(0.135)

Al Fin (1.5)Adhesive(0.05)

Subsystem-S



(COS)

I/O Table-S

Constraint Graph-S


STEPExpress

Express-GXML UML

Russell.P

eak@m

arc.gatech.edu -- 2003-05-12

29

COB-based Libraries ofAnalysis Building Blocks (ABBs)

Material Model ABB

Continuum ABBs

modularre-usage

E

O n e D L in e a rE la s t i c M o d e l

T

G

e

t

m a t e r i a l m o d e l

p o la r m o m e n t o f i n e r t i a , J

r a d iu s , r

u n d e f o r m e d l e n g t h , L o

t w i s t ,

t h e t a s t a r t , 1

t h e t a e n d , 2

r 1

12

r 3

0L

r

J

rT r

t o r q u e , T r

x

TT

G , r , , ,J

L o

y

m ateria l m odel

tem perature, T

reference tem perature, T o

force, F

area, A

undeform ed length, L o

to ta l e longation,L

length, L

start, x1

end, x2

E

O ne D LinearE lastic M odel

(no shear)

T

e

t

r1

12 xxL

r2

oLLL

r4

A

F

edb.r1

oTTT

r3

L

L

x

FF

E , A ,

LL o

T , ,

yL

Torsional Rod

Extensional Rod


cte,

youngs modulus, E

stress,

shear modulus, G

poissons ratio,

shear stress, shear strain,

thermal strain, telastic strain, e

strain,

r2

r1)1(2

EG

r3

r4Tt

Ee

r5

G

te

1D Linear Elastic Model

30

Flap Link ExampleParametric Design Description

ts1

A

Sleeve 1

A ts2

ds2

ds1

Sleeve 2

L

Shaft

b

h

t

b

h

t

sleeve_2

shaft

rib_1

material

flap_link

sleeve_1

rib_2

w

t

r

x

name

R3

R2

t2f

wf

tw

t1f

cross_section

w

t

r

x

R1

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;

Extended Constraint Graph

COB Structure (COS)

31

L

ws1

ts1

rs2

ws2

ts2

rs2

wf

tw

tf

E

name

linear_elastic_model

wf

tw

tf

inter_axis_length

sleeve_2

shaft

material

linkage

sleeve_1

w

t

r

E

cross_section:basic

w

t

r

x,max

r1

mode: tension

ux,max

Fcondition reaction

Representing External Tools as COB RelationsParametric FEA Model

ts1

rs1

L

rs2

ts2tf

ws2ws1

wf

tw

F

L L

x

y

L C

Plane Stress Bodies

),,,...,,,,(),( 1111max,max, FErstswsLru xx

FEA Tool

32

Constrained Object (COB) RepresentationCurrent Technical Capabilities - Generation 2

Capabilities & features:– Various forms: computable lexical forms, graphical forms, etc.

» Enables both computer automation and human comprehension– Sub/supertypes, basic aggregates, multi-fidelity objects– Multi-directionality (I/O changes)– Reuses external programs as white box relations– Advanced associativity added to COTS frameworks & wrappers

Analysis module/template applications (XAI/MRA): – Analysis template languages– Product model idealizations– Explicit associativity relations with design models & other analyses– White box reuse of existing tools (e.g., FEA, in-house codes)– Reusable, adaptable analysis building blocks

– Synthesis (sizing) and verification (analysis)

33

Constrained Objects (cont.) Representation Characteristics & Advantages - Gen. 2

Overall characteristics– Declarative knowledge representation (non-causal)– Combining object & constraint graph techniques– COBs = (STEP EXPRESS subset) +

(constraint graph concepts & views)

Advantages over traditional analysis representations– Greater solution control– Richer semantics

(e.g., equations wrapped in engineering context)– Unified views of diverse capabilities (tool-independent)– Capture of reusable knowledge – Enhanced development of complex analysis models

Toolkit status (XaiTools v0.4)– Basic framework, single user-oriented, file-based

34

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 (Boeing)» Circuit Board Thermomechanical Analysis

(DoD: ProAM; JPL/NASA)» Chip Package Thermal Analysis (Shinko)

– Summary

Part 4: Advanced Topics & Current Research

35

Techniques for Complex System Representation & Model Interoperability (CAD-CAE)

http://eislab.gatech.edu/research/

a. Multi-Representation Architecture (MRA)

1 Solution Method Model

ABB SMM

2 Analysis Building Block

4 Context-Based Analysis Model3

SMMABB

APM ABB

CBAM

APM

Design Tools Solution Tools

Printed Wiring Assembly (PWA)

Solder Joint

Component

PWB

body3body2

body1

body4

T0

Printed Wiring Board (PWB)

SolderJoint

Component

AnalyzableProduct Model

b. Explicit Design-Analysis Associativity

c. Analysis Module Creation Methodology

I n f o r m a l A s s o c i a t i v i t y D i a g r a m

C o n s t r a i n e d O b j e c t - b a s e d A n a l y s i s M o d u l eC o n s t r a i n t S c h e m a t i c V i e w

P l a n e S t r a i n B o d i e s S y s t e m

P W A C o m p o n e n t O c c u r r e n c e

CL

1

m a t e r i a l ,E( , )g e o m e t r y

b o d y

p l a n e s t r a i n b o d y , i = 1 . . . 4P W B

S o l d e rJ o i n t

E p o x y

C o m p o n e n tb a s e : A l u m i n a

c o r e : F R 4

S o l d e r J o i n t P l a n e S t r a i n M o d e l

t o t a l h e i g h t , h

l i n e a r - e l a s t i c m o d e l

A P M A B B

3 A P M 4 C B A M

2 A B Bc

4b o d y 3b o d y

2b o d y

1h oT

p r i m a r y s t r u c t u r a l m a t e r i a l

ii

i

1 S M M

D e s i g n M o d e l A n a l y s i s M o d e l

A B B S M M

s o l d e rs o l d e r j o i n t

p w b

c o m p o n e n t

1 . 2 5


t o t a l h e i g h t

d e t a i l e d s h a p e

r e c t a n g l e

[ 1 . 2 ]

[ 1 . 1 ]

a v e r a g e

[ 2 . 2 ]

[ 2 . 1 ]

cT c

T s

i n t e r - s o l d e r j o i n t d i s t a n c ea p p r o x i m a t e m a x i m u m

s j

L s

p r i m a r y s t r u c t u r a l m a t e r i a l

t o t a l t h i c k n e s s


P l a n e S t r a i n

g e o m e t r y m o d e l 3

a

s t r e s s - s t r a i nm o d e l 1



B o d i e s S y s t e m

x y , e x t r e m e , 3

T 2

L 1

T 1

T 0

L 2

h 1

h 2

T 3

T s j

h s

h c

L c

x y , e x t r e m e , s jb i l i n e a r - e l a s t o p l a s t i c m o d e l


p r i m a r y s t r u c t u r a l m a t e r i a l l i n e a r - e l a s t i c m o d e l

c o m p o n e n to c c u r r e n c e

s o l d e r j o i n ts h e a r s t r a i nr a n g e

[ 1 . 2 ]

[ 1 . 1 ]l e n g t h 2 +

3 A P M 2 A B B 4 C B A M

F i n e - G r a i n e d A s s o c i a t i v i t y

ProductModel Selected Module

Analysis Module Catalogs

MCAD

ECAD

Analysis Procedures

CommercialAnalysis Tools

Ansys

Abaqus

Solder Joint Deformation Model

Idealization/Defeaturization

CommercialDesign Tools

PWB

Solder Joint

Component

APM CBAM ABB SMM

Ubiquitous Analysis(Module Usage)

Ubiquitization(Module Creation)

CAE

Physical Behavior Research,Know-How, Design Handbooks, ...

36

Circuit Board Design-Analysis IntegrationElectronic Packaging Examples: PWA/B

Analysis Modules (CBAMs) of Diverse Mode & Fidelity

Design Tools

Laminates DB

FEA Ansys



XaiToolsPWA-B

XaiToolsPWA-B

Solder JointDeformation*

PTHDeformation & Fatigue**

1D,2D

1D,2D,3D


ECAD Tools Mentor Graphics,

Accel*


material model

temperature, T


cte,

youngs modulus, E

force, F

area, A stress,


strain,

total elongation,L

length, L

start, x1

end, x2

mv6

mv5

smv1

mv1mv4

E

One D LinearElastic Model(no shear)

T

et

thermal strain, t

elastic strain, emv3

mv2

x

FF

E, A,

LLo

T, ,

yL

r1

12 xxL

r2

oLLL

r4

A

F

sr1

oTTT

r3L

L

m a t e r i a l

e f f e c t i v e l e n g t h , L e f f


l i n e a r e l a s t i c m o d e l

L o

T o r s i o n a l R o d

G

J

r

2

1

s h e a r m o d u l u s , G

c r o s s s e c t i o n :e f f e c t i v e r i n g p o l a r m o m e n t o f i n e r t i a , J

a l 1

a l 3

a l 2 a

l i n k a g e

m o d e : s h a f t t o r s i o n

c o n d i t i o n r e a c t i o n

t s 1

A

S l e e v e 1

A t s 2

d s 2

d s 1

S l e e v e 2

L

S h a f t

L e f f

s

T

o u t e r r a d i u s , r o a l 2 b

s t r e s s m o s m o d e l

a l l o w a b l e s t r e s s

t w i s t m o s m o d e l


a l l o w a b l e

a c t u a l

M S


a l l o w a b l e

a c t u a l

M S

a l l o w a b l et w i s t Analysis Tools

PWBWarpage

1D,2D

Materials DB

PWB Stackup ToolXaiTools PWA-B

STEP AP210‡ GenCAM**,

PDIF*

37

Iterative Design & Analysis PWB Stackup Design & Warpage Analysis

AnalyzableProduct Model

PWB Stackup Design Tool

1 Oz. Cu

1 Oz. Cu

1 Oz. Cu

1 Oz. Cu

2 Oz. Cu

2 Oz. CuTetra GF

Tetra GF

3 x 1080

3 x 1080

2 x 2116

2D Plane Strain Model

b L T

t

2

Detailed FEA Check

bi i i

i

w y

t w/ 2

1D Thermal Bending Model

LayupRe-design

PWB Warpage Modules

Quick Formula-based Check

38

total_thicknesspwa

layup layers[0]

layers[1]

layers[2]

TOTAL

CU1T

CU2T

POLYT

PREPREGT

TETRA1T

EXCU

ALPXCU

EXEPGL

ALPXEGL

TO

deformation model

ParameterizedFEA Model

ux mos model


allowable

actual

MS

UX

condition

UY

SX

associated_pwb

nominal_thickness

prepregs[0] nominal_thickness

top_copper_layer nominal_thickness

related_core nominal_thickness

prepregs[0] nominal_thicknesslayers[3]

primary_structure_material linear_elastic_model E

cte

primary_structure_material linear_elastic_model E

cte

reference temperature

temperatureDELTAT

APM ABB

SMM

PWB Warpage Modulesa.k.a. CBAMs: COB-based analysis templates

deformation model

Thermal Bending Beam

L

b

T

Treference

t

T

total diagonalassociated_pwb

total thickness

coefficient of thermal bending

al1

al2

al6

al3

t

TLb

2

warpage

wrapage mos model

allowable

MSactual

Marginof Safety

associated condition

al5

al4

temperature

reference temperature

pwa

APM

ABBPWB Thermal Bending Model

(1D formula-based CBAM)

PWB Plane Strain Model (2D FEA-based CBAM)

APMUsage of Rich Product Models

39

Example Chip Package Products Source: www.shinko.co.jp

Plastic Ball Grid Array (PBGA) Packages Quad Flat Packs (QFPs)

Wafer Level Package (WLP)System-in-Package (SIP)

Glass-to-Metal Seals

40

Flexible High Diversity Design-Analysis Integration

Electronic Packaging Examples: Chip Packages/Mounting Shinko Electric Project: Phase 1 (production usage)

EBGA, PBGA, QFP

CuGround

PKG

Chip

Analysis Modules (CBAMs) of Diverse Behavior & Fidelity

FEAAnsys



XaiTools

XaiToolsChipPackage

ThermalResistance

3D

Modular, ReusableTemplate Librariestemperature change,T

material model

temperature, T


cte,

youngs modulus, E

force, F

area, A stress,


strain,

total elongation,L

length, L

start, x1

end, x2

mv6

mv5

smv1

mv1mv4

E

One D LinearElastic Model(no shear)

T

et

thermal strain, t

elastic strain, emv3

mv2

x

FF

E, A,

LLo

T, ,

yL

r1

12 xxL

r2

oLLL

r4

A

F

sr1

oTTT

r3L

L

m a t e r i a l

e f f e c t i v e l e n g t h , L e f f


l i n e a r e l a s t i c m o d e l

L o

T o r s i o n a l R o d

G

J

r

2

1

s h e a r m o d u l u s , G

c r o s s s e c t i o n :e f f e c t i v e r i n g p o l a r m o m e n t o f i n e r t i a , J

a l 1

a l 3

a l 2 a

l i n k a g e

m o d e : s h a f t t o r s i o n

c o n d i t i o n r e a c t i o n

t s 1

A

S l e e v e 1

A t s 2

d s 2

d s 1

S l e e v e 2

L

S h a f t

L e f f

s

T

o u t e r r a d i u s , r o a l 2 b

s t r e s s m o s m o d e l

a l l o w a b l e s t r e s s

t w i s t m o s m o d e l


a l l o w a b l e

a c t u a l

M S


a l l o w a b l e

a c t u a l

M S

a l l o w a b l et w i s t Analysis Tools

Design Tools

PWB DB

Materials DB*

Prelim/APM Design ToolXaiTools ChipPackage

ThermalStress

Basic3D**

** = Demonstration module

BasicDocumentation

AutomationAuthoringMS Excel

41

Typical Issues: Knowledge Representation,Inter-Model Associativity (Model Interoperability)

CAD Modelbulkhead assembly attach point

CAE Model channel fitting analysis

materialproperties

idealizedanalysis

geometry

analysisresults

detaileddesigngeometry

No explicit

fine-grained

CAD-CAE

associativity

inconsisten

cy littleautomationlittleknowledge capture

42

Analysis Tools

0.4375 in

0.5240 in

0.0000 in

2.440 in

1.267 in

0.307 in

0.5 in

0.310 in

2.088 in

1.770 in

67000 psi

65000 psi

57000 psi

52000 psi

39000 psi

0.067 in/in

0.030 in/in

5960 Ibs

1

10000000 psi

9.17

5.11

9.77

rear spar fitting attach point

BLE7K18


L29 -300



Program

Part

Feature


Template

1 of 1Dataset

strength model

r1

e

b

h

tb

te

Pu

Ftu

E

r2

r0

a

FtuLT

Fty

FtyLT

epuLT

tw

MSwall

epu

jm

MSepb

MSeps


Fsu

IAS FunctionRef D6-81766

end pad

base

material

wall

analysis context


condition:


bolt

fitting

headradius, r1

hole radius, ro

width, b

eccentricity, e


radius, r2

thickness, tb

hole










load, Pu

Ftu

Fty

FtyLT

Fsu

epu

epuLT

E

FtuLT


Flexible High Diversity Design-Analysis Integration Phases 1-3 Airframe Examples:

“Bike Frame” / Flap Support Inboard Beam

Analysis Modules (CBAMs) of Diverse Feature:Mode, & Fidelity

Design Tools

Materials DBFEA

Elfini*MATDB-like


XaiTools

XaiTools

Fitting:Bending/Shear

3D

1.5D


MCAD ToolsCATIA v4, v5

Lug:Axial/Oblique; Ultimate/Shear

1.5D

Assembly:Ultimate/

FailSafe/Fatigue*

* = Item not yet available in toolkit (all others have working examples)


0.7500 in

0.35 in

0.7500 in

1.6000 in

2

0.7433

14.686 K

2.40

4.317 K

8.633 K

k = norm


7050-T7452, MS 7-214

67 Ksi

L29 -300



Program

Part

Feature


Template


Dataset

material

deformation model


effective width, W

analysis context

objective


condition



allowable

actual

MS


thickness, t

edge margin, e

Plug joint

size,n

lugs

lugj hole

diameters


r1

n

P jointlug

L [ j:1,n ]

Plug

L [ k]Dk

oversize diameter, Dover

D

PaxuW

e

t

Ftuax

Kaxu


BDM 6630

Fasteners DB

FASTDB-like

General Math Mathematica

In-HouseCodes

Image API(CATGEO);

VBScript

43

Explicit Capture of Idealizations (part-specific template adaptation in bike frame case)

DetailedFeatures/ParametersTagged in CAD Model (CATIA)

zf

xf

cavity3.base.minimum_thickness

yf

xf

rib8

cavity 3

rib9

= t8,t 9

rib8.thicknessrib9.thickness

cavity3.width, w3

zf

yf

xf

zfxf

yf

i - Relations between idealized CAE parameters and detailed CAD parameters1 : b = cavity3.inner_width + rib8.thickness/2 + rib9.thickness/2

2 : te = cavity3.base.minimum_thickness

Idealized Features in CAE Model

Tension Fitting Analysis

yf

Often missing in

today’s process

2

1

te

b

44

Today’s Fitting Catalog Documentation from DM 6-81766 Design Manual

Channel Fitting End Pad Bending Analysis

AngleFitting

BathtubFitting

ChannelFitting

Categories of Idealized FittingsCalculation Steps

45

Modular Fitting TemplatesObject-Oriented Hierarchy of Analysis Building Blocks (ABBs)

Fitting Casing Body

Channel Fitting Casing Body*

Bathtub Fitting Casing Body

Angle FittingCasing Body

Fitting System ABB

Fitting Wall ABBFitting End Pad ABB

Fitting Bolt Body*

Open Wall FittingCasing Body

Fitting End Pad Bending ABB Fitting End Pad

Shear ABB*

Open Wall Fitting End Pad Bending ABB

Channel FittingEnd Pad Bending ABB*

e

se

tr

Pf

02

3 )2( b 1 teKC

21

e

be

ht

PCf

21 1 KKC

),,,( 011 erRrfK

),(2 we ttfK

),,( 13 hbrfK

baR

2

dfRe

),min( wbwaw ttt

bolt

load

Fitting Washer Body

Specialized Analysis Body

P

ABB

Specialized Analysis System

washercasing

* = Working Examples

ABB: - independent of specific products - usable on many designs

46

r1

sefactual shear stress,bolt.head.radius, r0

end_pad.thickness, te

load, P e

setr

Pf

02

Channel Fitting System ABBs

End Pad Bending Analysis

End Pad Shear Analysis

e n d _ p a d .e cce n tr ic ity , e

e n d _ p a d .w id th , b

b o lt.h o le .ra d iu s , r1

r2 r3

r1

h

r1

h

be n d _ p a d .h e ig h t, h3K

befa c tu a l b e n d in g s tre ss ,

ch a n n e l f itt in g fa c to r,

D M 6 -8 1 7 6 6 F ig u re 3 .3

b a se .th ickn e ss , tb

e n d _ p a d .th ickn e ss , te

lo a d , P

23 )2(e

bbeht

PteKf

0.1

0.2

0.3

0.41

1.5

2

2.5

3

0.4

0.6

0.8

1

0.1

0.2

0.3

0.4

ABB = analysis building block

47

“Bike Frame” Bulkhead Fitting Analysis TemplateUsing Constrained Object (COB) Knowledge/Info Representation

0.4375 in

0.5240 in

0.0000 in

2.440 in

1.267 in

0.307 in

0.5 in

0.310 in

2.088 in

1.770 in

67000 psi

65000 psi

57000 psi

52000 psi

39000 psi

0.067 in/in

0.030 in/in

5960 Ibs

1

10000000 psi

9.17

5.11

9.77

bulkhead fitting attach point

LE7K18


L29 -300



Program

Part

Feature


Template

1 of 1Dataset

strength model

r1

e

b

h

tb

te

Pu

Ftu

E

r2

r0

a

FtuLT

Fty

FtyLT

epuLT

tw

MSwall

epu

jm

MSepb

MSeps


Fsu

IAS FunctionRef DM 6-81766

end pad

base

material

wall

analysis context


condition:


bolt

fitting

headradius, r1

hole radius, ro

width, b

eccentricity, e


radius, r2

thickness, tb

hole










load, Pu

Ftu

Fty

FtyLT

Fsu

epu

epuLT

E

FtuLT


e

se

tr

Pf

02

21

e

be

ht

PCf

),,( 13 hbrfK

48

Bike Frame Bulkhead Fitting AnalysisCOB-based Analysis Template - in XaiTools

Detailed CAD datafrom CATIA

Idealized analysis features in APM

Explicit multi-directional associativity between detailed CAD data & idealized analysis features

Modular generic analysis templates(ABBs)

Library data for materials & fasteners

Focus Point ofCAD-CAE Integration

Object-oriented spreadsheet

49

Cost of Associativity GapsReference: http://eislab.gatech.edu/pubs/reports/EL004/

Categories of Gap Costs• Associativity time & labor - Manual maintenance - Little re-use - Lost knowledge• Inconsistencies• Limited analysis usage - Fewer parts analyzed - Fewer iterations per part• “Wrong” values - Too conservative: Extra part costs and performance inefficiencies - Too loose: Re-work, failures, law suits

e

se

tr

Pf

02

21

e

be

ht

PCf

),,( 13 hbrfK

Analysis Model(with Idealized Features)

Detailed Design Model

Channel Fitting Analysis

idealizations

No explicit

fine-grained

CAD-CAE

associativity

000,000,10$gap

$10 gaps000,000,1

gaps000,000,1analysis

variables 10

part

analyses 10parts 000,10

OOO

OOOO

Initial Cost Estimate per Complex Product (only for manual maintenance costs of structural analysis problems)

50

Information Capture Gaps:Content Coverage and Semantics

Existing Tools

Tool A1 Tool An...

“dumb” information capture(only human-sensible,I.e., not computer-sensible)

LegendContent

Coverage Gaps

ContentSemantic Gaps

Smart Product ModelBuilding Blocks • Models & meta-models

• International standards• Industry specs• Corporate standards• Local customizations

• Modeling technologies:• Express, UML, XML, COBs, …

Example “dumb” figures

51

Summary Tool independent model interoperability

– Application focus: analysis template methodology

Multi-representation architecture (MRA) & constrained objects (COBs):– Addresses fundamental gaps:

» Idealizations & CAD-CAE associativity: multi-fidelity, multi-directional, fine-grained

– Based on information & knowledge theory– Structured, flexible, and extensible

Improved quality, cost, time:– Capture engineering knowledge in a reusable form – Reduce information inconsistencies– Increase analysis intensity & effectiveness

» Reducing modeling cycle time by 75% (production usage)

52

For Further Information ...

Contact: [email protected]

Web site: http://eislab.gatech.edu/– Publications, project overviews, tools, etc.– See: X-Analysis Integration (XAI) Central

http://eislab.gatech.edu/research/XAI_Central.doc

– Engineering Framework Interest Group (EFWIG)http://eislab.gatech.edu/efwig/

XaiTools™ home page: http://eislab.gatech.edu/tools/XaiTools/

Pilot commercial ESB: http://www.u-engineer.com/– Internet-based self-serve analysis– Analysis module catalog for electronic packaging– Highly automated front-ends to general FEA & math tools

elements towards next-generation knowledge representations and product modeling techniques...

Documents

instance state

instance slide

cob slide

instance example

example cob instance

triangle base

shape schematics

triangle volume