1

Enhancing engineering design and analysis interoperability, Part 1. Constrained Objects

First M.I.T. Conference on Computational Fluid and Solid MechanicsJune, 2001

Miyako W. Wilson, Russell Peak, and Robert E. FultonGeorgia Institute of Technology

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Motivation

• The need for a unified physical behavior modeling representation with the following characteristics– Has tailoring for design-analysis integration including

supports for multi-fidelity idealization, product-specific analysis templates, and CAD-CAE tool interoperability.

– Supports product information-driven analysis (I.e., supports plugging in detail design objects and idealizing them into a diversity of analysis models).

– Has computer-processible lexical forms along with human-friendly graphical forms.

– Represents relations in a non-casual matter (I.e., enables multi-directional combinations of model inputs/outputs).

– Capture engineering knowledge in a modular reusable form

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Constrained Object (COB) Overview - Techniques Leveraged

• Object-oriented modeling [Lalonde & Pugh, et al.1990, Muller 1997]

– class vs instance – inheritance

• Constraint graph techniques [Borning, et al. 1990]

– relations without fixed input/output direction – Declarative knowledge representation (non-casual)

• Characterized by entities, attributes, and relations

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DefinitionLanguages

GraphicalRepresentations

COB RepresentationComponents

COB

MetaInformation

ModelProtocol

MetaInformation

ModelProtocol

Developers

Users

DefinitionLanguages

GraphicalRepresentations

5

L

L

Fk

u n d e fo rm e d le n g th ,

s p r in g c o n s ta n t, fo rc e ,

to ta l e lo n g a tio n ,

1x

Lle n g th ,0

2x

s ta rt,

e n d ,

oLLL

12 xxL

LkF

r1

r2

r3

Constraint Schematic-S

Spring

LL

Fk

1x L

0

2x

Subsystem View(for reuse by other COBs)

COB spring ; undeformed_length, L₀ : REAL; spring_constant, k : REAL; start, x₁ : REAL; end, x₂ : REAL; length, L : REAL; total_elongation, &Delta;L : REAL; force, F : REAL; RELATIONS r1 : "<length> == <end> - <start>"; r2 : "<total_elongation> == <length> - <undeformed_length>"; r3 : "<force> == <spring_constant> * <total_elongation>";END_COB;

COS Language

FF

k

L

deformed state

Lo

L

x2x1

Figure

LkFr

LLLr

xxLr

:

:

:

3

02

121Relations

Traditional Form

Example COB Structure (COS)Spring Primitive

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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 Instance (COI)Spring Primitive

Constraint Schematic-I Lexical COB Instance (COI)

state 1.0 (unsolved):

INSTANCE_OF spring; undeformed_length : 20.0; spring_constant : 5.0; total_elongation : ?; force : 10.0;END_INSTANCE;

state 1.1 (solved):

INSTANCE_OF spring; undeformed_length : 20.0; spring_constant : 5.0; start : ?; end : ?; length : 22.0; total_elongation : 2.0; force : 10.0;END_INSTANCE;

Basic Constraint Schematic-I Notation

22 mm

10 N

2 mm

5 N/mm

20 mm

L

L

Fk

undeformed length,

spring constant, force,

total elongation,

1x

Llength,0

2x

start,

end,

oLLL

12 xxL

LkF

r1

r2

r3

example 1, state 1.1

7

2 mm

40 N20 N/mm

20 mm

10 mm

32 mm

22 mm

L

L

Fk

undeformed length,

spring constant, force,

total elongation,

1x

Llength,0

2x

start,

end,

oLLL

12 xxL

LkF

r1

r2

r3

Multi-Directional I/O (non-causal)Spring Primitive

Constraint Schematic-I Lexical COB Instance (COI)

state 5.0 (unsolved):

INSTANCE_OF spring; undeformed_length : 20.0; spring_constant : ?; start : 10.0; length : 22.0; force : 40.0;END_INSTANCE;

state 5.1 (solved):

INSTANCE_OF spring; undeformed_length : 20.0; spring_constant : 20.0; start : 10.0; end : 32.0; length : 22.0; total_elongation : 2.0; force : 40.0;END_INSTANCE;

Design Verification

Design Synthesis

example 1, state 1.1

example 1, state 5.1

22 mm

10 N

2 mm

5 N/mm

20 mm

L

L

Fk

undeformed length,

spring constant, force,

total elongation,

1x

Llength,0

2x

start,

end,

oLLL

12 xxL

LkF

r1

r2

r3

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System Figure

P

k1 k2

2u1u

L10

k1

x12

F1

L1

L1

x11

F1

L20

k2

x22

F2

L2

L2

x21

F2

Free Body Diagrams

Variables and Relations

COB Representation Traditional Form: Spring System

System-Level Relations(Boundary Conditions)

22223

202222

2122221

11113

101112

1112111

:

:

:

:

:

:

LkFr

LLLr

xxLr

LkFr

LLLr

xxLr

1226

115

24

213

21122

111

:

:

:

:

:

0:

uLubc

Lubc

PFbc

FFbc

xxbc

xbc

Spring 1

Spring 2

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COB Representation Constraint Graph: Spring System

P

k1 k2

2u1u

spring2spring1

L10

k1

L1

L1

L20

k2

x21

x22

F2

L2

L2

F1

bc4

r12

r13

r22

r23

bc5bc6

bc3

r11r21

bc2

bc1

x11

x12

u1 u2

P

1226

115

24

213

21122

111

:

:

:

:

:

0:

uLubc

Lubc

PFbc

FFbc

xxbc

xbc

Constraint Graph-S

22223

202222

2122221

11113

101112

1112111

:

:

:

:

:

:

LkFr

LLLr

xxLr

LkFr

LLLr

xxLr

Spring 1

Spring 2

System level

10

spring2

spring1

L10

k1

L1

L1

L20

k2

x21

x22

F2

L2

F1

x11

x12

u1 u2

P

L2

bc4

r12

r13

r22

r23

bc5bc6

bc3

r11r21

bc2

bc1

COB Representation Extended Constraint Graph-S: Two Spring System

Extended Constraint Graph-S

Constraint Graph-S

• Groups objects & relations into parent objects• Object-oriented vs. flattened

spring 2

L

Lundeformed length,

spring constant, k

Fforce,

total elongation,

1xLlength,

0

2x

start,

end,

oLLL

12 xxL

LkF

r1

r2

r3

spring 1two-spring system

deformation 1, u1

deformation 2, u2

force , P

L

Lundeformed length,

spring constant, k

Fforce,

total elongation,

1xLlength,

0

2x

start,

end,

oLLL

12 xxL

LkF

r1

r2

r3

partial(BC relations not included)

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COB Representation Constraint Schematic: Spring System

bc1

spring 1

2u

spring 2

1u

P

SpringElementary

LL

Fk

1x L

0

2x

122 uLu

bc2 bc3

bc4

bc6

SpringElementary

LL

Fk

1x L

0

2x

bc5

011 x

spring2spring1

L10

k1

L1

L1

L20

k2

x21

x22

F2

L2

L2

F1

bc4

r12

r13

r22

r23

bc5bc6

bc3

r11r21

bc2

bc1

u1 u2

P

x11

x12

Constraint Schematic-S

Constraint Graph-S

• Encapsulated form (hides details)•Template re-usage

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bc1

spring 1

2u

spring 2

1u

P

SpringElementary

LL

Fk

1x L

0

2x

122 uLu

bc2 bc3

bc4

bc6

SpringElementary

LL

Fk

1x L

0

2x

bc5

011 x

COB Representation Constraint Schematic-S: Spring System

22223

202222

2122221

11113

101112

1112111

:

:

:

:

:

:

LkFr

LLLr

xxLr

LkFr

LLLr

xxLr

P

k1 k2

u2u1

System-Level Relations(Boundary Conditions)

Analysis Primitiveswith

Encapsulated Relations

1226

115

24

213

21122

111

:

:

:

:

:

0:

uLubc

Lubc

PFbc

FFbc

xxbc

xbc

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COB Representation COS Language: Spring System

COB spring_system ; spring1 : spring; spring2 : spring; deformation1, u₁ : REAL; deformation2, u₂ : REAL; load, P : REAL; RELATIONS r1 : "<spring1.start> == 0.0"; r2 : "<spring1.end> == <spring2.start>"; r3 : "<spring1.force> == <spring2.force>"; r4 : "<spring2.force> == <load>"; r5 : "<deformation1> == <spring1.total_elongation>"; r6 : "<deformation2> == <spring2.total_elongation> + <deformation1>";END_COB;

Constraint Schematic-S

b c 1

s p r i n g 1

2u

s p r i n g 2

1u

P

S p r i n gE l e m e n t a r y

LL

Fk

1x L

0

2x

122 uLu

b c 2 b c 3

b c 4

b c 6

S p r i n gE l e m e n t a r y

LL

Fk

1x L

0

2x

b c 5

011 x

COS Language

P

k1 k2

u2u1

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b c 1

s p r i n g 1

2u

s p r i n g 2

1u

P

S p r i n gE l e m e n t a r y

LL

Fk

1x L

0

2x

122 uLu

b c 2 b c 3

b c 4

b c 6

S p r i n gE l e m e n t a r y

LL

Fk

1x L

0

2x

b c 5

011 x

1 . 8 1 8

1 0 . 0 6 . 0

8 . 0

5 . 5

8 . 0

3 . 4 8 5

9 . 8 1 8

1 0 . 0

1 0 . 0

9 . 8 1 8

1 . 6 6 7

9 . 6 6 7

1 9 . 4 8

1 . 8 1 8

9 . 8 1 8

COB Representation COB Instance (COI): Spring System

Constraint Schematic-ICOI Language

P

k1 k2

u2u1

state 1.0 (unsolved):INSTANCE_OF spring_system; spring1.undeformed_length : 8.0; spring1.spring_constant : 5.5; spring2.undeformed_length : 8.0; spring2.spring_constant : 6.0; load : 10.0; deformation2 : ?;END_INSTANCE;

state 1.1 (solved):INSTANCE_OF spring_system; spring1.undeformed_length : 8.0; spring1.spring_constant : 5.5; spring1.start : 0.0; spring1.end : 9.818; spring1.force : 10.0; spring1.total_elongation : 1.818; spring1.length : 9.818; spring2.undeformed_length : 8.0; spring2.spring_constant : 6.0; spring2.start : 9.818; spring2.force : 10.0; spring2.total_elongation : 1.667; spring2.length : 9.667; spring2.end : 19.48; load : 10.0; deformation1 : 1.818; deformation2 : 3.485;END_INSTANCE;

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COB Representation Lexical and Graphical Views

COB Instance(COI)

Language

Extended Constraint Graphs-I

Constraint Schematic-I

STEP

Part 21

200 lbs

30e6 psi

100 lbs 20.2 in

R101

R101

100 lbs

30e6 psi 200 lbs

20.2 inHTML

Subsystem -S view

Object Relationship Diagram

COB Structure (COS)

Language

I/O Tables

Extended Constraint Graphs-S

Constraint Schematic-S

STEP

Express

Express-G

HTML

COB Structure (COS) COB Instance (COI)

Constraint Graphs-S

Constraint Graph = Constraint Network

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DefinitionLanguages

GraphicalRepresentations

COB RepresentationComponents (see Wilson,2000)

COB

MetaInformation

ModelProtocol

MetaInformation

ModelProtocol

Developers

Users

DefinitionLanguages

GraphicalRepresentations

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COB Meta Information Model & Protocol Generic Nature

GenericMetadata

GenericData

SpecificStructureData

SpecificInstanceData

COBInstanceDefinitionData

COBStructureDefinitionData

Example:

COICOICOSCOS

L

kx2

F

LL

x1F 10.010.0

20.020.0

5.05.0

22.022.02.02.0

10.010.0 32.032.0

Graphical Representations

Pro

toco

l

Definition Languages

Meta InformationModel

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COB Instances

COB Structures

Constraint Network

XaiTools ™

X-Analysis Integration Toolkit

GenericViewer

ConstraintSolverMathematica

FEAANSYS

COB Definition Files

COB basedDesign/Analysis

Tools

Solvers

API

Java

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Using Internet/Intranet-based Analysis Solvers Thick Client Architecture

Client PCs

XaiTools

Thick Client

Users

Internet

Iona orbixdj

Mathematica

AnsysInternet/Intranet

XaiTools AnsysSolver Server

XaiTools AnsysSolver Server

XaiTools Math.Solver Server

CORBA Daemon

XaiTools AnsysSolver Server

FEA Solvers

Math Solvers

CORBA Servers

CO

RB

A IIO

P

...

Engineering Service BureauHost Machines

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XaiTools ™ COB BrowserSpring System

Functionality:

• View

• Change value

• Change I/O

• Activate/Disactivate relations

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Constrained Object (COB) Representation

• Capabilities & features:– Various forms: computable lexical forms, graphical forms– Sub/supertypes, basic aggregates, multi-fidelity objects– Multi-directionality (I/O change)– Wrapping external programs as white box relations

• Analysis module/template applications (XAI): – 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)

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Constrained Objects (cont.) Representation Characteristics & Advantages

• 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 view of diverse capabilities– Capture of reusable knowledge– Enhanced development of complex analysis models