An Introduction to X-Analysis Integration (XAI) Part 4: Advanced Topics & Current Research Georgia Tech Engineering Information Systems Lab eislab.gatech.edu

An Introduction toX-Analysis Integration (XAI)

Part 4: Advanced Topics & Current Research

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.

2Engineering Information Systems Lab eislab.gatech.edu© 1993-2001 GTRC

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


Advanced Topics & Current ResearchOutline

Advanced Product Information-Driven FEA Modeling– Focus on cases with:

» Variable topology multi-body geometries» Different design & analysis geometries» Mixed analytical bodies and idealized interfaces

Constrained Object (COB) Extensions– Automating support for multiple views– Next-generation capabilities

Optimization and the MRA


1

2

3

1

2

3

12

4

1a

2

3a

1b

1c

3b 3c

3a 3b

2

1a 1b 1c

1d 1e

3

1a 1b

1c1d

23

4a 4b 4c

Analytical Bodies FEA Model Decomposed Volumes

original

topology change (no body change)

variable body change(includes topology change)

Variable Topology Multi-Body (VTMB) FEA Meshing Challenges

Labor-intensive “chopping”


Product Information-Driven FEA MethodologyPurpose of VTMB Methodology [Gen. 1 - Koo, 2000]

algorithmij

Design Types i = 1…m Analysis Types j = 1…n

Design Instances Analysis Instances

VTMB FEA ModelsVTMB

Methodologycreate algorithmij

once

for a given ij j{1…n} (not all design types have all analysis types)e.g.) for i=1(EBGA), j=1(thermal resistance) j=2 (thermal stress) for i=2 (PWB), j=1 (warpage)

Chip package APMs thermal resistance CBAMs

PWB APMsthermal stress CBAMs

ANSYS SMMs

VTMB= variable topology multi-body

use algorithmij

many times


Gen. 2 Research Questionsa) How to represent ABB assembly?

Overall Objectives [Zeng thesis] Develop broader algorithm(s)

vs. Koo method [2000] Clarify & generalize representations

vs. Zhou method [1997]

L1

C1C2

C1 C2

S1

Distributed Force

Slip bonding

Glue bonding

Shell Body A

Continuum B

Fully constraint

Assembly Framework

L1 : Loading Constraints

C1,C2 :Connectivity Constraints

S1 :Support Constraints

Example ABB assembly


ABB assembly view ABB assembly view combined with ANSYS-specific consideration

Research Questionsb) How represent Preprocessor Solution Method Model (PSMM)?

(FEA model specific)


L1 L1

C1 C1

C1 C1

C2

C2 S1

S1

S1

PSMM framework

Research Questionsb) How represent Preprocessor Solution Method Model? (cont.)

(FEA model specific)


Research Questions c) How map ABB assembly model to PSMM?

L1

C1

C2

C1

C2

S1

ABB Assembly Framework

L L

C C

C1

C1

C

C2

SS

S

Preprocessor SMM Framework

ABBPSMM


Chip Package Applications

Automatic FEA Pre/Post-processing & Solution (in vendor-specific Solution Method Model)

Idealized Model(ABB Assembly)


Benchmark ExampleExtended wing in-deck galley end tie (ewidget) - case 1

Case 1.a• Blocks = analytical solids (turns into FEA elements)• Sheet = analytical shell• Idealized body interfaces = no-slip

Case 1.bSame as 1.a except:• Idealized body interfaces = mixture of no-slip and possible gap regions

Design model

Idealized geometry for analytical model(not shown yet)


Benchmark ExampleExtended wing in-deck galley end tie (ewidget) - case 2

Case 2

Same as 1.a except:• Need transition between blocks for shell surfaces (matching outer vs. inner faces vs. mid-plane faces)

Design model

Idealized geometry for analytical model(not shown yet)


Airframe ApplicationsAutomatic FEA Pre/Post-processing & Solution

(in vendor-specific Solution Method Model)Design Model


Status: Advanced Product Info-Driven FEA Modeling

Building on previous work PhD thesis proposal underway [Zeng] Target applications identified & work underway:

– Chip package thermal analysis (Shinko)– Airframe structural analysis (Boeing)



Advanced Product Information-Driven FEA Modeling




Constrained Object (COB) RepresentationCurrent Technical Capabilities - Generation 2

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

Analysis module/template applications: – 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)


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)– Capture of reusable knowledge– Enhanced development of complex analysis models

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


Planned Generation 3 + COB Enhancements

Use standard forms: Express v3, STEP Parametrics, XML, UML OCL, …

Leverage standard content: STEP generic resources, APs, ... Support concurrent multiple users (block points/buffering,

synchronization, …) Enable interactive COS and COI construction Provide variety of interaction views/forms:

– textual/graphical– geometric/logical– definition/solution/documentation– traditional (e.g., classical equation form)


Interaction Views/Forms information structure navigation template/instance textual/graphical geometric/logical definition/solution/documentation traditional (e.g., classical equation form) native CAD/CAE tool specialized application view

Novice Users: Graphical forms and specialized applicationsExpert Users: All forms

Each form has its niche


COB Modeling Views

COB InstanceLanguage

Extended Constraint Graphs-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

Subsystem Views

Object Relationship Diagram

COB SchemaLanguage

I/O Tables

Extended Constraint Graphs

Constraint Schematic

STEPExpress

Express-G

HTML

HTML


COB Structure: Graphical Forms

Spring 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 NotationTemplate Structure (Schema )

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


FF

k

L

deformed state

Lo

L

x2x1

Parameterized Figure

LkFr

LLLr

xxLr

:

:

:

3

02

121

Relations

SpringElementary

LL

Fk

1x L

0

2x

Subsystem View(for reuse by other COBs)


COB Structure: Lexical Form Spring Primitive

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


Lexical COB Schema Template

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


22 m m

10 N

2 m m

5 N /m m

20 m m

e xa m p le 1 , s ta te 1

L

L

Fk

unde fo rm ed leng th ,

sp ring cons tan t, fo rce ,

to ta l e longa tion ,

1x

Lleng th ,0

2x

s ta rt,

end ,

oLLL

12 xxL

LkF

r1

r2

r3

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

COB Instance ViewsSpring Primitive

Constraint Schematic Instance Views Lexical COB Instances

Basic Constraint Schematic NotationInstances

input:

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

result (reconciled):

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;


spring2

spring1

Constraint Graph-STwo Spring System

P

k1 k2

2u1u

22223

202222

2122221

11113

101112

1112111

:

:

:

:

:

:

LkFr

LLLr

xxLr

LkFr

LLLr

xxLr

L10

k1

L1

L1

L20

k2

x21

x22

F2

L2

F1

x11

x12

u1 u2

P

1226

115

24

213

21122

111

:

:

:

:

:

0:

uLubc

Lubc

PFbc

FFbc

xxbc

xbc

L2

bc4

r12

r13

r22

r23

bc5bc6

bc3

r11r21

bc2

bc1


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

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)


Multi-Disciplines/Users Constraint Schematic

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 (CBAMs) of Diverse Mode & Fidelity

MCAD Tools

Materials DB

FEA Ansys

Abaqus*

CATIA Elfini*

MSC Nastran*

MSC Patran*

General MathMathematica

Matlab*

MathCAD*

Analyzable Product Model(APM)

Extension

Torsion

1D

1D

Generic Analysis Templates(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

E

One D LinearElastic Model

T

G

e

t

material model

polar moment of inertia,J

radius, r

undeformed length,Lo

twist,theta start,1

theta end,2

r1

12

r3

0Lr

JrTr

torque,Tr

temperature change,T

cte,

youngs modulus, E

stress,

shear modulus, G

poissons ratio,

shear stress, shear strain,

thermal strain, t

elastic strain, e

strain,

r2

r1)1(2

EG

r3

r4Tt

Ee

r5

G

te

1D Linear Elastic Model

Continuum ABB

Extensional Rod

Linear-Elastic

E

One D Linear

(no shear)

T

e

t

temperature change,T

material model

temperature,T

reference temperature,To

cte,youngs modulus,E

force,F

area,A stress,

undeformed length,Lo

strain,

total elongation,L

length,L

start,x1

end,x2

mv6

mv5

smv1

mv1mv4

thermal strain,t

elastic strain,e

mv3

mv2

x

FF

E, A,

LLo

T, ,

yL

r1

12 xxL

r2

oLLL

r4

A

F

sr1

oTTT

r3L

L

Elastic Model

x

TT

G, r, ,

,J

Lo

y

Material Model ABB

Torsional Rod

ts1

B

sleeve1

B ts2

ds2

ds1

sleeve2

L

shaft

Leff

s

rib1 rib2

material


deformation 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)


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

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

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

L o

E x t e n s i o n a l R o d( i s o t h e r m a l )

F

L

A

L

E

x 2

x 1

y o u n g s m o d u l u s , E

c r o s s s e c t i o n a r e a , A

a l 1

a l 3

a l 2

l i n k a g e

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

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

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

y

xPP

E , A

LL e f f

,

Lt 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

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

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

Pullable Documentation Views

* Boundary condition objects & pullable views are WIP*

(1) Extension Analysisa. 1D Extensional Rodb. 2D Plane Stress FEA

1. Mode: Shaft Tension

2. BC ObjectsFlaps down : F =

3. Part Feature (idealized)

4. Analysis Calculations

1020 HR Steel

E= 30e6 psi

Leff = 5.0 in

10000 lbs

AF

ELL eff

5. Objective

A = 1.13 in2

allowable 18000 psi

1

allowableMS 1.03

(2) Torsion Analysis

(1a) Analysis Problem for 1D Extension Analysis

Solution Tool Links

BC Object Links(other analyses)*

Design/Idealization Links

Material Links

Pullable Views*

Flap Link SCN


Views with FEA templates & Native CAE

ts1

rs1

L

rs2

ts2tf

ws2ws1

wf

tw

F

L L

x

y

L C

Plane Stress Bodies

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


Generic COB Browser with design and analysis objects

(attributes and relations)

SpecializedAnalysis Module Tool

with idealized package cross-section

Idealized Graphical Views, Generic Browser,& Specialized Applications


Parameterized Geometry at Preliminary Design Fidelity

APM = analyzable product model


Native CAD

inter_axis_length

sleeve2.width

sleeve2.inner_diameter


Planned Generation 3 + Other COB Enhancements

Support units and automatic conversions Extend COI language capabilities Improve constraint graph algorithms

– Support structural loops– Support multiple subsolvers (for specified subgraphs)

Enable hybrid declarative/procedural approaches Allow constraint hierarchies

(i.e., relations with variable satisfaction priorities) Support enhanced relations Support explicit COS categories

(e.g., APMs, CBAMs, ABBs) Versioning & configuration management of structure


Enhanced Relations

Inequalities– Enable capture of model assumptions & limitations

Arbitrary aggregate elements: a[ i ] = 5 + a[i+1] a[n/2] = 9

Object relations: vs. Real no. relations: point1 = point2 point1.x = point2.x

Conditionals (higher order constraints): if (x > y) then (a = b)

Buffered relations


Status: Next Gen. COBs and Views

Building on previous work Needs and anticipated approaches identified Seeking extension opportunities



Advanced Product Information-Driven FEA Modeling




Thesis AbstractObject Oriented Paradigm for Optimization Model Enhancement

Doctoral ThesisGeorgia Institute of Technology, Atlanta.

http://eislab.gatech.edu/Selçuk Cimtalay

Nov. 2000

The modeling process that transforms a detailed product design and its multi-fidelity analysismodels into an optimization model is a non-trivial task requiring large amounts of diverseinformation, engineering theory, and experienced-based heuristics, as well as the support ofoptimization, design, and analysis tools. Engineering optimization can be viewed as aninformation intensive problem that requires engineering information solutions.

This research has focused on developing a new information representation of optimizationmodels, termed Enhanced Optimization Model (EOM). EOM represents an informationframework for an object oriented design methodology for optimization model construction,enhancement, classification and solution. EOM utilizes a combination of constraint graph andobject techniques to provide semantically rich mappings. EOM representation consists of aninformation model structure and protocol, and modeling languages for creating EOM objects.Specifically, EOM representation is developed as an information representation by focusing onthe optimization aspects to partition the optimization area into more trackable and modularobjects. Key distinctions are the explicit representation of the associativity between anoptimization model and its analysis and design models and the ability to support multi-fidelityoptimization models as the design progresses.

EOM concepts have been prototyped in Java in conjunction with optimizers (Bolink, CONMINetc.), analyzers (Ansys FE) and symbolic solvers (Mathematica). Structural analysis andelectronic packaging test cases illustrate the different characteristics and help to evaluate theEOM representation with respect to the thesis objectives. Results show that EOM representationenables the enhancement ability to capture optimization model building information, to modifythe models easily, and provide flexibility to designers.


Mfg. CAD/CAM,Measurements

etc.

Conditions

MCAD

ECAD

Analysis Results

Ansys

Abaqus

CAE

Analysis Results

Ansys

Abaqus

CAE

Analysis Module Catalogs

SelectedAnalysis Module (CBAM)

AutomatedIdealization/

Defeaturization

Product Model

Optimization Integration Thrust(work-in-process)

ImprovedDesign / Process

Optimization Module (OMEP)

CONMIN

DSIDES

X 1

X 2

F e a s i b l e R e g i o n

x x u p2

x xl o w 2

g x p1 0( , )

g x p2 0( , )

X 1

X 2

F e a s i b l e R e g i o n

x x u p2

x xl o w 2

g x p1 0( , )

g x p2 0( , )


Optimization Model Diversity

Min Weight

g (x)<0h(x) =0

subject toStressDesign variablesArea

Min Weight

OPTIMIZATION MODEL CLASS

Optimization Object 1 Optimization Object 2

Min Weight

subject to

X(H)

Min Weight

subject to

X(H,LL,LR)

OPTIMIZATION MODEL CLASS

Optimization Object 1 Optimization Object 2

Min Weight, Cost

subject to

Optimization Object 3

X(H,LL,LR,Mat)

g (x)<0h(x) =0

g (x)<0h(x) =0

2D PLANE STRAIN MODEL

1D EXTENSIONAL STRESS MODEL

Analysis Model(s)Enhancement and/or Addition

subject toStressBucklingDesign variablesArea, Material

y

xPP

E, A

LLeff

,

L

Objective, design variable, and/or constraint function enhancement


Optimization Model Enhancement

MinimizeLAf

1 WeightSubject to

0)(1 AMSg stress Normal Stress Margin of Safety

Design variables

X={A}

MinimizeLAf

1 WeightSubject to


Design variables

X={A, material}

OPTIMIZATION MODEL I

OPTIMIZATION MODEL II


Minimization of Weight of a LinkageX(area) subject to (extensional stress)

Leff

product structure: linkage

material


deformation model


Lo


F

L

A

L

E

x2

x1

youngs modulus, E


al1

al3

al2

analysis context

goal: optimization

mode: shaft tension

condition: flaps down

linkage reaction

allowable stressMargin of Safety

(> case)

allowableactual

MS

ts1

A

Sleeve 1

A ts2

ds2

ds1

Sleeve 2

L

Shaft

Leff

s

y

xPP

E, A

LLeff

,

L

minimize weight

constraint

Design VariableA

weight,WW AL

MS 0

density,

MSstress

1

allowablestressMS


Minimization of Weight of a LinkageX(area, material) subject to (extensional stress)

Leff


material


deformation model


Lo


F

L

A

L

E

x2

x1

youngs modulus, E


al1

al3

al2

analysis context

goal: optimization

mode: shaft tension


linkage reaction

allowable stressMargin of Safety

(> case)

allowableactual

MS

ts1

A

Sleeve 1

A ts2

ds2

ds1

Sleeve 2

L

Shaft

Leff

s

y

xPP

E, A

LLeff

,

L

minimize weight

constraint

Design Variablearea,A

weight,WW AL

MS 0

density,

MSstress

1

allowablestressMS

material


Optimization Model Enhancement

M i n i m i z eLAf 1 W e i g h t

S u b j e c t t o0)(1 AMSg stress N o r m a l S t r e s s M a r g i n o f S a f e t y

0)(2 AMSg buckling B u c k l i n g M a r g i n o f S a f e t yD e s i g n v a r i a b l e s

X = { A }

MinimizeLAf

1 WeightSubject to


0)(2 AMSg buckling Buckling Margin of SafetyDesign variables

X={A, material}

OPTIMIZATION MODEL III

OPTIMIZATION MODEL IV


Minimization of Weight of a LinkageX(area) subject to (extensional stress, buckling load)

Leff


material


deformation model


Lo

Extensional Rod(isothermal, buckling)

F

L

A

L

E

x2

x1

youngs modulus, E


analysis context

goal: optimization

mode: shaft tension


linkage reaction

allowable stress


allowableactual

MS

ts1

A

Sleeve 1

A ts2

ds2

ds1

Sleeve 2

L

Shaft

Leff

s

y

xPP

E, A

LLeff

,

L

minimize weight

constraints

Design VariablesA

weight,W W AL

MS 0MSstress


allowableactual

MS

moment of inertia, I

L

EIPcr

2

1

allowablestressMS

1F

PcrMSbuckling

load,P

MSbuckling

Lo

Extensional Rod(Buckling)

PcrI

E

density,


Minimization of Weight of a LinkageX(area, material) subject to (extensional stress, buckling load)

Leff


material


deformation model


Lo

Extensional Rod(isothermal, buckling)

F

L

A

L

E

x2

x1

youngs modulus, E


analysis context

goal: optimization

mode: shaft tension


linkage reaction

allowable stress


allowableactual

MS

ts1

A

Sleeve 1

A ts2

ds2

ds1

Sleeve 2

L

Shaft

Leff

s

y

xPP

E, A

LLeff

,

L

minimize weight

constraints

Design Variables A

weight,W W AL

MS 0MSstress


allowableactual

MS

moment of inertia, I

L

EIPcr

2

1

allowablestressMS

1F

PcrMSbuckling

load,P

MSbuckling

Lo

Extensional Rod(Buckling)

PcrI

E

density,

material


Status: Optimization

Initial PhD thesis completed [Cimtalay, 2001] Seeking insertion & extension opportunities Need to leverage recent optimization tools

– Ex. iSIGHT, ProductCenter, …– Provide enhanced modularity & knowledge capture

Documents

An Introduction to X-Analysis Integration (XAI) Part 4: Advanced Topics & Current Research Georgia Tech Engineering Information Systems Lab eislab.gatech.edu