GIT Product & System Lifecycle Management (PSLM) Center
www.pslm.gatech.edu
GIT SysML Work Update
Part 0: Overview
Part 1: Representing Executable Physics-based CAE Models in SysML
Russell.Peak@gatech.edu
Presenter
Diego.Tamburini@gatech.edu
Chris.Paredis@gatech.edu
Presentation to
v. 2005-12-28
OMG Systems Engineering
Domain-Specific Interest Group (SE DSIG)
December 6, 2005
Burlingame, California
Copyright © 1992-2005 by Georgia Tech Research Corporation, Atlanta, Georgia 30332-0415 USA. All Rights Reserved.
Permission to reproduce and distribute without changes for non-commercial purposes (including internal corporate usage) is hereby granted provided this notice and a proper citation are included.
Acknowledgements
Sponsors:
NASA, NIST
http://eislab.gatech.edu/projects/
GIT Team:
Manas Bajaj, Injoong Kim, Raphael Kobi, Chris Paredis,
Russell Peak, Diego Tamburini, Miyako Wilson
Other Collaborators:
Copyright © 2005
Roger Burkhart (Deere), Alan Moore et al. (Artisan),
Sandy Friedenthal (LMCO)
2
Resources
GIT SysML resources
Main web
http://www.pslm.gatech.edu/topics/sysml/
Presentations
http://www.marc.gatech.edu/events/pde2005/presentations/
See Presentations 1.1 and 1.2 (includes webcast video archive)
http://eislab.gatech.edu/pubs/seminars-etc/2005-09-omg-se-dsig-peak/
http://eislab.gatech.edu/pubs/seminars-etc/2005-12-omg-se-dsig-peak/
See also videos showing SysML-driven CAE execution (via COB interfaces)
http://eislab.gatech.edu/tmp/sysml/2005-12-06-burlingame/
Related GIT techniques
Composable objects
http://eislab.gatech.edu/projects/nasa-ngcobs/
Multi-representation architecture (MRA)
for simulation templates and CAD-CAE interoperability
http://eislab.gatech.edu/research/dai/
Copyright © 2005
3
Part 0: Overview
Presentation purpose = overview recent progress:
Validation: executability of SysML parametrics
Usage for SysML-driven CAE execution (math and FEA solvers)
Usage for knowledge capture & usage:
relations and intent in design & analysis
Development: further examples
Part 1: Representing Executable Physics-based
CAE Models in SysML (Peak, Tamburini, et al.)
See below
Part 2: SysML-based Reference Models for
Fluid Power Components (Paredis, et al.)
Copyright © 2005
See GIT_SysML_Part_2_Fluid_Pwr_Ref_Models.ppt
4
SysML-based Examples by GIT
= Primary Updates since 9/2005 OMG Meeting
Test Cases
Introductory tutorials (A)
Triangle
Spring systems
Simulation template
tutorials (A, B)
Simulation building blocks
Mechanical CAD & CAE: flap link
Tool Interfaces
A. Math solvers:
1.
Mathematica
B. Finite element analysis
(FEA) solvers:
1.
Ansys
C. Dynamics solvers:
1.
Modelica/Dymola
Space systems: FireSat satellite
Fluid power & system dynamics (C) -- see Part 2
Electrical/mechanical CAD & CAE
Model train (for Mechatronics pilot)
Racing bike
Copyright © 2005
Note: The SysML notation used in these slides roughly corresponds to SysML draft v0.9 plus more recent updates (approximately R. Burkhart blocks inputs as contained
in SysML spec v0.98 by SST) and experimental variations. We intend to update these examples with the final official notation when v1.0 that becomes available.
5
Status of Our SysML Examples - p.1/2
2005-12-06
1.
About the SysML notation used in these slides
1.
It roughly corresponds to a ~9/2005 form of the blocks-based
parametrics & structure approach developed by R. Burkhart et al.
1.
2.
2.
2.
This approach was updated & provided to both SysML teams 11/2005
The SST SysML v0.98 draft spec adopted this approach, whereas
the SP SysML v1.0a draft spec adopted a collaborations-based approach
We recently received a SysML tool that corresponds to the v.0.98 spec.
We hope to update these examples and solver interfaces accordingly
in the near future.
SST SysML v0.98 vs. our current examples:
1.
2.
3.
3.
Block properties should be shown as small boxes flush with block boundaries vs. our current
overlapping style
Bindings between regular blocks and constraint blocks should show their role names (as binding
identifiers) vs. our current elision
Instances should be underlined vs. our current underlining omission
(see also note below about instance causality)
Other notes
1.
We hope to include the following notation in future versions (they are not required by the
current specs, but we believe they will enhance parametric diagram usefulness):
1.
2.
Include symbols and subscripts for properties per traditional engineering notation
1.
E.g., spring constant in spring 1: k1
Include relation expressions in constraint blocks in terms of their bound properties
(continued next page)
Copyright © 2005
6
Status of Our SysML Examples - p.2/2
3.
Other notes (continued)
1.
In these examples we tested the following notation or practices on an experimental basis
to see if they might be useful:
1.
2.
3.
4.
5.
2.
We did the following to enable our constraint manager, XaiTools, to process SysML parametrics
(which provides subsequent solver execution using COTS math and FEA tools):
1.
2.
3.
Copyright © 2005
We distinguished parametric diagrams used for defining a block (par-d) vs. those used to capture instances
(par-i) of that block. Similar suffixes may be useful for definitional vs. instance use of all SysML diagrams.
We have a library of constraint blocks representing specific commonly used expressions (e.g., a=b+c,
a**2=b**2+c**2, etc.) that can be utilized in composing other blocks. To represent specialized relations, we
tried defining a generic “algebraic” constraint block in this library, which can be redefined wherever it is used. In
future versions we will likely replace this generic “algebraic” relation with relations defined in the context of the
blocks that use them.
We implemented equality relations as usages of an explicit “a=b” constraint block. We will likely replace such
cases with binding relations in the future.
We used a black dot graphical symbol to denote true junctions where equality relations intersect (e.g., as a
shorthand for a set of relations like a=b, a=c, a=d, and a=e). This approach is similar to that used with
electrical schematics and a Manhattan routing style. It enables cleaner and more compact diagram layout.
We depict instance-level causality in the Triangular Prism example using a double-lined box to indicate the
primary desired result (and red italics to indicate other ancillary results).
Added stereotypes to denote composable object (COBs) constructs: «git-schema», «git-use-from», etc.
Added stereotypes to denote the patterns defined in our multi-representation architecture (MRA) approach
for CAD-CAE interoperability: «apm», «cbam», «abb», «smm»
Handled reference properties (e.g., flap link material) via ad-hoc associations (this is due to a limitation in
XaiTools we hope to resolve in the near future).
7
Contents - Part 1
Purpose
CAD-CAE simulation template background
MCAD-MCAE benchmark example: flap link
Modularity & reusability
Executable SysML parametrics (math, FEA)
Summary
Recommended prerequisites
Copyright © 2005
Triangle tutorial
Spring systems tutorial
Multi-representation architecture (MRA)
for simulation templates and CAD-CAE interoperability
8
GIT SysML Involvement - Overall Purpose
Collaborate within SE DSIG:
composable object (COB) concepts SysML
(esp. SysML parametrics)
Leverage COB-based simulation template work
to demonstrate and verify SysML capabilities
CAD-CAE interoperability
Systems-of-systems (SoS) knowledge representations
...
For further background and GIT SysML work-to-date:
- See SE DSIG minutes/archives - Atlanta - 9/2005 - http://syseng.omg.org/
- http://www.pslm.gatech.edu/topics/sysml/
Copyright © 2005
9
Contents - Part 1
Purpose
CAD-CAE simulation template background
Leveraging test cases from existing work
See http://eislab.gatech.edu/research/dai/
MCAD-MCAE benchmark example: flap link
Summary
Recommended prerequisites (backup slides)
Copyright © 2005
Triangle tutorial
Spring systems tutorial
Multi-representation architecture (MRA)
for simulation templates and CAD-CAE interoperability
10
SysML-based Examples by GIT
Test Cases
Tool Interfaces
Introductory tutorials (A)
Triangle
Spring systems
1.
Simulation template
tutorials (A, B)
A. Math solvers:
Simulation building blocks
Mechanical CAD & CAE: flap link
Mathematica
B. Finite element analysis
(FEA) solvers:
1.
Ansys
C. Dynamics solvers:
1.
Modelica/Dymola
Space systems: FireSat satellite
Fluid power & system dynamics (C) -- see Part 2
Electrical/mechanical CAD & CAE
Model train (for Mechatronics pilot)
Racing bike
See slide entitled “Status of Our SysML Examples” regarding spec version used in these examples, and so on.
Copyright © 2005
11
COB Structure: Graphical Forms
Tutorial: Right Triangle
a. Shape Schematic-S
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
h
COB = composable object
c. Constraint Schematic-S
d
A
r1
base, b
b
height, h
r2
d b h
2
r1 : A 1 bh
2
b. Relations-S
r2 : d 2 b 2 h 2
Basic Constraint Schematic-S Notation
variable a
a
subvariable a.d
d
s
h
subsystem s
of cob type h
a b
subvariable s.b
relation r1(a,b,s.c)
r1
b
r2
e bc
c d
g
equality relation
e=f
c
w
L [ j:1,n]
© 1993-2005 GTRC
aggregate c.w
wj
option 1.2:
f=g
element wj
diagonal, d
Triangle
option 1.1:
[1.2]
2
(for reuse by other COBs)
option category 1
f
2
d. Subsystem-S
[1.1] f = s.d
e
area, A
A 1 bh
2
b
A
h
d
Aside: This is a “usage view” in AP210 terminology
(vs. the above “design views”)
Engineering Information Systems Lab eislab.gatech.edu
12
COB Structure (cont.): Lexical Form
Tutorial: Right Triangle
e. Lexical COB Structure (COS)
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
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;
for reference: c. Constraint Schematic-S
base, b
height, h
r1
r2
d b h
2
© 1993-2005 GTRC
area, A
A 1 bh
2
2
2
diagonal, d
Engineering Information Systems Lab eislab.gatech.edu
13
Right Triangle Implemented
using SysML Blocks and Parametrics
SysML Parametric Diagram
Note: The outmost block should be depicted as a frame (of type par),
as in conformant flap_link examples elsewhere in this presentation.
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
14
COBs as Building Blocks
Tutorial: Triangular Prism COB Structure
a. Shape Schematic-S
c. Constraint Schematic-S
cross-section
h
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
Triangle
l
V
A
b
b. Relations-S
r1 : V Al
A
h
d
r1
length, l
V Al
volume, V
d. Subsystem-S
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;
b
(for reuse by other COBs)
Triangular
Prism
b
h
V
l
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
15
Triangular Prism Implemented
using SysML Blocks and Parametrics
SysML Parametric Diagram
Note: The outmost block should be depicted as a frame (of type par),
as in conformant flap_link examples elsewhere in this presentation.
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
16
Example COB Instance
Tutorial: Right Triangle
Constraint Schematic-I
example 1, state 1.1
2 in
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
3 in
r1
base, b
A 1 bh
2
height, h
d 2 b2 h2
example 1, state 2.1
2 in
9 in
r2
r1
base, b
A 1 bh
2
height, h
d b h
2
2
r2
2
Lexical COB Instance (COI)
area, A
diagonal, d
area, A
diagonal, d
3 in2
3.60 in
9 in2
9.22 in
Basic Constraint Schematic-I Notation
100 lbs
30e6 psi
200 lbs
X
a
Input a = 100 lbs
b
Result b = 30e6 psi
(output or intermediate variable)
c
Result c = 200 lbs
(output of primary interest)
Equality relation is suspended
X r1
Relation r1 is suspended
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
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;
.
.
.
state 2.1 (solved):
INSTANCE_OF triangle;
base
: 2.0;
height
: 9.0;
area
: 9.0;
diagonal : 9.22;
END_INSTANCE;
17
Multi-Directional I/O
Tutorial: Right Triangle
Constraint Schematic-I
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
example 1, state 2.1
2 in
9 in
base, b
height, h
r1
A 1 bh
2
d 2 b2 h2
example 1, state 3.1
2 in
6 in
base, b
height, h
r2
r1
A 1 bh
2
d b h
2
2
r2
2
Lexical COB Instance (COI)
area, A
diagonal, d
area, A
diagonal, d
9 in2
9.22 in
6 in2
6.32 in
Concepts illustrated:
- Non-causal COB structure (no predefined I/O direction)
- Causality of COB instances and states
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
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;
18
Example COB Instance
Tutorial: Triangular Prism - State 1.1 (Solved) in XaiTools
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
19
Example COB Instance
Tutorial: Triangular Prism
Constraint Schematic-I
Lexical COB Instance (COI)
example 1, state 1.1 (solved)
state 1.0 (unsolved):
INSTANCE_OF triangular_prism;
cross-section.base
: 2.0;
cross-section.height : 3.0;
length : 5.0;
volume : ?;
END_INSTANCE;
cross-section
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
Triangle
5 in
2 in
b
A
3 in
h
d
length, l
state 1.0 (unsolved)
3 in2
r1
V Al
volume, V
15 in3
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;
SysML Parametric Diagram-I
state 1.1 (solved)
=3
= 15
Note: The current prototype exports instances with input values for solving. The model is then executed successfully in external solvers. However, the prototype interface
for importing resulting solutions is not ready yet; thus, the solved state depicted here inside the SysML tool is an envisioned notation.
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
20
SysML-COB Architecture - Prototype v0.1
as of 2005-12-06
COB Solving & Browsing
SysML-based COB Authoring
Artisan Studio
XaiTools
COB export
Exchange
File
COB API
XaiTools
COB Services (constraint graph manager, including COTS solver access)
Composable Objects (COBs)
...
Native Tools Models
Traditional
COTS or in-house
solvers
© 1993-2005 GTRC
Ansys
Mathematica
(FEA Solver)
(Math Solver)
Engineering Information Systems Lab eislab.gatech.edu
21
Engineering Web Services
Engineering Service Bureau
Client PCs
Host Machines
Rich Client
Soap Servers
XaiToolsAnsys
Ansys
XaiTools
XaiTools
Math.
XaiTools
SolverSolver
Server
Solver
Server
Solver
Server
Server
Internet/Intranet
FEA Solvers
Ansys, Patran,
Abaqus, ...
Math Solvers
...
HTTP/XML
Wrapped Data
Web Server
SOAP
Internet
XaiTools
Servlet container
Apache Tomcat
Mathematica
Status: In prototype & production usage since 1999 (CORBA), 2002 (SOAP),
including remote access from AZ, DC, WV, UK, Japan, …
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
22
SysML-COB Architecture - Prototype v0.2
Anticipated 2006-1Q
COB Solving & Browsing
SysML-based COB Authoring
Artisan Studio
XaiTools
COB in/out
Exchange
File
COB API
XaiTools
COB Services (constraint graph manager, including COTS solver access)
Composable Objects (COBs)
...
Native Tools Models
Traditional
COTS or in-house
solvers
© 1993-2005 GTRC
Ansys
Mathematica
(FEA Solver)
(Math Solver)
Engineering Information Systems Lab eislab.gatech.edu
23
Envisioned SysML-COB Architecture
http://eislab.gatech.edu/projects/nasa-ngcobs/ - 2005-10
CMS Management Client Tools
COB Authoring
COB Configuration
Management
COB Browsing
COB-Enabled End-User Applications
COTS SysML Tools
Other COB Apps.
SysML
UI Control
COB API
COB API
COB API
COB API
Domain-specific
Simulation tools
COB
Tree
COB API
COB Services (graph mgt, conf. control, meta-solving, persistence, tool access, UI,…)
COB API
COB SDK
UI Components
Composable Objects (COBs)
Traditional
COTS and in-house
end-user tools
(authoring, viewing,
solving,..)
Tool
Native Tools Models
Tool
Tool
Tool
© 1993-2005 GTRC
COB Management System
(CMS)
Standards-based
tool wrappers
Engineering Information Systems Lab eislab.gatech.edu
24
Contents - Part 1
Purpose
CAD-CAE simulation template background
Leveraging test cases from existing & new work
See http://eislab.gatech.edu/research/dai/
MCAD-MCAE benchmark example: flap link
Summary
Recommended prerequisites (see backup slides)
Copyright © 2005
Triangle tutorial
Spring systems tutorial
Multi-representation architecture (MRA)
for simulation templates and CAD-CAE interoperability
25
X-Analysis Integration Techniques
for CAD-CAE Interoperability
http://eislab.gatech.edu/research/
a. Multi-Representation Architecture (MRA)
3
Analyzable
Product Model
Design Model
4 Context-Based Analysis Model
APM
1 Solution Method Model
CBAM
Solder
Joint
Component
i
ABB
T0
Component
body 1
body4
Solder Joint
linear-elastic model
primary structural
material
SMM
APM ABB
Solder Joint Plane Strain Model
4 CBAM
C
L
h1
base: Alumina
Epoxy
PWB
body3
APM ABB
core: FR4
Plane Strain Bodies System
2 ABB
total height, h c
Component
Solder
Joint
ABBSMM
Analysis Model
PWA Component Occurrence
3 APM
2 Analysis Building Block
Printed Wiring Assembly (PWA)
b. Explicit Design-Analysis Associativity
body 1
body 4
body
body 2
body 2
PWB
To
3
plane strain bodyi , i = 1...4
geometryi
materiali (E, , )
Printed Wiring Board (PWB)
Design Tools
Informal Associativity Diagram
Solution Tools
4 CBAM
c. Analysis Module Creation Methodology
Analysis Module Catalogs
Analysis Procedures
3 APM
sj
solder joint
shear strain
range
Lc
(Module Creation)
total height
hc
primary structural material
T0
linear-elastic model
1.25
[1.1]
length 2 +
total thickness
pwb
Ubiquitous Analysis
Product
Model
(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]
© 1993-2005 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
Composable
Constrained Object-based Analysis Module
PWB
APM CBAM ABB SMM
Tc
Ls
[1.2]
[2.2]
MCAD
Plane Strain
Bodies System
approximate maximum
inter-solder joint distance
Physical Behavior Research,
Know-How, Design Handbooks, ...
Commercial
Design Tools
deformation model
Fine-Grained Associativity
component
1 SMM
2 ABB
Ubiquitization
component
occurrence
c
ABB SMM
Constraint Schematic View
Abaqus
Engineering Information Systems Lab eislab.gatech.edu
COB = composable object
26
Flexible High Diversity Design-Analysis Integration
Phases 1-3 Airframe Examples:
“Bike Frame” / Flap Support Inboard Beam
Design Tools
strength model
product structure
(channel fitting joint) bolt BLE7K18
head
end pad
fitting
hole
radius, r1
0.4375 in
radius, ro
0.5240 in
2.440 in
width, b
mode: (ultimate static strength)
1.267 in
eccentricity, e
thickness, te
0.5 in
2.088 in
height, h
base
0.0000 in
radius, r2
thickness, tb
0.307 in
thickness, tw
0.310 in
1.770 in
angled height, a
material
r1
r0
b
e
te
Channel Fitting
Static Strength Analysis
IAS Function
Ref D6-81766
h
hole
wall
MCAD Tools
CATIA v4, v5
Modular, Reusable
Template Libraries
rear spar fitting attach point
analysis context
max allowable ultimate stress, Ftu
67000 psi
r2
tb
tw
a
Ftu
65000 psi
diagonal brace lug joint
analysis context product structure (lug joint)
allowable ultimate long transverse stress, FtuLT
FtuLT
57000 psi diameters
lugs max allowable yield stress, Fty
LF[tyk] k = norm
L [ j:1,n ] max allowable
52000 psi
F diameter
j = top long transverse stress,
normaltyLT
, Dnorm FtyLT Dk
hole
lugj shear
39000 psi
max allowable
stress, Fsu oversize diameter,
Dover Fsu
0.7500 in
0.067 in/in
plastic ultimate strain, epu
epu
2
0.35 in
thickness,
size,n ultimate strain long transverse,
epuLT t 0.030 in/in
plastic
epuLT
young modulus of elasticity, E
2G7T12U (Detent 0, Fairing Condition 1)
condition:
mode (ultimate static strength)
load, Pu
Pu
material
max allowable ultimate stress,
jm FtuL
r1
Plug
Program
Plug joint
L29 -300
Part
Outboard TE Flap, Support
No 2;
n
8.633
K 123L4567
Inboard
Beam,
objective
deformation model
Lug Axial Ultimate
Strength Model
D
MSwall
9.17
BDM 6630
MSepb
t
MSeps
e
W
5960
effective width,
W Ibs
1.6000 in
5.11
9.77
Kaxu
0.7433
Paxu
14.686 K
7050-T7452, MS 7-214
heuristic: overall fitting factor, Jm 1
Max. torque brake setting
detent 30, 2=3.5º
condition
10000000
psi
edge margin,
e
0.7500 E
in
Analysis Modules (CBAMs)
of Diverse Feature:Mode, & Fidelity
Plug joint
F tuax
Channel Fitting67 Ksi
Template
4.317 K
Static Strength Analysis
Dataset
XaiTools
1 of 1
Bulkhead Fitting Joint
Feature
Margin
of Safety
(> case)
actual
estimated axial ultimate strength
allowable
MS
2.40
Program
L29 -300
Part
Outboard TE Flap, Support No 2;
Inboard Beam, 123L4567
Feature
Diagonal Brace Lug Joint
Template Lug Joint
Axial Ultimate Strength Model
Dataset
j = top lug
k = normal diameter
(1 of 4)
1.5D
Image API
(CATGEO);
VBScript
Analyzable
Product Model
XaiTools
Lug:
Axial/Oblique;
Ultimate/Shear
Fasteners DB
FASTDB-like
General Math
Mathematica
In-House
Codes
1.5D
Fitting:
Bending/Shear
Materials DB
MATDB-like
Analysis Tools
3D
Assembly:
Ultimate/
FailSafe/Fatigue*
FEA
Elfini*
* = Item not yet available in toolkit (all others have working examples)
27
Fitting Analysis Template Applied to “Bike Frame” Bulkhead
COB-based CBAM constraint schematic - instance view
18 associativity relations
bulkhead fitting attach point
analysis context
product structure
(channel fitting joint) bolt LE7K18
end pad
fitting
head
hole
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
mode: (ultimate static strength)
base
material
0.5240 in
2.440 in
eccentricity, e
thickness, te
1.267 in
height, h
2.088 in
0.5 in
r1
r0
b
Channel Fitting
Static Strength Analysis
e
te
IAS Function
Ref DM 6-81766
h
0.0000 in
radius, r2
thickness, tb
0.307 in
thickness, tw
0.310 in
angled height, a
1.770 in
max allowable ultimate stress, Ftu
67000 psi
allowable ultimate long transverse stress, FtuLT
65000 psi
max allowable yield stress, Fty
57000 psi
max allowable long transverse stress, FtyLT
52000 psi
max allowable shear stress, Fsu
39000 psi
plastic ultimate strain, epu
0.067 in/in
plastic ultimate strain long transverse, epuLT
0.030 in/in
load, Pu
heuristic: overall fitting factor, Jm
COB = composable object
radius, ro
young modulus of elasticity, E
2G7T12U (Detent 0, Fairing Condition 1)
condition:
0.4375 in
width, b
hole
wall
radius, r1
strength model
10000000 psi
5960 Ibs
1
r2
tb
K3 f (r1,b, h)
tw
a
fbe
Ftu
fse
P
2
hte
C1
P
2pr0te
FtuLT
Fty
FtyLT
Fsu
MSwall
9.17
epu
MSepb
5.11
MSeps
9.77
epuLT
E
Pu
jm
Program
L29 -300
Part
Outboard TE Flap, Support No 2;
Inboard Beam, 123L4567
Feature
Bulkhead Fitting Joint
Template Channel Fitting
Static Strength Analysis
Dataset
1 of 1
28
Lug Template Applied to an Airframe Analysis Problem
COB-based CBAM constraint schematic - instance view
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
CAD-CAE Associativity
(idealization usage)
lugs
diagonal brace lug joint
L [ j:1,n ]
j = top
hole
lugj
analysis context product structure (lug joint)
Geometry
2
size,n
mode (ultimate static strength)
deformation model
diameters
L [ k] k = norm
Dk
normal diameter, Dnorm
oversize diameter, Dover
Max. torque brake setting
detent 30, 2=3.5º
thickness, t
0.35 in
edge margin, e
0.7500 in
Plug joint
condition
r1
Plug joint
Plug
e
W
Paxu Kaxu (
4.317 K
n
(links to other analyses)
actual
0.7433
Paxu
14.686 K
W
1) DtFtuax
D
Solution Tool
Interaction
Boundary Condition Objects
Margin of Safety
(> case)
Kaxu
F tuax
67 Ksi
8.633 K
objective
DM 6630
t
Material Models
max allowable ultimate stress, FtuL
material
D
0.7500 in
effective width, W 1.6000 in
7050-T7452, MS 7-214
Lug Axial Ultimate
Strength Model
estimated axial ultimate strength
allowable
b
MS
Model-based Documentation
2.40
c
R
Requirements
Program
L29 -300
Part
Outboard TE Flap, Support No 2;
Inboard Beam, 123L4567
Template Lug Joint
Axial Ultimate Strength Model
Diagonal Brace Lug Joint
D
= f( c , b , R )
W = f( R , D , )
e
Dataset
Feature
axial direction
j = top lug
k = normal diameter
(1 of 4)
Legend: Annotations highlight model knowledge capture capabilities. Other notation is COB constraint schematics notation.
29
Generalized MRA Patterns for Systems-of-Systems (SoS) M&S
Traditional Patterns
(for CAD-CAE)
Traditional CAD-CAE Purpose
regarding Design-Analysis Integration (DAI)
- Define systems (parts, assemblies, …) in necessary &
sufficient descriptive terms (not behavioral)
- Usually are COTS tools
analyzable product models
- Represent design aspects of products and enable connections
(APMs)
with design tools
- Support idealizations usable in numerous analysis models
- Have possibly many associated CBAMs that verify
requirements
context-based
- Contain linkages explicitly representing design-analysis
analysis models
associativity, indicating usage of APM idealizations
(CBAMs)
- Create analysis models from ABBs and automatically connect
them to APM attributes
- Represent common analysis models as automated, predefined
templates
- Support interaction of analysis models of varying complexity
and solution method
- Enable parametric design studies via multi-directional
input/output (in some cases)
analysis building blocks
- Represent analytical concepts as composable objects
(ABBs)
- Act as semantically rich 'pre-preprocessor' & 'postpostprocessor' models.
(generic analytical concepts) - ABB instances create SMM instances based on solution
method considerations and receive results after automated
solution tool execution
solution method models
- Packages solution tool inputs, outputs, and control as
(SMMs)
integrated objects (often as a componentized wrapping of
solution tool native files)
- Automates solution tool access and results retrieval via tool
agents and wrappers
solution tools
- Execute simulation models (often as vendor-specific native
(CAE)
files)
- Usually are COTS tools
design tools
(CAD)
version: 2005-12-06
Generalized Patterns
(for complex systems-of-systems)
system description tools
augmented descriptive model
(federated descriptive model +
idealizations and other relations)
context-based
simulation model
(system-specific
simulation model)
simulation building block
(generic analytical concepts)
simulation method model
simulation tool
(solver)
30
Diversity Demonstrated in Test Cases
[based on Peak and Wilson et al. 2001]
Test Case Analysis Templates
Target
Characteristics
Flap Link
CBAMs
PWA/B
CBAMs
Aerospace
CBAMs
Electrical Chip
Package CBAMs
Product Domain
airframe
printed circuit board (PWA/B)
airframe
chip package
CAD Tools
CATIA (MCAD)
Mentor Graphics (ECAD)
XaiTools PWA/B
CATIA (MCAD)
XaiTools
Chip Package (XCP)
Discipline
structural
thermo-mechanical
structural
thermal
deformation
(warpage)
lug & fitting
ultimate shear,
bending shear
temperature
1.5D
thermal body
(3D, linear)
Diversity Dimensions
deformation
(extension)
Behavior
extensional rod
(1D, linear)
plane stress body
(2D, linear)
Solution Method
(and Tools)
formula-based
(Mathematica)
FEA (Ansys,
Patran, Abaqus),
formula-based
(Mathematica)
Directionality
multi
oneway
(partially multi)
Fidelity
deformation
(torsion)
torsional rod
(1D, linear)
thermal bending
(1D, linear)
plane strain body
(2D, linear)
formula-based
(Mathematica)
formula-based
(Mathematica)
FEA
(Ansys, Cadas),
formula-based
(Mathematica)
formula-based
(Mathematica)
FEA (Ansys),
formula-based
(Mathematica);
custom cob-based
mesh algorithm
multi
multi
oneway
(partially multi)
oneway
(partially multi)
oneway
(partially multi)
COB Usage Characteristics
Product Design
Info Usage
detailed design
(COI via CATIA interface)
detailed design
(STEP AP210 -Part 21
via Mentor Graphics interface)
detailed design
(COI via
CATIA interface)
preliminary design
(COI via
XCP design tool)
Automation
fully automated
fully automated
fully automated
fully automated
[after Wilson, 2000]
Patran and Abaqus links are work-in-progress
31
Test Case Statistics: Overall
# 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
Totals
airplane
electrical chip package (cp)
product specific
lib
cbams.cos
fastener.cos
materials.cos
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
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
32
Test Case Statistics: Flap Link and Associated Building Blocks
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 complexity
33
Example COB Reuse as Modular Simulation 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
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
34
Contents - Part 1
Purpose
CAD-CAE simulation template background
Leveraging test cases from existing work
See http://eislab.gatech.edu/research/dai/
MCAD-MCAE benchmark example: flap link
Summary
Recommended prerequisites (backup slides)
Copyright © 2005
Triangle tutorial
Spring systems tutorial
Multi-representation architecture (MRA)
for simulation templates and CAD-CAE interoperability
35
SysML-based Examples by GIT
Test Cases
Tool Interfaces
Introductory tutorials (A)
Triangle
Spring systems
1.
Simulation template
tutorials (A, B)
A. Math solvers:
Simulation building blocks
Mechanical CAD & CAE: flap link
Mathematica
B. Finite element analysis
(FEA) solvers:
1.
Ansys
C. Dynamics solvers:
1.
Modelica/Dymola
Space systems: FireSat satellite
Fluid power & system dynamics (C) -- see Part 2
Electrical/mechanical CAD & CAE
Model train (for Mechatronics pilot)
Racing bike
See slide entitled “Status of Our SysML Examples” regarding spec version used in these examples, and so on.
Copyright © 2005
36
Flap Link Mechanical Part
A simple design ... a benchmark problem.
L
B
ts2
ts1
s
sleeve1
sleeve2
shaft
rib1
rib2
ds1
ds2
B
red = idealized parameter
Leff
Background
This simple part provides the basis for a benchmark tutorial for CAD-CAE interoperability and
simulation template knowledge representation. This example exercises multiple capabilities relevant to
such contexts (many of which are relevant to broader simulation and knowledge representation
domains), including:
• Diversity in design information source, behavior, fidelity, solution method, solution tool, ...
• Modular, reusable simulation building blocks and fine-grained inter-model associativity
See the following for further information (including papers overviewing this example):
http://eislab.gatech.edu/research/dai/
(begin with [Wilson et al. 2001] under Suggested Starting Points)
37
Design-Analysis Interoperability (DAI) Panorama
Flap Link Benchmark Tutorial - Composable Object (COB)-based Constraint Schematic
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,
t T
E
2(1 )
e
T
t
r4
area, A
T, , x
Extension
r3
r2
undeformed length, Lo
G
F
E, A,
shear strain,
r5
L
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,L
r1
start, x1
shear modulus, G
linkage
y
temperature change,T
r4
thermal strain, t
e
stress, E
Torsional Rod
T
One D Linear
Elastic Model
strain,
r3
effective length, Leff
mode: shaft tension
Lo
material model
elastic strain, e
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
L
x2
al2
linear elastic model
Lo
x1
E
F
G
stress mos model
torque, Tr
polar moment of inertia, J
e
radius, r
T
t
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
mode: shaft torsion
Torsion
area
b
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)
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
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
shear modulus, G
2
FEA
Ansys
Abaqus*
CATIA Elfini*
MSC Nastran*
MSC Patran*
...
Flap Link Torsional Model
38
Flap Linkage Example
Manufacturable Product Model (MPM) = Design Description
flap_link
Extended Constraint Graph
L
A
ts
ts1
w
sleeve_1
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
t
2
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
wf
tw
t1f
t2f
rib_1
b
h
t
rib_2
R2
b
h
t
material
R3
COB Structure (COS)
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
39
Flap Linkage Example
Analyzable Product Model (APM) = MPM Subset + Idealizations
flap_link
L
Extended Constraint Graph
effective_length
A
w
sleeve_1
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
ds1
Leff
w
R1
t
R1
r
R2
x
Product Attribute
cross_section
Product Relation
wf
R3
tw
R4
t1f
Idealized Attribute
Ri
ds2
A
x
Ri
Sleeve 2
Shaft
r
shaft
2
s
Sleeve 1
t
sleeve_2
ts
ts1
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
R8
area
tw
R3
name
stress_strain_model
linear_elastic
E
hw
tf
cte
area
R9
R10
R12
40
Flap Link APM
Implementation in CATIA v5
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
Design-Idealization
Relation
Design Model
flap_link
Extended Constraint Graph
effective_length
w
sleeve_1
t
r
x
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
Idealized Model
R6
R5
t2f
critical_section
critical_detailed
Idealization Relation
wf
tw
rib_1
R11
hw
b
R7
t1f
h
t
rib_2
t2f
R2
critical_simple
wf
h
t
material
R8
area
b
tw
R3
E
name
stress_strain_model
linear_elastic
hw
tf
cte
area
R9
R10
R12
41
Flap Link APM
SysML Block Definition Diagram (bdd) - basic view
bdd flap_link bdd - basic view
part
[1]
tapered_beam
L
B
shaft
ts2
ts1
1
s
sleeve1
critical_cross_section
1
sleeve2
shaft
rib1
rib2
ds1
1
ds2
B
flap_link
** git tool caveat:
material link
1
origin
1
point
cross_section
1
1
sleeve1
1
1
sleeve2
1
1
rib1
1
sleeve
1
rib2
1
1
basic
1
tapered
1
1
basic_I_section
rib
design
1
tapered_I_section
1
hole1
1
material
1
hole
Note [1]: The term “part” is used here as a regular block name in the traditional engineering sense of
part-assembly (i.e., it is not used here in the UML/SysML meta-entity context of part/class).
filleted_tapered_I_section
v. 2005-12-19
42
Flap Link APM: SysML Block Definition Diagram (bdd)
Implementing COB Concepts in SysML
bdd flap_link bdd
apm
hole
«git-root-cob»
part
1
hole1
description : STRING
designer : STRING
material : STRING
tapered_beam
1 length : REAL
taper_angle : REAL
shaft
1
«git-root-cob»
flap_link
sleeve
part_number : STRING
inter_axis_length : REAL
allowable_twist : REAL
allowable_twist_factor : REAL
allowable_inter_axis_length_change_factor : REAL
allowable_inter_axis_length_change : REAL
effective_length : REAL
description : STRING
designer : STRING
material : STRING
1
1
width : REAL
1 wall_thickness : REAL
sleeve1 outer_diameter : REAL
1
inner_diameter : REAL
sleeve2
1
1
critical_cross_section
1
rib
cross_section
1
1
** git tool caveat: material link
height : REAL
volume : REAL
rib1
1 base : REAL
height : REAL
1 thickness : REAL
1
rib2
1
1
basic
design
tapered
1
materials
origin
geometry
1
«git-root-cob»
material
name : STRING
yield_stress : REAL
point
1
1
basic_I_section
tapered_I_section
filleted_tapered_I_section
area : REAL
total_height : REAL
web_thickness : REAL
flange_thickness : REAL
flange_width : REAL
web_height : REAL
flange_base_thickness : REAL
flange_taper_thickness : REAL
flange_taper_angle : REAL
web_thickness : REAL
total_height : REAL
flange_width : REAL
area : REAL
web_height : REAL
flange_thickness : REAL
flange_fillet_radius : REAL
web_thickness : REAL
total_height : REAL
flange_width : REAL
flange_base_thickness : REAL
flange_taper_thickness : REAL
flange_taper_angle : REAL
area : REAL
web_height : REAL
flange_thickness : REAL
x : REAL
y : REAL
z : REAL
v. 2005-12-19
1
43
See slide entitled “Status of Our SysML Examples” regarding spec version used in these examples, and so on.
Flap Link APM: SysML Parametric Diagram (par)
Implementing COB Concepts in SysML
Class flap_link
par-d
sleeve1 : sleeve
sleeve2 : sleeve
wall_thickness
hole1 : hole
origin : point
x y z
inner_diameter
diameter
area
cross_section : circle
outer_diameter
radius
z
origin : point
c
a
thickness
rib1 : rib
height
base
wall_thickness
y
a
pr5 : algebraic
b
hole1 : hole
inner_diameter
diameter
area
cross_section : circle
outer_diameter
x
width
b
pr3 : algebraic
pr1 :
algebraic
a
b
b
pr2 : algebraic
b
x
origin : point
y
a
c
width
a
b
thickness
rib2 : rib
base
height
a
pr6 : algebraic
pir2 : algebraic
radius
z
b
pr4 : algebraic
a
c
part_number
description
designer
inter_axis_length
shaft : tapered_beam
d
c
pir1 : algebraic
b
a
taper_angle
critical_cross_section : cross_section
effective_length
total_height
area
a
c
pir4 : algebraic
b
allowable_twist
allowable_twist_factor
web_thickness
I_section.web_height
I_section.flange_thickness
allowable_inter_axis_length_change
allowable_inter_axis_length_change_factor
length
a
c
pir3 : algebraic
b
design : filleted_tapered_I_section
flange_base_thickness
flange_taper_thickness
flange_fillet_radius
flange_taper_angle
flange_width
material
name
material
«git-external-ref»
v. 2005-12-19
v. 2005-12-17
44
Class
par-i flap_link_XYZ-510
part_number = "XYZ-510"
rib1 : rib
designer = "J. Smith"
description = "flap link type 5"
material = "steel"
base
x
height
y origin : point
z
thickness
inter_axis_length = 6.250000
x = 0.0
origin : point
y = 0.0
effective_length
allowable_inter_axis_length_change_factor = 0.001
rib2 : rib
z = 0.0
allowable_inter_axis_length_change
base
x
allowable_twist_factor = 0.001
height
y origin : point
z
allowable_twist
thickness
Flap Link APM:
SysML Parametric
Diagram - Instance
(inputs - unsolved state)
sleeve1 : sleeve
hole1 : hole
wall_thickness
Solving supported via
math tool execution
width = 2.0
x
outer_diameter = 2.0
inner_diameter = 1.0
y
x
y
origin : point
radius
diameter
cross_section : circle
origin : point
area
z
z
sleeve2 : sleeve
L
B
hole1 : hole
wall_thickness
width = 2.50
outer_diameter = 2.70
x
y
radius
x
origin : point
y
origin : point
s
diameter
cross_section : circle
sleeve1
sleeve2
shaft
rib1
area
z
z
ts2
ts1
rib2
ds1
inner_diameter = 1.50
B
ds2
shaft : tapered_beam
critical_cross_section : cross_section
taper_angle = 3.210243
length
basic :
basic_I_section
y origin : point
z
tapered :
tapered_I_section
web_thickness = 0.25
flange_thickness
area
x
flange_fillet_radius = 0.13
total_height
web_height
design :
filleted_tapered_I_section
flange_taper_angle = 10.0
flange_width = 1.5
flange_base_thickness = 0.25
flange_taper_thickness = 0.05
v. 2005-12-19
45
Design-Analysis Interoperability (DAI) Panorama
Flap Link Benchmark Tutorial - Composable Object (COB)-based Constraint Schematic
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,
t T
E
2(1 )
e
T
t
r4
area, A
T, , x
Extension
r3
r2
undeformed length, Lo
G
F
E, A,
shear strain,
r5
L
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,L
r1
start, x1
shear modulus, G
linkage
y
temperature change,T
r4
thermal strain, t
e
stress, E
Torsional Rod
T
One D Linear
Elastic Model
strain,
r3
effective length, Leff
mode: shaft tension
Lo
material model
elastic strain, e
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
L
x2
al2
linear elastic model
Lo
x1
E
F
G
stress mos model
torque, Tr
polar moment of inertia, J
e
radius, r
T
t
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
mode: shaft torsion
Torsion
area
b
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)
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
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
shear modulus, G
2
FEA
Ansys
Abaqus*
CATIA Elfini*
MSC Nastran*
MSC Patran*
...
Flap Link Torsional Model
46
COB-based Libraries of Analysis Building Blocks (ABBs)
Material Model and Continuum ABBs - Constraint Schematic-S
Continuum ABBs
Regarding classical COB notation and examples,
see References/Backup Slides
Extensional Rod
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
Material Model ABB
reference temperature, To
force, F
1D Linear Elastic Model
shear stress,
poissons ratio,
r1
cte,
temperature change,T
t T r4
thermal strain, t
elastic strain, e
r3
stress,
e
start, x1
shear modulus, G
E
G
2(1 )
E
r4
F
A
modular
re-usage
end, x2
r1
e
T
t
length, L
theta end, 2
y
Lo
T
T
G, r, , ,J
x
G
Trr
J
undeformed length, Lo
theta start, 1
total elongation,L
L L Lo
E
torque, Tr
radius, r
T, , x
r3
L
L
One D Linear
Elastic Model
r2
polar moment of inertia, J
F
E, A,
material model
Torsional Rod
L
F
L x2 x1
strain,
e t
L
Lo
E
r2
undeformed length, Lo
G
youngs modulus, E
area, A
T T To
One D Linear
Elastic Model
(no shear)
shear strain,
r5
edb.r1
temperature, T
y
material model
e
T
t
r1
2 1
r3
r
L0
twist,
47
Libraries of Analysis Building Blocks (ABBs)
Material Model & Continuum ABBs - SysML Parametric Diagrams
par-d extensional_rod
Class
youngs_modulus
name
cte
temperature
reference_temperature
material_model :
one_D_linear_elastic_model_noShear
a
b
r1edb : algebraic
c
thermal_strain
temperature_change
par-d one_D_linear_elastic_model
Class
force
youngs_modulus
poissons_ratio
shear_modulus
strain
stress
r4 : algebraic
c
name
c
b r1 : algebraic
yield_stress
a
r3 : algebraic
b
c
undeformed_length
a
c
stress
a
b
area
a
elastic_strain
total_elongation
a
c
r2 : algebraic
elastic_strain
b
r3 : algebraic
length
b
start
cte
temperature_change
a
b
thermal_strain
r4 : algebraic
c
modular
re-usage
c
end
r1 : algebraic
a
b
Class
par-d torsional_rod
b
r2 : algebraic c
a
shear_modulus
torque
a
c
shear_stress
r5 : algebraic
b
shear_strain
polar_moment_of_inertia
radius
material_model :
one_D_linear_elastic_model_isothermal
b
d r3 : algebraic
a
c
strain
stress
shear_strain
shear_stress
a
c
r2 : algebraic
undeformed_length
d
theta_start
c
theta_end
v. 2005-12-19
name
youngs_modulus
strain
twist
b
a
r1 : algebraic
b
48
Design-Analysis Interoperability (DAI) Panorama
Flap Link Benchmark Tutorial - Composable Object (COB)-based Constraint Schematic
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,
t T
E
2(1 )
e
T
t
r4
area, A
T, , x
Extension
r3
r2
undeformed length, Lo
G
F
E, A,
shear strain,
r5
L
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,L
r1
start, x1
shear modulus, G
linkage
y
temperature change,T
r4
thermal strain, t
e
stress, E
Torsional Rod
T
One D Linear
Elastic Model
strain,
r3
effective length, Leff
mode: shaft tension
Lo
material model
elastic strain, e
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
L
x2
al2
linear elastic model
Lo
x1
E
F
G
stress mos model
torque, Tr
polar moment of inertia, J
e
radius, r
T
t
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
mode: shaft torsion
Torsion
area
b
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)
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
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
shear modulus, G
2
FEA
Ansys
Abaqus*
CATIA Elfini*
MSC Nastran*
MSC Patran*
...
Flap Link Torsional Model
49
Flap Link Simulation Templates & Generic Building Blocks
SysML Block Definition Diagram (bdd) - basic view
bdd flap_link_cbams bdd - basic view
condition
1
1
«cbam»
link_analysis_model
«apm»
flap_link
associated_condition
git tool caveat
Generalization45
«cbam»
link_extensional_model
1
«cbam»
link_plane_stress_model
1
1
1
sx_mos_model ux_mos_model
1
1
1
1
«abb»
stress_mos_model margin_of_safety_model
1
«cbam»
link_torsional_model
1
deformation_model
1
1
stress_mos_model
twist_mos_model
deformation_model
1
1
«abb»
extensional_rod_isothermal
1
1l
1
deformation_model
«abb»
link_plane_stress_abb
«abb»
torsional_rod
«abb»
one_D_linear_elastic_model
1
material_model
1
«abb»
one_D_linear_elastic_model_noShear
material_model
1
«abb»
one_D_linear_elastic_model_isothermal
50
Tutorial Example: Flap Link Analysis Template
COB-based CBAM - Constraint Schematic (classical view)
(1a) Analysis Template: Flap Link Extensional Model
CBAM
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
L
A
ts2
ts1
s
Sleeve 1
Sleeve 2
Shaft
ds1
y
E, A
effective length, Leff
APM
Geometry
mode: shaft tension
cross section
material
condition
al1
linear elastic model
x
Extensional Rod
(isothermal)
x1
al2
youngs modulus, E al3
reaction
P
,
L
Lo
Material Models
area, A
L
deformation model
Leff
linkage
L
Leff
P
(idealization usage)
ds2
A
CAD-CAE
Associativity
ABB
L
x2
A
E
F
SMM
stress mos model
Margin of Safety
(> case)
allowable
ABB
allowable stress
actual
MS
Boundary Condition Objects
Requirements &
Objectives
(links to other analyses)*
Solution Tool
Interaction
51
Analysis Template: Flap Link Extensional Model
COB-based CBAM - SysML Parametric Diagram
par-d
Class link_extensional_model
«apm»
flap_link
link
«part»
«abb»
deformation_model : extensional_rod_isothermal
part_number
effective_length
material
b
al1 : a=b
a
al2 : a=b
a
shaft : tapered_beam
critical_cross_section :
cross_section
undeformed_length
basic : basic_I_section
area
b
area
material
stress_strain_model :
material_levels
material_model :
one_D_linear_elastic_model_noShear
linear_elastic :
linear_elastic_model
youngs_modulus
b
al3 : a=b
a
youngs_modulus
name
name
stress
yield_stress
b
al4 : a=b
a
b
Solving supported via
math tool execution
al6 : a=b
associated_condition : condition
description
reaction
length
a
b
al5 : a=b
a
a
al7 : a=b
b
force
total_elongation
margin_of_safety
«part»
allowable
«abb»
stress_mos_model : margin_of_safety_model
determined
v. 2005-12-19
52
Analysis Template Instance with Multi-Directional I/O
Flap Link Extensional Model - COB Constraint Schematics (classical view)
deformation model
linkage
Flap Link #3
Leff
effective length,
5.0 in
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
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
L
x1
L
1.43e-3 in
- Input: design details
- Output:
i) idealized design parameters
ii) physical response criteria
x2
A
8888 psi
E
F
Design Verification
description
flaps mid position
stress mos model
Margin of Safety
18000 psi
(> case)
allowable stress
allowable
actual
MS
1.025
example 1, state 1
deformation model
Design Synthesis
- Input: desired physical
response criteria
- Output:
i) idealized design
parameters
(e.g., for sizing), or
ii) detailed design
parameters
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
L
x1
L
3.00e-3 in
x2
A
E
F
18000 psi
description
flaps mid position
stress mos model
Margin of Safety
(> case)
18000psi
allowable stress
allowable
actual
MS
0.0
example 1, state 3
53
Flap Link Extensional Model
Example COB Instance in XaiTools (object-oriented spreadsheet)
example 1, state 1
Library data for
materials
Detailed CAD data
from CATIA
Idealized analysis features
in APM
Modular generic analysis templates
(ABBs)
Explicit multi-directional associativity
between design & analysis
54
Design-Analysis Interoperability (DAI) Panorama
Flap Link Benchmark Tutorial - Composable Object (COB)-based Constraint Schematic
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,
t T
E
2(1 )
e
T
t
r4
area, A
T, , x
Extension
r3
r2
undeformed length, Lo
G
F
E, A,
shear strain,
r5
L
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,L
r1
start, x1
shear modulus, G
linkage
y
temperature change,T
r4
thermal strain, t
e
stress, E
Torsional Rod
T
One D Linear
Elastic Model
strain,
r3
effective length, Leff
mode: shaft tension
Lo
material model
elastic strain, e
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
L
x2
al2
linear elastic model
Lo
x1
E
F
G
stress mos model
torque, Tr
polar moment of inertia, J
e
radius, r
T
t
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
mode: shaft torsion
Torsion
area
b
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)
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
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
shear modulus, G
2
FEA
Ansys
Abaqus*
CATIA Elfini*
MSC Nastran*
MSC Patran*
...
Flap Link Torsional Model
55
FEA-based Analysis Template: Link Plane Stress Model
COB-based CBAM - Constraint Schematic (classical view)
Plane Stress Bodies
y
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
Higher fidelity version
vs. Link 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
56
FEA-based Analysis Template: Link Plane Stress Model
COB-based CBAM - SysML Parametric Diagram (draft layout)
link
link_plane_stress_model
description
associated_condition :
condition
load
reaction
margin_of_safety
ux_mos_model :
margin_of_safety_model
flap_link
allowable
a
al8 : a=b
b
al3 : a=b
allowable_inter_axis_length_change
a
part_number
determined
b
effective_length
a
a
al14 : a=b
al9 : a=b
b
b
al5 : a=b
a
width
b
sleeve1 : sleeve
b
force
ux
wall_thickness
al6 : a=b
a
outer_diameter
l
shaft : tapered_beam
b
ws1
al7 : a=b*2.0
critical_cross_section : cross_section
a
ts1
flange_thickness
b
rs1
al12 : a=b
total_height
a
flange_width
basic : basic_I_section
web_height
tf
b
al13 : a=b
a
al11 : a=b
a
al9 : a=b
a
web_thickness
wf
b
deformation_model : link_plane_stress_abb
wall_thickness
tw
b
sleeve2 : sleeve
width
ts2
outer_diameter
ws2
b
al8 : a=b
b
al10 : a=b*2.0
material
a
name
rs2
material
a
stress_strain_model : material_levels
ex
b
nuxy
al1 : a=b
a
youngs_modulus
linear_elastic :
linear_elastic_model
sx
Solving supported
via math tool and
FEA tool execution
b
b
al7 : a=b
a
al2 : a=b
a
al6 : a=b
b
poissons_ratio
margin_of_safety
sx_mos_model :
margin_of_safety_model
determined
allowable
a
yield_stress
Note: The outmost block should be depicted as a frame (of type par),
as in conformant flap_link examples elsewhere in this presentation.
57
SMM with Parameterized FEA Model
Flap Link Plane Stress Model
ANSYS Prep7 Template
Preprocessor Model Figure
Plane Stress Bodies
y
@EX1@ = Parameters populated by context ABB
ts2
tf
wf
ts1
ws1
tw
rs1
ws2
rs2
F
C
L x
!EX,NIUX,L,WS1,WS2,RS1,RS2,TS1,TS2,TW,TF,WF,FORCE
...
/prep7
! element type
et,1,plane42
L
SMM wrapped inside an ABB subsystem
as SysML parametric constraints
Class
par-d link_plane_stress_abb
ws1
ts1
rs1
ts2
rs2
tw
p4
p3
l
p8
p5
ws2
p6
p12
wf
r1 : CobExternalToolFunction
p1
p9
ex
p7
p13
force
p10
p2
nuxy
p11
r
tf
ux
sx
p4
p3
p8
p5
p6
p12
r2 : CobExternalToolFunction
p1
p9
p7
p13
p10
p2
p11
r
! material properties
mp,ex,1,@EX@
mp,nuxy,1,@NIUX@
! geometric parameters
L
= @L@
ts1
= @TS1@
rs1
= @RS1@
tf
= @TF@
...
! elastic modulus
! Poissons ratio
!
!
!
!
length
thickness of sleeve1
radius of sleeve1 (rs1<rs2)
thickness of shaft flange
! key points
k,1,0,0
k,2,0,rs1+ts1
k,3,-(rs1+ts1)*sin(phi),(rs1+ts1)*cos(phi)
...
! lines
LARC,3,2,1,rs1+ts1,
LARC,7,3,1,rs1+ts1,
...
! areas
FLST,2,4,4
AL,P51X
SMM = solution method model
...
58
Design-Analysis Interoperability (DAI) Panorama
Flap Link Benchmark Tutorial - Composable Object (COB)-based Constraint Schematic
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,
t T
E
2(1 )
e
T
t
r4
area, A
T, , x
Extension
r3
r2
undeformed length, Lo
G
F
E, A,
shear strain,
r5
L
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,L
r1
start, x1
shear modulus, G
linkage
y
temperature change,T
r4
thermal strain, t
e
stress, E
Torsional Rod
T
One D Linear
Elastic Model
strain,
r3
effective length, Leff
mode: shaft tension
Lo
material model
elastic strain, e
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
L
x2
al2
linear elastic model
Lo
x1
E
F
G
stress mos model
torque, Tr
polar moment of inertia, J
e
radius, r
T
t
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
mode: shaft torsion
Torsion
area
b
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)
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
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
shear modulus, G
2
FEA
Ansys
Abaqus*
CATIA Elfini*
MSC Nastran*
MSC Patran*
...
Flap Link Torsional Model
59
Analysis Template: Flap Link Torsional Model
COB-based CBAM - Constraint Schematic (classical view)
Diverse Mode (Behavior) vs. Link Extensional Model
L
A
ts2
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
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
shear modulus, G
al3
2
J
r
G
T
stress mos model
allowable
twist
Margin of Safety
(> case)
allowable
actual
actual
MS
MS
60
Analysis Template: Flap Link Torsional Model
COB-based CBAM - SysML Parametric Diagram (draft layout)
link_torsional_model
flap_link
allowable
margin_of_safety
load
associated_condition :
condition
description
twist_mos_model :
margin_of_safety_model
a
al8 : a=b
b
part_number
allowable_twist
determined
reaction
effective_length
a
al9 : a=b
b
b
shaft : tapered_beam
deformation_model : torsional_rod
al5 : a=b
critical_cross_section : cross_section
a
torque
twist
total_height
a
theta_start
al1 : a=b
material_model :
one_D_linear_elastic_model_isothermal
b
basic : basic_I_section
undeformed_length
area
temperature
name
shear_stress
shear_modulus
a
radius
al1a : a=b/2.1
b
theta_end
material
reference_temperature
polar_moment_of_inertia
al2 : a=b*0.9
a
b
material
name
b
a
Solving supported via
math tool execution
al4 : a=b
stress_strain_model : material_levels
b
al7 : a=b
shear_modulus
a
a
al3 : a=b
b
al6 : a=b
b
linear_elastic :
linear_elastic_model
determined
margin_of_safety
stress_mos_model :
margin_of_safety_model
allowable
a
yield_stress
Note: The outmost block should be depicted as a frame (of type par),
as in conformant flap_link examples elsewhere in this presentation.
61
Modularity and Reusability in
Flap Link Benchmark Problem
SysML Package Structure
cobs
common
«git-schema»
flap_link_apm
«git-schema»
apm
«git-use-from»
«git-use-from»
«git-schema»
abbs
«git-schema»
flap_link_cbams
«git-schema»
geometry
«git-schema»
materials
«git-use-from»
62
Next Steps
Update current examples and tool interfaces
Conformance to SysML spec
SysML v0.98 (SST) - ~2006-01
SysML v1.0 - ~2006-1Q
Draft recommended practices for SysML-based CAD/CAE
and general parametrics usage
Expand examples: other system levels, constructs,
domains, CAD tools, CAE solvers, ...
Copyright © 2005
63
Summary
Completed several test cases on representing
executable physics-based CAE models in SysML
Tutorial & benchmark problems
Triangles, analytical springs, flap link
Includes interfaces to representative COTS solvers
General math: Mathematica
FEA: Ansys
Leverages composable object (COB)
and simulation template techniques
Usage for knowledge capture & usage
MRA for CAD-CAE and systems-of-systems (SoS)
Diverse CAD/CAE tools, behaviors, fidelity, ...
Modular, reusable simulation building blocks
Copyright © 2005
and fine-grained inter-model associativity
64
Copyright © 2005
65
Reference & Backup Slides
Copyright © 2005
67
Contents - Part 1
Purpose
CAD-CAE simulation template background
MCAD-MCAE benchmark example: flap link
Modularity & reusability
Executable SysML parametrics (math, FEA)
Summary
Recommended prerequisites
Triangle tutorial
Spring systems tutorial
Multi-representation architecture (MRA)
for simulation templates and CAD-CAE interoperability
[plus see flap link example above and references]
Copyright © 2005
68
Frame of Reference
CAD-CAE Model Representation & Interoperability R&D
~1992 - Present
Design Models
Other Model
Abstractions
(Patterns)
Design
Models
Analysis
Models
Analysis Models
Resulting techniques to date:
Architecture with new model abstractions (patterns)
– Enables modular, reusable building blocks
– Supports diversity:
» Product domains and physical behaviors
» CAD/E methods and tools
– Supports multiple levels of fidelity
© 1993-2001 GTRC
Engineering Information Systems Lab eislab.gatech.edu
69
Frame of Reference (cont.)
CAD-CAE Model Representation & Interoperability R&D
Key Capabilities
Idealization & Associativity Relations
Design Models
Other Model Abstractions (Patterns)
Analysis Models
Represent design-analysis model associativity
as tool-independent knowledge
Provide methodology
– Capture analysis idealization knowledge
– Create highly automated analysis templates
– Support product design
© 1993-2001 GTRC
Engineering Information Systems Lab eislab.gatech.edu
70
Frame of Reference (cont.)
CAD-CAE Model Representation & Interoperability R&D
Mapping to a Conceptual Architecture
Idealization & Associativity Relations
Other Model Abstractions (Patterns)
Design Models
ProductSpecific
3
Analyzable
Product Model
Analysis Models
ProductIndependent
4 Context-Based Analysis Model
APM
2 Analysis Building Block
Printed Wiring Assembly (PWA)
1 Solution Method Model
CBAM
Solder
Joint
Component
i
ABB
SMM
APM ABB
Component
Solder Joint
PWB
T0
body 1
body4
ABBSMM
body3
body 2
Printed Wiring Board (PWB)
Design Tools
© 1993-2001 GTRC
Solution Tools
Multi-Representation
Architecture (MRA)
Engineering Information Systems Lab eislab.gatech.edu
71
A Basic Solder Joint Deformation Template
Informal Associativity Diagram
Design Model
3 APM
PWA Component Occurrence
linear-elastic model
primary structural
material
Solder
Joint
Analysis Model
total height, h c
Component
base: Alumina
Epoxy
PWB
core: FR4
Solder Joint Plane Strain Model
4 CBAM
Plane Strain Bodies System
2 ABB
C
L
h1
APM ABB
body 1
body 4
To
body 3
body 2
plane strain bodyi , i = 1...4
geometryi
materiali (E, , )
ABB SMM
1 SMM
FEA Model
Printed Wiring Board/Assembly (PWA/PWB)
© 1993-2001 GTRC
Engineering Information Systems Lab eislab.gatech.edu
72
http://eislab.gatech.edu/pubs/conferences/2003-asme-detc-peak/
Preliminary Characterization of CAD-CAE Interoperability Problem
Estimated quantities for all structural analyses of a complex system (airframe)
Idealization & Associativity Relations
Other Model Abstractions (Patterns)
Design Models
O(10K) relevant parts
3
Analyzable
Product Model
Analysis Models
O(10K) template types and
O(100K) template instances
4 Context-Based Analysis Model
O(100) building blocks
APM
2 Analysis Building Block
Printed Wiring Assembly (PWA)
1 Solution Method Model
CBAM
Solder
Joint
Component
i
ABB
SMM
APM ABB
Component
T0
Solder Joint
PWB
body 1
body4
ABBSMM
body3
body 2
Printed Wiring Board (PWB)
Design Tools
© 1993-2001 GTRC
O(100) tools
Engineering Information Systems Lab eislab.gatech.edu
Solution Tools
73
Preliminary Characterization of CAD-CAE Interoperability Problem
Estimated quantities for all structural analyses of a complex system (airframe) - cont.
CAD-CAE associativity relations are represented
as APM-ABB relations, APMABB , inside CBAMs
3
Analyzable
Product Model
O(100K) template instances containing
O(1M) associativity relations
4 Context-Based Analysis Model
APM
2 Analysis Building Block
Printed Wiring Assembly (PWA)
1 Solution Method Model
CBAM
Solder
Joint
Component
i
ABB
SMM
APM ABB
Component
Solder Joint
PWB
T0
body 1
body4
ABBSMM
body3
body 2
Printed Wiring Board (PWB)
Design Tools
Solution Tools
associativity gap = computer-insensible relation
© 1993-2001 GTRC
Engineering Information Systems Lab eislab.gatech.edu
~1M gaps
74
Contents - Part 1
Purpose
CAD-CAE simulation template background
MCAD-MCAE benchmark example: flap link
Modularity & reusability
Executable SysML parametrics (math, FEA)
Summary
Recommended prerequisites
Copyright © 2005
Triangle tutorial
Spring systems tutorial
Multi-representation architecture (MRA)
for simulation templates and CAD-CAE interoperability
75
SysML-based Examples by GIT
Test Cases
Introductory tutorials (A)
Triangle
Spring systems
Simulation template
tutorials (A, B)
Simulation building blocks
Mechanical CAD & CAE: flap link
Tool Interfaces
A. Math solvers:
1.
Mathematica
B. Finite element analysis
(FEA) solvers:
1.
Ansys
C. Dynamics solvers:
1.
Modelica/Dymola
Space systems: FireSat satellite
Fluid power & system dynamics (C) -- see Part 2
Electrical/mechanical CAD & CAE
Model train (for Mechatronics pilot)
Racing bike
Copyright © 2005
Note: The SysML notation used in these slides roughly corresponds to SysML draft v0.9 plus more recent updates (approximately R. Burkhart blocks inputs as contained
in SysML spec v0.98 by SST) and experimental variations. We intend to update these examples with the final official notation when v1.0 that becomes available.
76
COB Structure: Graphical Forms
Tutorial: Analytical Spring Primitive
a. Shape Schematic-S
c. Constraint Schematic-S
L
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
L
Lo
F
x1
F k L
F
x2
k
r3
spring constant, k
deformed state
r1 : L x2 x1
b. Relations-S r2 : L L L0
undeformed length, L 0
r2
L L Lo
start, x1
L x2 x1
end, x2
force, F
total elongation, L
length, L
r1
r3 : F kL
Basic Constraint Schematic-S Notation
variable a
a
subvariable a.d
d
s
h
subsystem s
of cob type h
(for reuse by other COBs)
a b
subvariable s.b
Elementary
Spring
k
F
relation r1(a,b,s.c)
r1
b
r2
e bc
c d
option category 1
option 1.1:
[1.1] f = s.d
e
f
g
[1.2]
equality relation
e=f
c
w
L [ j:1,n]
© 1993-2005 GTRC
d. Subsystem-S
aggregate c.w
wj
option 1.2:
f=g
L0
L
x1
L
x2
element wj
Engineering Information Systems Lab eislab.gatech.edu
77
Analytical Spring Implemented
using SysML Block and Parametrics
SysML Parametric Diagram
spring
c
r1 : c=a-b
a
total_elongation
b
length0
undeformed_length
b
r2 : c=a-b
c
end0
a
start
force
b
c
r3 : c=a*b
a
spring_constant
Note: The outmost block should be depicted as a frame (of type par),
as in conformant flap_link examples elsewhere in this presentation.
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
78
COB Structure (cont.): Lexical Form
Spring Primitive
Constraint Schematic-S
spring constant, k
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
© 1993-2005 GTRC
r3
F k L
undeformed length, L 0
r2
L L Lo
start, x1
L x2 x1
end, x2
force, F
total elongation, L
length, L
r1
Lexical COB Structure (COS)
COB spring SUBTYPE_OF abb;
undeformed_length, L<sub>0</sub> : REAL;
spring_constant, k : REAL;
start, x<sub>1</sub> : REAL;
end, x<sub>2</sub> : 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;
Engineering Information Systems Lab eislab.gatech.edu
79
Example COB Instance
Spring Primitive
Constraint Schematic-I
Lexical COB Instance (COI)
example 1, state 1.1
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
5 N/mm
20 mm
r3
spring constant, k
F kL
undeformed length, L 0
r2
L L Lo
start, x1
L x2 x1
end, x2
state 1.0 (unsolved):
force, F
total elongation, L
length, L
10 N
2 mm
22 mm
r1
Basic Constraint Schematic-I Notation
100 lbs
30e6 psi
200 lbs
X
a
Input a = 100 lbs
b
Result b = 30e6 psi
(output or intermediate variable)
c
Result c = 200 lbs
(output of primary interest)
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;
Equality relation is suspended
X r1
Relation r1 is suspended
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
80
Multi-Directional I/O (non-causal)
Spring Primitive
Constraint Schematic-I
Design Verification
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
5 N/mm
20 mm
example 1, state 1.1
r3
spring constant, k
F kL
undeformed length, L 0
r2
L L Lo
start, x1
L x2 x1
end, x2
Design Synthesis
20 N/mm
total elongation, L
length, L
state 5.0 (unsolved):
10 N
2 mm
22 mm
spring constant, k
r3
F kL
L L Lo
10 mm
start, x1
L x2 x1
32 mm
end, x2
INSTANCE_OF spring;
undeformed_length : 20.0;
spring_constant : ?;
start : 10.0;
length : 22.0;
force : 40.0;
END_INSTANCE;
state 5.1 (solved):
example 1, state 5.1
undeformed length, L 0
© 1993-2005 GTRC
force, F
r1
r2
20 mm
Lexical COB Instance (COI)
force, F
total elongation, L
length, L
40 N
2 mm
22 mm
r1
Engineering Information Systems Lab eislab.gatech.edu
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;
81
Traditional Mathematical Representation
Tutorial: Two Spring System
System Figure
k1
k2
P
u1
u2
Free Body Diagrams
L2
L1
L1
L10
F1
x11
Kinematic Relations
Constitutive Relations
© 1993-2005 GTRC
k1
x12
F1
L2
L20
F2
x21
k2
x22
F2
Variables and Relations
r11 : L1 x12 x11
bc1 : x11 0
r12 : L1 L1 L10
bc2 : x12 x21
r13 : F1 k1L1
bc3 : F1 F2
r21 : L2 x22 x21
bc4 : F2 P
r22 : L2 L2 L20
bc5 : u1 L1
r23 : F2 k 2 L2
bc6 : u2 L2 u1
Engineering Information Systems Lab eislab.gatech.edu
Boundary Conditions
82
COB Constraint Schematic-S
Two Spring System
k1
k2
P
u1
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
Analysis Primitives
with
Encapsulated Relations
spring 1
r13 : F1 k1L1
r21 : L2 x22 x21
r22 : L2 L2 L20
r23 : F2 k 2 L2
System-Level Relations
(Boundary Conditions)
Elementary
Spring
k
r11 : L1 x12 x11
r12 : L1 L1 L10
u2
x11 0
bc1
F
L0
L
x1
L
bc5
u1
bc1 : x11 0
bc2 : x12 x21
bc3 : F1 F2
x2
bc2
bc4 : F2 P
bc3
bc5 : u1 L1
spring 2
bc6 : u2 L2 u1
Elementary
Spring
k
bc4
F
L0
L
x1
L
u 2 L2 u1
P
u2
bc6
x2
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
83
Spring System Implemented
using SysML Blocks and Parametrics
SysML Block Definition Diagram (bdd)
«git-root-cob»
«abb»
two_spring_system
«abb»
spring
1
1
spring1
deformation1 : REAL
deformation2 : REAL
load : REAL
1
spring2
undeformed_length : REAL
1 spring_constant : REAL
start : REAL
end0 : REAL
length0 : REAL
total_elongation : REAL
force : REAL
SysML Parametric Diagram
par-d
Class two_spring_system
deformation2 : REAL
c
bc6 : c=a+b
a
b
total_elongation
undeformed_length
1
start
1
end0
deformation1 : REAL
spring_constant
total_elongation
«part»
«abb»
spring1 : spring
length0
a
bc2 : a=b
«part»
«abb»
spring2 : spring
undeformed_length
b
length0
end0
spring_constant
force
start
force
a
a
bc3 : a=b
load : REAL
b
a
a
bc5 : a=b
b
bc1 : a=0
bc4 : a=b
b
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
84
Constraint Graph-S
Two Spring System
k1
k2
P
u1
u2
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
r11 : L1 x12 x11
r12 : L1 L1 L10
r13 : F1 k1L1
F1
r21 : L2 x22 x21
r13
r23 : F2 k 2 L2
bc2 : x12 x21
bc3 : F1 F2
bc4 : F2 P
bc5 : u1 L1
bc6 : u2 L2 u1
k2
spring2
L1
spring1
r23
L2
x22
L1
r11
bc4
F2
k1
r22 : L2 L2 L20
bc1 : x11 0
P
bc3
bc1
L2
r21
r12
r22
x12
x21
L10
L20
bc6
bc5
u1
u2
bc2
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
85
COB Representation
Constraint Schematic-S: Two Spring System
Constraint Graph-S
P
bc3
bc1
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
F1
Constraint Schematic-S
F2
k1
r13
spring 1
x11
Ele me nta ry
S pring
k
F
L0
x11 0
bc1
x1
L
u1
r22
x12
x21
L10
L20
bc6
bc5
L
u1
x2
bc2
L2
r21
r12
bc5
r23
L2
x22
L1
r11
k2
spring2
spring1
L1
bc4
u2
bc2
bc3
spring 2
Ele me nta ry
S pring
k
bc4
F
L0
L
x1
L
u 2 L2 u1
P
u2
• Encapsulated form (hides details)
bc6
x2
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
86
COBs as Building Blocks
Two Spring System
k1
k2
P
u1
u2
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
Constraint Schematic-S
spring 1
Elementary
Spring
k
x11 0
bc1
Lexical COB Structure (COS)
F
L0
L
x1
L
bc5
x2
bc2
bc3
spring 2
Elementary
Spring
k
bc4
F
L0
L
x1
L
u 2 L2 u1
bc6
COB spring_system SUBTYPE_OF analysis_system;
spring1 : spring;
spring2 : spring;
deformation1, u<sub>1</sub> : REAL;
deformation2, u<sub>2</sub> : REAL;
load, P : REAL;
RELATIONS
bc1 : "<spring1.start> == 0.0";
bc2 : "<spring1.end> == <spring2.start>";
bc3 : "<spring1.force> == <spring2.force>";
bc4 : "<spring2.force> == <load>";
bc5 : "<deformation1> ==
P
<spring1.total_elongation>";
bc6
:
"<deformation2>
==
u2
<spring2.total_elongation> + <deformation1>";
END_COB;
u1
x2
© 1993-2005 GTRC
Engineering Information Systems Lab eislab.gatech.edu
87
Analysis System Instance
Two Spring System
Constraint Schematic-I
Lexical COB Instance (COI)
state 1.0 (unsolved):
INSTANCE_OF spring_system;
spring1.undeformed_length
spring1.spring_constant :
spring2.undeformed_length
spring2.spring_constant :
load : 10.0;
deformation2 : ?;
END_INSTANCE;
example 2, state 1.1
Classical COB Notation [Peak, 1993; Tamburini, 1999; Wilson, 2000]
spring 1
Elementary
Spring
10.0
5.5
k
8.0
L0
L
1.818
x1
L
9.818
x11 0
bc1
F
bc5
u1 1.818
x2
9.818
bc2
bc3
spring 2
Elementary
Spring
6.0
k
8.0
L0
L
9.818
x1
L
19.48
x2
© 1993-2005 GTRC
F
10.0
bc4
1.667
u 2 L2 u1
9.667 bc6
: 8.0;
5.5;
: 8.0;
6.0;
P
10.0
u2 3.485
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;
Engineering Information Systems Lab eislab.gatech.edu
88
