l8 optimize
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16.810 (16.682)16.810 (16.682)Engineering Design and Rapid PrototypingEngineering Design and Rapid Prototyping
Design Optimization- Structural Design OptimizationInstructor(s)
Prof. Olivier de Weck Dr. Il Yong Kim
January 23, 2004
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Course Concept
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today
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Course Flow Diagram
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CAD/CAM/CAE Intro
Overview
ManufacturingTraining
Structural TestTraining
Design Optimization
Hand sketching
CAD design
FEM analysis
Produce Part 1
Test
Produce Part 2
Optimization
Problem statement
Final Review
Test
Learning/Review Deliverables
Design Sketch v1
Part v1
Experiment data v1
Design/Analysis
output v2
Part v2
Experiment data v2
Drawing v1
Design Intro
today
Wednesday
FEM/Solid MechanicsAnalysis output v1
3
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What Is Design Optimization?
Selecting the best design within the available means
1. What is our criterion for best design? Objective function
2. What are the available means? Constraints
(design requirements)
3. How do we describe different designs? Design Variables
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Optimization Statement
MinimizeSubject to
f
g
h(x)
( ) 0x( ) 0x
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Constraints
- Design requirementsInequality constraints
Equality constraints
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Objective Function- A criterion for best design (or goodness of a design)
Objective function
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Design VariablesParameters that are chosen to describe the design of a system
Design variables are controlled by the designers
The position of upper holes along the design freedom line
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Design VariablesFor computational design optimization,
Objective function and constraints must be expressedas a function of design variables (or design vector X)
Objective function: f(x) Constraints:g(x), h(x)Cost = f(design)Displacement = f(design)
What is f for each case?Natural frequency = f(design)Mass = f(design)
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Optimization Statement( )
( ) 0
( ) 0
f
h
x
x
x
Minimize
Subject to g
f(x) : Objective function to be minimized
g(x) : Inequality constraints
h(x) : Equality constraints
x : Design variables
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Optimization Procedure
Improve Design Computer Simulation
START
Converge ?
Y
N
END
( )
Subj ( ) 0
( ) 0
f
g
h
x
x
x
Change x
Determine an initial design (x0)
termination criterion?
Minimize
ect to
Evaluate f(x), g(x), h(x)
Does your design meet a
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Structural OptimizationSelecting the beststructuraldesign
- Size Optimization - Shape Optimization- Topology Optimization
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Structural Optimization
( )
j ( ) 0
( ) 0
f
g
h
x
x
x
BCs are given Loads are given
minimize
sub ect to
1. To make the structure strong Min. f (x)
e.g. Minimize displacement at the tip
g(x) 02. Total mass MC
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Size OptimizationBeams
( )j ( ) 0
( ) 0
fg
h
xx
x
minimizesub ect to
Design variables (x) f(x) : compliance
x : thickness of each beam g(x) : mass
Number of design variables (ndv)
ndv = 5
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Size Optimization
- Shapeare given
Topology- Optimize cross sections
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Shape OptimizationB-spline
( )j ( ) 0
( ) 0
fg
h
xx
x
Hermite, Bezier, B-spline, NURBS, etc.
minimizesub ect to
Design variables (x) f(x) : compliancex : control points of the B-spline
g(x) : mass(position of each control point)
Number of design variables (ndv)
ndv = 8
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Shape OptimizationFillet problem Hook problem Arm problem
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Shape OptimizationMultiobjective & Multidisciplinary Shape OptimizationObjective function
1. Drag coefficient, 2. Amplitude of backscattered wave
Analysis
1. Computational Fluid Dynamics Analysis
2. Computational Electromagnetic WaveField Analysis
Obtain Pareto Front
Raino A.E. Makinen et al., Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic
algorithms, International Journal for Numerical Methods in Fluids, Vol. 30, pp. 149-159, 1999
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Topology OptimizationCells
( )j ( ) 0
( ) 0
fg
h
xx
x
minimizesub ect to
Design variables (x) f(x) : compliance
x : density of each cell g(x) : massNumber of design variables (ndv)
ndv = 27
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Topology OptimizationShort Cantilever problem
Initial
Optimized
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Topology Optimization
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Topology OptimizationBridge problem
Obj = 4.16105Distributed
loading
Obj = 3.29105Minimize
i idzF ,
)toSubject ( dx M ,o0 (x) 1 Obj = 2.88105
Mass constraints: 35%
Obj = 2.7310516.810 (16.682) 22
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Topology OptimizationDongJak Bridge in Seoul, Korea
H
L
H
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Structural OptimizationWhat determines the type of structural optimization?
Type of the design variable(How to describe the design?)
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Optimum Solution Graphical Representation
f(x)
x: design variable
f(x): displacement
Optimum solution (x*)x
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Optimization Methods
Gradient-based methods
Heuristic methods
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Gradient-based Methodsf(x)
Start
Move
Gradient=0 Stop!
You do no c ore optimization
Check gradient
Check gradient
t know this fun tion bef
No active constraints Optimum solution (x*)x
(Termination criterion: Gradient=0)
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Gradient-based Methods
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Global optimum vs. Local optimumf(x) Termination criterion: Gradient=0
Global optimum
Local optimum
Local optimum
xNo active constraints
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Heuristic Methods A Heuristic is simply a rule of thumb that hopefully will find a
good answer.
Why use a Heuristic?
Heuristics are typically used to solve complex optimization
problems that are difficult to solve to optimality.
Heuristics are good at dealing with local optima without
getting stuck in them while searching for the global optimum.
Schulz, A.S., Metaheuristics, 15.057 Systems Optimization Course Notes, MIT, 1999.
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Genetic AlgorithmPrinciple by Charles Darwin - Natural Selection
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Heuristic Methods Heuristics Often Incorporate Randomization
3 Most Common Heuristic Techniques
Genetic Algorithms
Simulated Annealing Tabu Search
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Optimization Software- iSIGHT
- DOT
- Matlab (fmincon)
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Topology Optimization Software ANSYS
Static Topology Optimization
Dynamic Topology Optimization
Electromagnetic Topology Optimization
Subproblem Approximation Method
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Design domain
First Order Method
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Topology Optimization Software MSC. Visual Nastran FEA
Elements of lowest stress are removed gradually.
Optimization results
Optimization results illustration
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MDO
Multidisciplinary Design Optimization
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Multidisciplinary Design OptimizationCentroid Jitter on Focal Plane [RSS LOS]NASA Nexus Spacecraft Concept
60
T=5 sec
14.97 m
1 pixel
Requirement: J =5 mz,2
OTA
4020
CentroidY[m]
0-20
SunshieldInstrument -40Module
0 1 2 -60
-60 -40 -20 0 20 40 60meters
Centroid X [m]
Goal: Find a balanced system design, where the flexible structure, the optics and the control systems worktogether to achieve a desired pointing performance, given various constraints
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Multidisciplinary Design OptimizationAircraft Comparison
le
Approx. 480 passengers each
Approx. 8,700 nm range each
TakeoffBWBA3XX-50R
18%
BWBA3XX-50R
19%Total
Sea-Level
19%BWBA3XX-50R
Operators
Empty
Fuel
Burn
per Seat
32%BWBA3XX-50R
Boeing Blended Wing Body Concept
Goal
Shown to Same Sca
Maximum
Weight
Static Thrust
Weight
: Find a design for a family of blended wing aircraftthat will combine aerodynamics, structures, propulsionand controls such that a competitive system emerges - as
measured by a set of operator metrics.
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Multidisciplinary Design OptimizationFerrari 360 Spider
Goal: High end vehicle shape optimization whileimproving car safety for fixed performance level
and given geometric constraints
Reference: G. Lombardi, A. Vicere, H. Paap, G. Manacorda,Optimized Aerodynamic Design for High Performance Cars, AIAA-98-4789, MAO Conference, St. Louis, 1998
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Multidisciplinary Design Optimization
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Multidisciplinary Design Optimization
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Multidisciplinary Design OptimizationDo you want to learn more about MDO?
Take this course!
16.888/ESD.77Multidisciplinary System
Design Optimization (MSDO)
Prof. Olivier de Weck
Prof. Karen Willcox
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Baseline DesignPerformance
Natural frequency analysis
Design requirements
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Baseline DesignPerformance and cost
1 0.070 mm
2 0.011 mmf 245Hz
m 0.224 lbs
C 5.16 $
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Baseline Design245 Hz 421 Hz
f1=0f2=0f3=0f4=0f5=0f6=0f7=421 Hzf8=1284 Hzf9=1310 Hz
f1=245 Hzf2=490 Hzf3=1656 Hz
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Design Requirement for Each Team#
Productname
mass(m)
Cost(c)
Disp(1) Disp(2)
NatFreq
(f)
Quality
F1(lbs)
F2(lbs)
F3(lbs)
Const Optim Acc
0Baseline
0.224lbs
5.16$
0.070mm
0.011mm
245Hz
3 50 50 100 c m f
1Family
economy20% -30% 10% 10% -20% 2 50 50 100 c m f
2Familydeluxe
10% -10% -10% -10% 10% 4 50 50 100 m c f
3Crossover
20% 0% -15% -15% 20% 4 50 75 75 m c f
4 City bike -20% -20% 0% 0% 0% 3 50 75 75 c m f
5 Racing -30% 50% 0% 0% 20% 5 100 100 50 m f c6 Mountain 30% 30% -20% -20% 30% 4 50 100 50 f m c7 BMX 0% 65% -15% -15% 40% 4 75 100 75 f m c
8 Acrobatic -30% 100% -10% -10% 50% 5 100 100 100 f m c
9Motorbike
50% 10% -20% -20% 0% 3 50 75 100 f c m
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Design OptimizationTopology optimization
Design domain
Shape optimization
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Design Freedom1 bar
2.50 mm
2 bars 0.80 mm
Volume is the same.
17 bars
0.63 mm
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Design Freedom1 bar
2 bars
2.50 mm
0.80 mm
17 bars
More design freedom More complex(Better performance) (More difficult to optimize)
0.63 mm
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Cost versus Performance17 bars
0
1
2
3
45
6
7
8
9
Cost
[$]
1 bar
2 bars
0 0.5 1 1.5 2 2.5 3Displacement [mm]
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Plan for the rest of the courseClass Survey
Jan 24 (Saturday) 7 am Jan 26 (Monday) 11am
Company tour
Jan 26 (Monday) : 1 pm 4 pm
Guest Lecture (Prof. Wilson, Bicycle Science)
Jan 28 (Wednesday) : 2 pm 3:30 pm
Manufacturing Bicycle Frames (Version 2)
Jan 28 (Wednesday) : 9 am 4:30 pm
Jan 29 (Thursday) : 9 am 12 pm
Testing
Jan 29 (Thursday) : 10 am 2 pm
GA GamesJan 29 (Thursday) : 1 pm 5 pm
Guest Lecture, Student Presentation (5~10 min/team)
Jan 30 (Friday) : 1 pm 4 pm
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ReferencesP. Y. Papalambros, Principles of optimal design, Cambridge University Press, 2000
O. de Weck and K. Willcox, Multidisciplinary System Design Optimization, MIT lecture note, 2003
M. O. Bendsoe and N. Kikuchi, Generating optimal topologies in structural design using ahomogenization method, comp. Meth. Appl. Mech. Engng, Vol. 71, pp. 197-224, 1988
Raino A.E. Makinen et al., Multidisciplinary shape optimization in aerodynamics andelectromagnetics using genetic algorithms, International Journal for Numerical Methods in Fluids,
Vol. 30, pp. 149-159, 1999
Il Yong Kim and Byung Man Kwak, Design space optimization using a numerical designcontinuation method, International Journal for Numerical Methods in Engineering, Vol. 53, Issue 8,pp. 1979-2002, March 20, 2002.
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Web-based topology optimization program
Developed and maintained by Dmitri Tcherniak, Ole Sigmund,
Thomas A. Poulsen and Thomas Buhl.
Features:1.2-D
2.Rectangular design domain
3.1000 design variables (1000 square elements)
4. Objective function: compliance (F)
5. Constraint: volume
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Web-based topology optimization programObjective function
-Compliance (F)
Constraint
-Volume
Design variables
- Density of each design cell
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Web-based topology optimization programNo numerical results are obtained.
Optimum layout is obtained.
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Web-based topology optimization programP 2P 3P
Absolute magnitude of load does not affect optimum solution
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Web-based topology optimization program
http://www.topopt.dtu.dk
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