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Transcript of Computational Morphogenesis - 名大の授業 (NU...
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Computational Morphogenesis- Its Current State and Possibility for the Future-
Hiroshi OhmoriNagoya University, Japan
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Finite Element Method• 1956 M. J. Turner, R. W. Clough, H. C. Martin
and L. J. Topp: “Stiffness and Deflection
Analysis of Complex Structures”
• Early 60s Infant Period - Vast Numbers of
Application to Structural Problems
• Late 60s Mathematical Proofs of Convergence
• 70s Application to Non-Structural Problems -
Fluid, Heat, Sound, Soil and Electro-Magnetic
Problems
• After 80s Visualization, Virtual Reality, Super
High Degree-of-Freedom Problem….
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Structural Optimization
• 1900 Michel Truss Problem - Truss Topology
Problem
• 60s Size Optimization Problem - Section Area of
Truss Structures, Linear Programming Scheme
• 70s Size Optimization - Section Area of Beam,
Linear Programming Scheme
• 80s - 90s Size Optimization - Shell Form, Shape
of Rigid Frames, Nonlinear Programming Scheme
• 1995 Truss Topology Optimization -
Homogenization Design Method, Genetic
Algorithms
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Com
pute
r
1K
10K
1T
100G
10G
1G
100M
10M
1M
100K
Parallel Processor
Plural Processors
Single Processor
HITAC 5020E
i PSC860S- 820
CRAY- 2
SX- 2
SX- 3R
CRAY Y- MP/ C90
S- 3800
T3D
SX- 4VPP500
CRAY Y- MP8
VP2600
Cenj u 3SR2001
I CUBE 2S
CM- 5E
40048008
8080
8086
286
386
486
Pentium
Pentium II
Pentium III
Pentium 4
Itanium
Itanium 2
Transistor *
i/Chip)
109
108
107
106
105
104
103
FORTRAN Virrtual Memory Cray fail
Performance
ENIAC
IBM701
IBM 7094
CDC 7600
ILLIAC IV
Paragon XP/S
CRAY-I
CRAY X-MP/2
* from Website of Intel
Floppy Disk PC Wearable Compuet
Earth Simulator
History of Computer Performance
1950 1960 1970 1980 1990 2000 2010
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Truss Optimization
f =1
W(x, A)g i
i
ÕFitness Function
• Constraints
on Nodal Displacement
on Axial Stress with Buckling Consideration
• Evaluation : Finite Element Analysis
• Genetic Algorithm (Selection, Crossover, Mutation)
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Truss Optimization
Young’s Modulus 210 GPa
Population 20
Elite 2
Generation for Layout 200
Generation for SectionalArea
200
Generation for Material 100
Generation for Connection
200
Displacement Limit 70 mm
Stress Limit (Tension) 160 MPa
(Compression) Buckling Stress
Variables
• Element Arrangement
• Sectional Area
Constraints
• Nodal Displacement
• Stress Resultant
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Truss Optimization
Frame Structure
Truss Structure
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Truss Optimization
• Rise
Population 20Elite 2Generation for Layout 500Generation for Sectional Area 500Generation for Material 50Displacement Limit 20 mmStress Limit (Tension) 160 MPa
(Compression) Buckling Stress
• Layer Thickness
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Truss Domes
Thickness 1m
Thickness 2m
平面図 側面図 鳥瞰図
平面図 側面図 鳥瞰図
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Truss Domes
Rise 5m
Rise 3m
平面図 側面図 鳥瞰図
平面図 側面図 鳥瞰図
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Hybrid System Domes
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Roof Truss
Target Region
500 Pa Vertical Load on the Top Plane
Whole Shape
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Trusses with Maximum Element Length
520 cm(Shortest)
1.8089
750 cm(Middle)
1.52129
1040 cm(Longest)
1.83456
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Trusses with Various Kinds of Element
4 Kinds 16 Kinds
Fitness=1.73684 Fitness=1.17865
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
4 Standard Elements 16 Standard Elements
Birds View
Plan
Truss Optimization
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Comparison between ESO & Extended ESO
ESO
Extended ESO
ESO Extended ESO
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Bridge Structures
1
2
1
4
1
8
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Shell hP
Plan Perspective
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
3D Bridge Structure
3B
B H
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
3D Bridge Structure
Final Configuration
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
3D Bridge Structure
Step 1 Step 2 Step 3
Step 4 Step 5 Step 6
Step 7 Step 8 Step 9
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
3D Bridge Structure
Plan
Elevation
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Firenze New Station Building Project
Global Structure Perspective
By Courtesy of Arata Isozaki Atelier + Mutsuro Sasaki Structural Design Office
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Final Shape
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Application to Office Building Design
West Elevation South Elevation
F-tai Architect + Iijima Structural Design Office, Cooperation: Mutoh Laboratory(Meijo Univ.)
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Akutagawa Westside Project
Northwest Elevation Southwest Elevation
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Q4
Q3
Q2
Q1
Q4
Q3
Q2
Q1
P4
P3
P2
P1
260cm
280cm
280cm
300cm
775cm
Q4
Q3
Q2
Q1
Q4
Q3
Q2
Q1
P4
P3
P2
P1
260cm
280cm
280cm
300cm
650cm
˚ … ˚
Loading Condition
South West
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Final
South WallEvolution
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Evolution Process
Final
Initial
設計:フータイアーキテクツ+飯島建築事務所、協力:名城大学・武藤研究室F-tai Architect + Iijima Structural Design Office, Cooperation + Mutoh Laboratory(Meijo Univ.)
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Perspective View
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan) Mold and Reinforcement Construction
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan) From Arcade
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Akutagawa Westside Project
Akutagawa Westside Project
Initial
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
• Background
• Purpose
Traditional Design Approach Sustainable Design Approach
Environmental ProblemWarming Temperature
Acid Precipitate etc.
Reduction of Environmental Impact
Design Approach Considering Life Cycle (LC) Life Cycle Design (LCD)
Life Cycle Design
Deteriorating Some Determining Factors During Life Cycle
Optimization
IDEAL WAYof building design
Life Cycle Design of Building Structures
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
• “Hierarchy” of Building Materials
Life Cycle Evaluation Method
Upper layer
Upper layer
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
• Evaluation of “Hierarchy”
Life Cycle Evaluation Method
:Rank of “Supporting” Member
:Rank of Member
CO2
Cost
Life Cycle CO2 (LCCO2)
Life Cycle Cost (LCC)
Physical Unit of Product
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
■ Problem Setting
– Design Variable• Component Parts
• Scenario of Building Maintenance
– Objective Function • Economic : Life Cycle Cost
• Environmental : Life Cycle CO2
– Optimization Method• Genetic Algorithm (GA)
– Evaluation Period
Treatment as an Optimization Problem
Multi-Objective Optimization
Multi-Variable Optimization
100 Years
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Life-Cycle Optimization
• Problem Area – Two-Storied House
– GA Parameters
Population 100Elite 2Generation 1000Probability of Crossover 0.01Probability of Mutation 0.01
Population 100Archive 25Generation 1000Probability of Crossover 0.01Probability of Mutation 0.01
Single-Objective Multi-Objective
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Single-Objective Optimization
• Life Cycle Cost
• Life Cycle CO2
Tra
de-o
ff
MinimumLCC
MinimumLCCO2
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Multi-Objective Optimization
100th Generation
1000th Generation
Pareto FrontPlural Reasonably Optimal Solutions
Moderately Dispersed Solutions
Structure of Solutions.
Enlarged
Can Support Decision-Maker's Judgement
Optimizing…
Optimizing…
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Optimum Arrangement in Space-Time Continuum
Spatial Coordinate A
Time
Spatial Coordinate B
Initial Design1st Repairment
2nd RepairmentN-th Repaiment
Waste
Reuse
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Structural System Proposer as Next Generation of CM
Structural Analysis(FEM)
Structural Optimization
1970’s 〜 2000’s
1970’s 〜 1980’s
1990’s
2000’s 〜
Strategic System Design
Strategic Scenario Design
2000’s 〜
2000’s 〜
Structural MechanicsMathematical Programming
Multi-Objective Programming
Structural System Proposer
Safety・Constructionability
Economics
Sustainability
ComputationalMorphogenesis Life Cycle Design
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
IASS WG/Sub-WG
WG13 – Numerical Methods in Shell and Spatial Structures (A. Samartin, H.Ohmori)
Sub-WG on Computational Morphogenesis (H. Ohmori)
WG15 – Structural Morphology (R. Motro)
WG on Free-Form Design (M. Grohman, A. Borgart)
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008 Hiroshi Omori(Nagoya University, Japan)
Computational Morphogenesis- Its Current State and Possibility for the Future-
“ The structure’s beauty can be found near its rationality.”
by Yoshikatsu TsuboiFormer President of IASS
Hiroshi OHMORI