Computational Morphogenesis- Its Current State and Possibility for the Future-

Hiroshi Ohmori
Nagoya 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. Martinand L. J. Topp: “Stiffness and Deflection
Analysis of Complex Structures”•Early 60s Infant Period - Vast Numbers ofApplication to Structural Problems•Late 60s Mathematical Proofs of Convergence•70s Application to Non-Structural Problems Fluid, Heat, Sound, Soil and Electro-MagneticProblems•

After 80s Visualization, Virtual Reality, SuperHigh 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 TopologyProblem• 60s Size Optimization Problem - Section Area ofTruss Structures, Linear Programming Scheme• 70s Size Optimization - Section Area of Beam,
Linear Programming Scheme• 80s - 90s Size Optimization - Shell Form, Shapeof Rigid Frames, Nonlinear Programming Scheme• 1995 Truss Topology Optimization Homogenization Design Method, GeneticAlgorithms
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Performance
1TSX- 4

VPP500Paragon XP/S

T3D
CM- 5E100G
S- 3800
SX- 3R
CRAY Y- MP/ C90

Parallel Processor

10G

I CUBE 2SSR2001
Cenj u 3i PSC860
VP2600S- 820 CRAY Y- MP8
CRAY- 2SX- 2

Plural Processors
Single Processor

1Gi/Chip)
109

Itanium 2

CRAY X-MP/2

Itanium

CRAY-I

100M

Transistor *108

Pentium 4
Pentium III

ComputerPentium II
107

ILLIAC IV

10M

Pentium

CDC 7600

486

1M* from Website of Intel386

HITAC 5020E

IBM 7094

106286

100K

105

8086
10410K

1K

8080

IBM701

8008

4004

103

ENIAC
1950

1960

FORTRAN

1970

1980

1990

Cray fail

Virrtual Memory
Floppy DiskPC

2000

2010

Earth Simulator

Wearable Compuet

History of Computer Performance
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Truss Optimization• Evaluation : Finite Element Analysis• Genetic Algorithm (Selection, Crossover, Mutation)
Fitness Function

1f =giÕW(x, A) i• Constraints
on Nodal Displacement
on Axial Stress with Buckling Consideration

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Truss Optimization

Variables• Element Arrangement• Sectional Area
Constraints• Nodal Displacement• Stress Resultant

Young’s Modulus

210 GPa

Population

20Elite2

Generation for Layout

200

Generation for Sectional
Area

200

Generation for Material

100

Generation forConnection

200

Displacement Limit

70 mm

Stress Limit

160 MPa

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

(Tension)(Compression) BucklingStressHiroshi 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• Layer Thickness• RisePopulation
Elite
Generation for Layout
Generation for Sectional Area
Generation for Material
Displacement Limit
Stress Limit (Tension)(Compression)
Stress20
2500500
5020 mm
160 MPa
Buckling

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Truss Domes
平面図

側面図

鳥瞰図Thickness 1m
平面図

側面図

鳥瞰図Thickness 2m
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Truss Domes
平面図

側面図

鳥瞰図Rise 5m
平面図

側面図

鳥瞰図Rise 3m
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

Whole Shape

Target Region
500 Pa Vertical Load on the Top Plane

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Trusses with Maximum Element Length
1.521291.8089520 cm(Shortest)

750 cm(Middle)

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

1.83456

1040 cm(Longest)

Hiroshi Omori(Nagoya University, Japan)

Trusses with Various Kinds of Element
Fitness=1.73684

4 Kinds

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Fitness=1.17865

16 Kinds

Hiroshi Omori(Nagoya University, Japan)

Truss Optimization

Birds View

Plan
4 Standard Elements

16 Standard Elements

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
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Extended ESO
Hiroshi Omori(Nagoya University, Japan)

Bridge Structures

114218IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

ShellPlan
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

PｈPerspective
Hiroshi Omori(Nagoya University, Japan)

3D Bridge Structure

HB
3B

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 9IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

3D Bridge Structure

PlanElevation
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 DesignWest ElevationSouth Elevation

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

F-tai Architect + Iijima Structural Design Office, Cooperation: Mutoh Laboratory(Meijo Univ.)Akutagawa Westside ProjectNorthwest Elevation
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Southwest Elevation
Hiroshi Omori(Nagoya University, Japan)

Loading Condition
P4Q4

P4Q4

P3Q3

Q4

P2
Q2

Q2
P1Q1P3260cm

Q3Q1Q4

Q3280cm

280cm

260cm

Q3P2Q2Q2P1Q1

Q1300cm

280cm

300cm

775cm

650cm

˚
South… ˚WestIASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

280cm

Hiroshi Omori(Nagoya University, Japan)

South WallEvolution

Final
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Evolution Process

InitialFinal

F-tai Architect + Iijima Structural
Design Office, Cooperation + Mutoh Laboratory(Meijo Univ.)
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

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
Hiroshi Omori(NagoyaUniversity, Japan)

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

From Arcade

Hiroshi Omori(Nagoya University, Japan)

Akutagawa Westside Project

InitialAkutagawa Westside Project

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Life Cycle Design of Building Structures• BackgroundTraditional Design Approach

Sustainable Design Approach

Environmental Problem
Warming Temperature
Acid Precipitate etc.

Reduction of Environmental Impact• Purpose
Design Approach Considering Life Cycle (LC)Life Cycle Design (LCD)

Deteriorating Some Determining Factors During Life Cycle
Optimization

Life Cycle Design
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

IDEAL WAYof building design
Hiroshi Omori(Nagoya University, Japan)

Life Cycle Evaluation Method• “Hierarchy” of Building Materials
Upper layer

Upper layer

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Life Cycle Evaluation Method• Evaluation of “Hierarchy”:Rank of Member:Rank of “Supporting” MemberPhysical Unit of ProductCO2

Life Cycle CO2 (LCCO2)

Cost

Life Cycle Cost (LCC)

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Treatment as an Optimization Problem■ Problem Setting–Design Variable••–

Objective Function••–Economic: Life Cycle Cost
Environmental : Life Cycle CO2
Multi-Objective Optimization

Optimization Method•–

Component Parts
Scenario of Building Maintenance
Multi-Variable Optimization

Genetic Algorithm (GA)

Evaluation Period

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
Single-Objective
Population
EliteGeneration
Probability of Crossover
Probability of Mutation

10021000
0.010.01

Multi-Objective
Population
ArchiveGeneration
Probability of Crossover
Probability of Mutation

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

100251000
0.010.01

Hiroshi Omori(Nagoya University, Japan)

Single-Objective Optimization

Trade-off• Life Cycle Cost

Minimum
LCC• Life Cycle CO2Minimum
LCCO2

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Multi-Objective Optimization
 Pareto FrontPlural Reasonably Optimal Solutions
Moderately Dispersed Solutions
Structure of Solutions.
Optimizing…

Can Support Decision-Maker's Judgement
100th Generation
Enlarged
Optimizing…

1000th Generation
IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi Omori(Nagoya University, Japan)

Optimum Arrangement in Space-Time Continuum
Spatial Coordinate B
Initial Design

1st Repairment
2nd Repairment

N-th Repaiment

Reuse

Time
Waste

Spatial Coordinate A
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 System Proposer
1970’s 〜 2000’s

2000’s 〜

ComputationalMorphogenesis

Life Cycle Design

Structural Analysis(FEM)

Strategic System Design

1970’s 〜 1980’s

2000’s 〜

Structural Optimization

Strategic Scenario Design

1990’s2000’s 〜

Structural Mechanics
Mathematical Programming

Multi-Objective Programming

Safety・Constructionability
Economics
Sustainability
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)

“ The structure’s beauty can befound near its rationality.”
by Yoshikatsu Tsuboi
Former President of IASS

Computational Morphogenesis- Its Current State and Possibility for the Future-

IASS-IACM2008 Cornell University, Ithaca, NY, USA 28-31 May 2008

Hiroshi OHMORI

Hiroshi Omori(Nagoya University, Japan)