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