task manager optimisation : gradient / genetic algorithms parallelism, winnt – unix...

Task Manager

Optimisation : Gradient / Genetic Algorithms

Parallelism, WinNT – UNIX Interoperability

Open Architecture

Graphic & Reporting Tools

Design of Experiments, Response Surfaces

Introduction to BOSS quattro

What does BOSS quattro ?

How does it work (data exchange & application control) ?

How does it work (task management) ?

“CAT-BOSS”

Applications

Today & Tomorrow

From Simulation Tools …• “Math model” to represent physics

Finite Elements Analytical codes EXCEL …

• Experimental data 표준 : Real-size or not Similar existing components

“ 주어진 설계에 관한 주어진 시스템에 대한 거동 예측”

… to Design Methodology• Trial-and-error(s)

• Exhaustive (combinatory) simulations

• Random simulations

• Design of experiments : 적절한 시뮬레이션• Optimisation methods

“ 요구되는 행동에 대한 설계 입력 값 요구”

Knowing the input, what is the output ?

Knowing the output, what is the input ?

Design Problems …

• 요구 값과 일치하는 해 찾기• 보다 나은 해 찾기• 더 나은 해 찾기• 몇몇의 목표에 사이에서의 타협 점 찾기• 확고한 해 찾기• 목표 기준과 근접한 해 찾기• 설계의 타당 영역 찾기 Find the validity domain of a design

• …

항상 가역 문제가 가능…

입력 모델• Variables = parameters• Size (section)

• Shape (geometry)

• Topology (concept)

• Configuration (material)

• …

변수는…• Continuous (radius)

• Discrete (ply thickness in library)

• Integer (number of holes)

• Non numeric (material name)

• Few or a lot

해석 결과 보기• Criteria = functions : any computable value• Multi-disciplinary (stress, acoustics, cost, ergonomy, performance, aesthetic, …)

• Multi-model (F.E. beam for structural, B.M. shape for fluid, EXCEL for cost, …)

• Objective(s) (“Minimise the cost but also the weight”)

• Constraint(s) (“Maximum stress lower than security value)

함수의 구성은…• Implicit

• Non-linear

• Not continuous

• In different unit systems

• A lot of values

• …

직접적인 관계 f(xi) 를 모르기 때문에 가역 문제는 근사에 의해 사용되고 있다 .

Parametric Design Tools• 목적 : 설계 공간의 개발• 전통적인 기법 (“trial & error”) 으로부터

역 변환 기법 (design tools) 까지• 국소적 및 전반적 근사

Open System• Multi-disciplinary, Multi-model

• 외부 소프트웨어와의 쉬운 통합 : 상업 소프트웨어와의 현존하는 연결 새로운 연결 생성을 위한 툴박스

• 초기 계획의 동기부여 !

Application Manager• 사용자 정의 응용과 체계• 기능 병합• Network resources 의 접근





“CAT-BOSS”

Applications

Today & Tomorrow

개요

Parametric Study

Design of Experiments Response Surfaces

Optimization

Monte Carlo

Updating

MODULES

최적화 / 용어

설계 변수 :

최적 조건에 도달하기 위해서 변할 수 있는 최적 알고리즘의 양능동 변수 :

Variable whose value lies on one of its bounds of definition

설계 공간 :

Space of variation of the design variables (dimension n, n is the number of design variables)

목적 함수 :

Function of the design variables whose value gives a choice criteria between several designs. They can be maximized or minimized

구속 :

These are the conditions the design has to respect (also called restrictions)

능동 구속 :

Constraint whose value lies on the boundary of the feasible space

실행 공간 :

Part of the design space where all constraints are satisfied

최적화 / 공식

• F(x) = Objective function(s)

• Xi = Design Variable(s)

• Cj = Constraint(s)

min f(x)

with ximin xi ximax i = 1,.. ncjmin cj(x) cjmax j = 1,.. m

Optimization : “ 경사도 (Gradient)”

• 최적화 문제는 설계 변수에 관련된 일반적인 non-linear, non-explicit 가 있다 .

• 해석에 제한되는 수를 피하기 위해서 민감도나 값에 기초한 explicit sub-problem ( 국소적 근사 ) 을 구성한다 .

• 예제 : linear, convex linear, quadratic...

• 알고리즘 라이버러리와 Explicit sub-problem 해결 : first and second order (CONLIN, SQP, GCM, ...)

• 하부의 문제는 실제 문제에 대한 근사이며 , 최적절차는 계속 반복적이다 .

• Multi-objective problems, discrete variables, non admissible starting point, large size problems, ...

• 다양한 제어 : Convergence Move Limits Relaxation Initial conditions

민감도 해석 (Sensitivity Analysis)

• Sensitivity is :

• Sensitivities are either: Computed (finite-differences) Read (SAMCEF, NASTRAN Sol200, NEUTRAL)

• Finite Difference scheme :

Perturbation run (10E-4 relative) => as many as variables. Prohibitive in some case !

d(Result)d(Variable)

Resultpert - Result_ VariablePert - Variable

형상최적화 : 민감도 해석• 유한 차분 기법 : CAD 변수 변경과 재

격자 생성으로… : 다른 수의 노드나 요소의 격자 생성 다른 번호를 가진 격자 생성 다른 방법을 사용한 격자의 매끄러움 … Build, in general, a different topology

• CAD-FE 최적 형상 : 격자 파생 관리 : Translate the variation of a CAD 변수에 대한 변화를 FEM mesh ("velocity field) 와 동등한 해석

• 노드의 재 배치 매카니즘

d(FEM)/d(CAD)=d(FEM)/d(XYZ)*d(XYZ)/d(CAD)

When ?

No sensitivities …

High number of variables

Integer (or non-numeric) variables

비 근사적 기법

결합된 문제

전반적인 해석

De Jong said…

“The key point in deciding whether or not to use genetic algorithms for a particular problem centers around the question: what is the space to be searched? If that space is well understood and contains structure that can be exploited by special-purpose search techniques, the use of GAs is generally computationally less efficient. If the space to be searched is not so well understood and relatively unstructured, then GAs provide a surprisingly powerful search heuristic for large, complex spaces”

Zero-Order Algorithms

To each parameter set S is associated a value representing the efficacy or fitness E(S) of this individual for the problem to be solved.

문제에 대한 변수들은 일반적으로 이진수나 실수에 의해 구성된 Strings S 에 의해 표현된다 . :

LSSSSS , , , , 321 여기서 , L 은 변수의 개수이다 .

Example : x=5, y=12 F=x+y

Binary Coding :

Real Coding :

S1 = 1001 S2 = 1100

S1 = 5 S2 = 12

S = 10011100

S = (5, 12)

E(S) = 17

E(S) = 17

Genetic Algorithms / Principle

START

Initialize population

Measure efficacity

Selection

CrossoverMutation

Transition between generation

END

Stop Criteria

satisfied

not satisfied

1. N 개 요소의 초기 집단에 대한 생성

2 각각 요소 i 에 대한 fitness Ei 측정 . Transformation of a multi-objective and constrained

problem into the fitness function.

3 적당한 값에 기초한 교배 영역 선택 Scaling operations.

4 새로운 새대에서 구해지는 교배 영역에서의 한 쌍의 수 Crossover; Mutation.

5 새로운 개체에 의한 오래된 새대의 교체 Elitism Strategy; Rebirth possibility.

6 조건이 만족할 때까지 단계 2 로의 계속 수행

Genetic Algorithms / Scenario

Multi-objective and Constraints Handling Options

Rebirth Strategy options

Genetic Operators Options

G.A. / BOSS Quattro Controls

General Options

Design of Experiments / Response Surfaces

• DOE 설계점의 선택 (Taguchi tables, D-

Optimal, User design,... 선택 함수의 계산을 위해 BOSS quattro

와 필요한 해석기법의 연결• RSM

근사적인 윤곽의 정의 (for each function) BOSS quattro finds the polynom

coefficients “best fit”

• 개발 (Exploitation)

• 새로운 점의 평가• 변수에 의한 영향• Surfaces plot

• Optimization using surfaces : cheap evaluation

3-levels factorial

Central Composite

Taguchi Table

Design of Experiments

• “Experiment” = Analysis

• 사용자 행위 모델 및 파라미터 선택 해석 작업 결정 관심 결과 선택 파라미터 경계 설정 설계 방법 선택 (n-level Factorial, Taguchi tables, D-

Optimal, User design,...)

• BOSS will : 새로운 파라미터 병합을 통한 모델 생성 해석 수행 선택된 결과의 갱생 (and clean disk...) Possibly use remote hosts

Response Surfaces

• Response Surfaces 전반적 근사 및 각각의 응답에

대해 속성 지시 변화 해석

• 사용자 행위 근사적인 형태 선택 (order,

terms, ...) 근사 절차 지시의 확인 다양한 기능을 가지고 표면에

Plot

• BOSS will : 다중 이름의 계수 계산 Make these explicit

approximations available for other tasks (optimization, ...)

Typical Applications

• 임무 자동화 Curves

• 설계 공간 탐구 , “what if ?” DOE, Curves

• Reverse engineering “ 주어진 응답에 대한 변수 구하기” “Find an admissible design”

• 보다 나은 설계 값 구하기 Local Optimization : Sensitivity analysis Global Optimization : Response Surfaces

• 최적의 설계 값 구하기 Combined Global - Local Optimization

Data-Base• “Cache” mechanism• For all BOSS quattro engines

(DOE, Optimization, Parametric…)

• Activation – Desactivation• Import/Export with external file

Predictors• Using Data-Base points

• “Meta-Models” Radial Basis Function “RBF” Neural Network Krig Function

Text Log File

• Characteristic values• Summary (selected options)• All iterations history• Detailed or not

HTML Report

• Similar contents• Automatic snapshots• Takes additional images• Starts your browser





“CAT-BOSS”

Applications

Today & Tomorrow

시스템 구조

Drivers

• “ 외부 프로그램과의 데이터 교환”• Mechanism: BOSS-Quattro 의 일반적인 요구에 부응하는 상호작용 제공

“ 적용 모델에 대한 가능한 변수 제공” “ 이러한 변수 값의 변경” “Update the model” …

• Drivers 분류… : Data type : parameters, results, … Software family : SAMCEF, CATIA, NEUTRAL, …

• Only data of BOSS-Quattro interest: CAD : parameters (“Length, Radii”), NOT surfaces, points, … Exhaustive list of requests, always the same

Scripts

• “ 외부 프로그램에서의 제어 절차”• Mechanism: BOSS-Quattro 자체만으로 사용자의 응용분야에 대한 정보 없음 .

“Shell script” (UNIX procedure) 가 반드시 제공되어야 하며 , 작동에 필요한 특별한 정보가 또한 제공되어야 함 :

파일 위치 환경 네트워크 , 배치 구조 …

• BOSS-Quattro 에 의해 시작되는 Script : Run the application Clean the disk (files created by the application)

• One argument = input model name

• Scripts 는 소프트 웨어 그룹에 의해 분류 됨 : SAMCEF, CATIA, NASTRAN, USER

예제 : 구조 해석 체계

Customization & Plug-In’s

• Analysis Scripts Template

• Drivers 사용자 자신의 특별한 코드 Templates 외부 시스템과의 상호작용

(SAMCEF, Neutral) Neutral drivers system

• Neutral drivers No coding Very easy to use Fast prototyping

? ? ?

Template : 키보드 위에 놓고 각 키에 할당된 명령의 내용을 보이는 시트

Neutral Parameter Driver• Text files (data, session, ...)

• Emulates parameterization

• Handles formatted fields, expressions, ...

begin "Mass" find "MASS AXIS" read 1 get word 2endbegin "Displacement X" find "D I S P L A C E M E N T" ignore " POINT " ignore "D I S P L A C E M E N T" while "G" 21 21 read 1 get word 3 endwhileend

DIRECTION MASS AXIS SYSTEM (S) MASS X-C.G. X 2.186500E+03 0.000000E+00 Y 2.186500E+03 2.263127E+01

.......................1 FEBRUARY 14, 1997 MSC/NASTRAN 9/12/95 PAGE 37

D I S P L A C E M E N T V E C T O R POINT ID. TYPE T1 T2 T3 R1 163 G -2.838602E-04 1.113209E-04 .0 .0 164 G -2.260632E-04 6.867784E-05 .0 .0 165 G -1.678017E-04 2.768552E-05 .0 .0

Neutral Results Driver• Text files (listing, ...)

• Navigator built-in language

• Loops, variables..

#define mybeam 0.2E+7

*BEAM GENERAL SECTION, ELSET=MAIN 1000., mybeam, 0.,0.1E+07, 0.1E+07, 0., 0. 0. 0. 1.21000. 8300.

*BEAM GENERAL SECTION, ELSET=MAIN 1000., 0.2E+7, 0.,0.1E+07, 0.1E+07, 0., 0. 0. 0. 1.21000. 8300.





“CAT-BOSS”

Applications

Today & Tomorrow

Flexibility• Internal Parser

• Links Editor

Customisable• Task I/O definition

• Configuration externally defined

• Setup : editor / viewer for each model type

Tools• Contextual button bar

• Parameters editor

• Optimization options control tab

• …

UNIX – Windows NT InteroperabilityUNIX – Windows NT Interoperability

BOSS quattro runs on UNIX/LINUX…• External tasks may run on PC Windows NT• Rsh-Rcp protocol :

“The rshd service included in the Windows NT Resource Kit does not fully follow the BSD specification for the rsh protocol. It works fine with the rsh client in NT, but other clients fail to connect”

• Coming with BOSS quattro, a daemon that : Implement RSH calls Perform RCP transferts (with appropriate file names…) Controls access rights (user/host with .rhosts basics)

• Typical : include some criteria coming from EXCEL in a design problem

BOSS quattro runs on Windows NT…• External tasks may run on a UNIX/Linux host

• Rsh-Rcp protocol

• Coming with Windows NT

Principles• For (independent) EXTERNAL tasks

Parametric studies, Monte-Carlo, Design of Experiments Optimization/Updating : for finite differences sensitivity analysis Optimization/Zero-Order : for generation evaluation

Implementation• Up to now only from UNIX, Rsh-Rcp default mechanism

• BOSS-Quattro asks for ALL design points by packets

• Processes are dispatched and synchronized , on a set of processors given by the user

Applications• SABCA : MECANO optimisation

Finite difference on 12 variables 12 processors : 1 day -> 1 hour

• VW Bench-mark Genetic, DOE, Optimization MADYMO through LSF batch manager 120 runs on 20 processors : 1day -> 1 hour

• UNIX-Windows BOSS-Quattro on UNIX Optimization on EXCEL data 5 PC working together





“CAT-BOSS”

Applications

Today & Tomorrow

CATGEO’s

CATUTIL’s

BOSS

quattro

generic

CAT/BOSS

for

CATIA V4

CAT/BOSS• Chains “BOSS quattro-CATIA-Fem”

• SAMCEF first

• Extension to ELFINI

• Extension to NASTRAN

CAA ProgramDASSAULT-SAMTECH

CAT/BOSS Models• CATIA V4 models

• Meshed with CATIA Fem, Ready for analysis

• Multi-Model approach

CAT/BOSS Parameters• CATIA V4 (PARAM3D)

• Get & set parameters value

• Management of : Unit Systems Relations (“HEIGHT H3 = HEIGHT H1 + HEIGHT H2”) Measured parameters (read-only parameters) Common parameters to several models Bounds (when available)

• Used as DESIGN VARIABLES in optimization engines

CAT/BOSS Analysis• ELFINI / Linear Static, Modal

• SAMCEF / Linear Static, Modal, Non-Linear, ...

• NASTRAN / Linear Static, Modal• Combination : Multi-Discipline

CAT/BOSS Responses• Analysis contextual• Mass, Frequency, Displacements,

Stresses, ...• Access to USER post-processors…

• Automatic handle on : Component extraction VonMises CATIA selections Min/Max values

RADIUS_P1_R1

RADIUS_P1_R2

RADIUS_P2_R1 LENGTH_P3_T1

PRIMITIV_CYLINDER_W1

RADIUS_P2_R2

LENGTH_P3_T2

CAT-BOSS OPTIMIZATION

• Set Design Variables bounds

• Define Optimization Problem Minimize Mass Upper limit for Von Mises stresses Upper limit for local displacement Lower limit for frequencies

CAT-BOSS DOE-RSM

• Select Design of Experiments method

• Select Function Models (Response Surfaces)

• Compute design points and build Response Surfaces

• Optimization Problem : Similar to previous Solved on Response Surfaces No sensitivity analysis on FE responses

In the (next) future… BOSS quattro• KnowledgeWare parameters (design table)

• VB Automation based, not CAA V5

• T.E.A. results access first

• Parametric studies, DOE, …

• Optimisation with free meshes : 0 order, gradient on global results

• Mesh derivatives up to now not available

Transparent Extended Analysis (TEA)• Domain: Non-linear Mechanical & Thermal Analyses• CAA V5 based• NO BOSS quattro





“CAT-BOSS”

Applications

Today & Tomorrow

Off-shore Structure• 형상 및 크기 최적화 : an offshore semi-

submersible catamaran platform

• 형상 변수 : radii and thicknesses of the bracing beams between the hulls

• 크기 변수 : shell thicknesses and beam stiffeners properties

• 목적 : minimise the heave motion

• Constraints on volumic displacement and von Mises stresses

BOSS quattro• 다 분야 (fluid + structure)

• ProEngineer, SAMCEF, in-house partner fluid code

Initial Design

Optimum Design

Analysis Chain

• CATIA model

• CATIA mesh

• FE Analysis (SAMCEF, 180000 dofs):

외부적인 입력으로의 하중(aerodynamic forces)

원심력

설계 변수

• CATIA parameters

• 특정 프로파일에 대한 위치 (translations in the section plane of the blade)

DELTA_Z

DELTA_Y

응답 및 목적 함수

• F.E. responses : 블래이드의 10 개 단면에 대한 응력 측정

• 설계 기준 =“allowable level - stress” Levels 은 모델의 위치에 따라 변함

• BOSS quattro 에서 사용자 기준으로 소개 :

Design of Experiments

• 4 variables, 5 levels

• “central composite” design : BOSS quattro 에 의해서 25 개의 해석 연쇄가 자동적으로 수행됨

Response Surfaces

• 2 차의 근사법

Optimization on Response Surfaces

• 목적 : “ 허용가능 단계 및 응력 사이에서의 최대 거리 산출”

• Globally Convergent Moving Asymptotes algorithm (GCM)

• 사용자 기준에 근거한 다 목적의 문제

Optimum on CATIA model

• 구하여진 최적의 값을 가지고 , 이러한 설계점에서의 주변에서의 전체적인 근사를 평가하기 위해서 새로운 해석이 수행되었다 .

FE Analysis Response Surf.

107.5103.255.445.549.047.815.472.855.540.3

Initial design

Final design

Composite Structure

• 적층 복합재 구조물에서의 크기 최적 (glass epoxy)

• 설계 변수 : ply thicknesses

• 목적 : Minimize mass

• Constraints on failure criteria and buckling

NASTRAN Sol200 응용

• 날개에 대한 크기 최적화

• 설계 변수 : 150 shell thicknesses• 목적 : Minimize mass• Constraints on normal stresses under 2

loadcases• Sol200 used for sensitivity analysis on a

remote host

AIRBUS ASSIST buckling analysis tool

• A340-500/600 center wing box static optimization

Design variables : panel characteristics (thicknesses, …)

Objective : minimize mass

Constraints on reserve factor

• 100 kg weight saving

• Re-design ongoing

BOSS quattro with MECANO

• Transient non-linear analysis

• Optimization

Design variables : location of attachement points

Objective : fit target trajectory

• First with finite differences scheme

• Now with MECANO sensitivity analysis

Welding Spots Optimization

• Welding spots idealized with small beam elements

• Sizing optimization on a car body

Design variables : discrete beam properties

Objective : Minimize number of welding spots Constraints on given displacements

• NASTRAN Sol200 for sensitivity analysis

• Neutral drivers for coupling with BOSS

• 5000 variables…

• = Nearly topology optimization

BOSS-Quattro with

EXCEL drivers

셀의 선택 사항들은 변수들로서 BOSS 에 의해 보여짐셀의 선택 사항들은 함수로서 BOSS 에 의해 보여짐 (EXCEL formulas…)BOSS 를 통한 입력과 쉬트에서의 변수로의 설정BOSS 를 통한 EXCEL 결과로의 재 출력

EXCEL scripts

BOSS 는 EXCEL 의 스프래드 쉬트에 대한 갱신하는데 구동됨EXCEL documents 는 BOSS 에서 직접적으로 열릴 수 있다 .

BOSS-Quattro with

변수수학적인 값을 지닌 어떠한 셀에 대해서도 ..주석을 지닌 선택적인 명칭 ..

결과계산될 수 있는 공식을 지닌 어떠한 셀에 대해서도 ..주석을 지닌 선택적인 명칭 ..

Vehicle Performance• Optimization of car performance

• No CAD, FE : In-house simulation codes chained by BOSS quattro

• Minimize a cost function based on results coming from performance simulation

• Constraints on given performances minimum level (max speed, ...)

BOSS quattro• Complete customization with the

neutral system

• Parameters emulation

• Results read directly in file(s) produced by the unmodified in-house code.

Configuration with G.A.

• « TRUSS » –simple !- example

• Unknowns : all rods except 2 6 12

• SAMCEF : IF-THEN + elements removal

• Non-symmetric loading

• Keep Y displacement lower than bound at the top of the structure

• Minimise mass





“CAT-BOSS”

Applications

Today & Tomorrow

CEE Projects• COMPOPT *Completed* (Composites)• AIT-DMUFS *Completed* (Task management, links to CATIA)• FIORES *Completed* (Optimization algorithms)• INTEREST *Completed* (Task management, link to Abaqus,

networking)• FIORES 2 *Running* (Optimization algorithms)• MECOMAT *Running* (SAMCEF Field-MECANO,

Control)• SYNAMEC *Running* (Mechanism design) Research Projects• ULG

Topology Optimization Optimization library Updating and Correlation

• ULB MINOS (IA methods, genetic algorithms, with TECHSPACE Aero)

• ACCESS Optimisation, Genetic algorithms

Another application of Another application of discrete variable optimisationdiscrete variable optimisation

Optimisation of

topology

WHAT IS TOPOLOGY ?WHAT IS TOPOLOGY ?

4L

L

P MBB Beam

• Load Case

• Results

Road (density = 1)

Bridge

Air (density = 0)

L5L

L

2L/3

L/3

Bridge

• Load Case

5L

L

Road: density=1

«Bridge» structure«Bridge» structureDDeessign domainign domain

Automatic and inventiveAutomatic and inventive

FORMULATION OF THE FORMULATION OF THE TOPOLOGY TOPOLOGY OPTIMISATIONOPTIMISATION PROBLEMPROBLEM

Abandon CAD model Optimal topology is given by an

OPTIMAL MATERIAL DISTRIBUTION PROBLEM

Functional definition of the component

Preliminary design

NUMERICAL FORMULATIONNUMERICAL FORMULATION

Finite element discretisation Density in each element = design variable Discrete variable 0-1 problem Continuous variable problem with penalisation

POWER LAW MODELPOWER LAW MODEL

Simplified model with penalty imposed on intermediate densities (~0,5)

Stiffness properties: <E> = µp E0

<r> = µ r0

0 µ 1 p>1

Strength properties:

<l> = µp l0

DESIGN PROBLEM DESIGN PROBLEM STATEMENTSSTATEMENTS

Minimize compliance with

• given volume

• (bounded perimeter)

• (other constraints)

Maximize frequency with

• given volume

• (bounded perimeter)

• (other constraints)

Minimize the maximum of local stresses with

given volume(other constraints)

Minimize volume withbounded displacementsbounded frequenciesbounded stresses(other constraints)

6L

L

F

MBB beamMBB beam (15000 (15000 elements elements))

Boundary conditions and obtained solution (50% of material)Boundary conditions and obtained solution (50% of material)

Penalty parameter p=3



MBB beamMBB beamSolution for different penaltSolution for different penaltyy parameters parameters



Solution with discrete variables, bounded perimeter and filter

MBB beamMBB beamSolution for different penaltSolution for different penaltyy parameters parameters

33-D Michell structure-D Michell structureBoundary conditionsBoundary conditions

20L

9L

3L

F

Whole volume

Cut in the middle of the volume

33-D Michell structure-D Michell structureObtained solution (50% of material)Obtained solution (50% of material)

5L

L

Road: density=1

«Bridge» structure«Bridge» structureDDeessign domainign domain

Bridge (8640 elements)Obtained solution(only densities > 0.8 are visualized)

0 5 10 15 20 25 30 35

Iteration number

Co

mp

lian

ce

Bridge (8640 elements)Compliance evolution

Bridge (29160 elements)Obtained solutions

(only densities > 0.8 are visualized)

(only densities > 0.3 are visualized)

Bridge (8640 elements)Solution with discrete variables, bounded perimeter and filter

Bridge (8640 elements)Obtained solution (20% of material)(only densities > 0.3 are visualized)

ORIGINAL ASPECTS OF OUR ORIGINAL ASPECTS OF OUR TOPOLOGY OPTIMISATION TOOLTOPOLOGY OPTIMISATION TOOL

Robust optimisation algorithms based on a mathematical programming approach

Several material laws2-D, 3-D plate elementsPerimeter constraintStress constraintsDiscrete value topology optimisation

ValveValveMesh: 14901 elemenMesh: 14901 elementtss

14901 éléments

ValveObtained solution (50% of material)

FuselageFuselageMesh (±8500 elemenMesh (±8500 elementts) & the 3 load casess) & the 3 load cases(courtesy of Airbus)(courtesy of Airbus)

FuselageFuselageObtained solution (50% of material)Obtained solution (50% of material)

The first airplane without a roof !!!

AIT-INTEREST• Best-Practice Advisor• Single Conceptual Model• Workflow Control• Architecture

JAVA CORBA

AIT-DMUFS• Integration

• CATIA V5 / CAA2

COMPOPT• Optimization

• Composites

AIT-DMUFSProject

CATIA V5 & MECANO with

AIT-DMUFSProject

CATIA V5 & BOSS quattro with

SYNAMEC• Aeronautics

• Mechanism synthesis

• Type synthesis (GA, AMAS)

• Dimensional synthesis (Gradient)

task manager optimisation : gradient / genetic algorithms parallelism, winnt – unix...

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