Maturation of topology optimization methods: Numerical strategy for optimal design of 3D aircraft components - Projet Fin d'études Master mécanique et ingénierie

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Maturation of topology optimization
methods: Numerical strategy for optimal
design of 3D aircraft components
Realized by
IBRAHMI Hamza
Mr. Thomas LIVEBARDON Mr. Jérôme CHAMBERT
Tutors
&
CT INGÉNIERIE UFC/FEMTO-ST
07/09/2018
Graduation project

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❝
Introduction
❞
CT INGENIERIE
Context and goals
❝
Construction and validation of the
finite element model
❞
Isolation & Idealization 2D
3D-2D-1D Meshing
Create a database of mechanical and physical properties
Applying boundary conditions
Assembly
Validation
❝
Setting up of the
optimization problem
❞
❝
Perspectives to
the Poster
❞
Configurat the optimization problem
Objective + Constraints
Results
Divided into four parts :
02.

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03.
01.❝
Introduction…
❞

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CADTECH was founded, which quickly becomes
CT INGENIERIE
1988
04.
CT INGENIERIE is an engineering company, a leader in technological innovation
throughout the product lifecycle..
Offices
ProjectS
Fig 1 CT INGENIERIE around the word
export knowledge and experience
Was chosen by the AIRBUS group , as its preferred
engineering partner
2008
04.

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Context …
 Mathematical technique
 Produces an optimized shape/material distribution
for a structure
 Some boundary conditions and loads
 STRUCTURAL TOPOLOGY OPTIMIZATION
 TOPOLOGY OPTIMIZATION FOR THE AIRCRAFT INDUSTRY
 Become an effective tool for least-weight and performance design
 The lightening of aeronautical structures is therefore a major issue.
Initialization :
Definition of domain space
Boundary load
Finite Element Method
Update design
Post-Processus
Final design
Fig 3 Topology optimization for the aircraft industry
Fig 2 Structural topology optimization
05.
Start by a briefly explaining of:

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REMINDER OF PROJECT OBJECTIVES ...
CT INGENIERIE provides its knowledge : DEFACTO program,
 CT INGENIERIE / DEFACTO
Fig 4 DEFACTO Methodology for 2D large structures
Unfortunately, this process is mainly and only dedicated to
large aircraft structures in 2D
My project : deals with an extension of this methodology :
 to build and develop guidelines for topology optimization of small and massive 3D
components
 that belong to large and complex environment
 Develop a numerical methodology
 Based on 2D structures optimization chain
 Expand Airbus forward fuselage components
06.

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❝
Construction and validation of the finite element model for
topology optimization
❞
02.
07.

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The A320NEO passenger door frame
Intercostal
Construction of the finite element model of the Airbus passenger door frame …
Global Finite Element Model of the forward
fuselage frame of an aircraft
Global Finite Element Model
DFEM
Design space (Ds)
Skin
Intercostal
Frame
Taking into account the boundary
conditions (dimensions, connections ...)
Identification / construction of 3D design volume
Start by a CATIA Model of the PDFr
This project is concerned with a relative_qualitative study
FR21 FR20
Fig 5 Construction of the finite element model of the A320NEO passenger door frame
08.
Represents the detailed environment (DFEM) which is located at the front end of the aircraft fuselage
On which the topology optimization
will be applied.
It’s necessary to remind :
This part of study deals with:
Optimizing a part in a complex assembly (aircraft) is a real challenge => It must be able to take into account different systems at different
degrees of modeling

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FRAMES_2D_SHELL
2D-1D Meshing
according to the geometric
complexity
Construction of the finite element model of the A320NEO passenger door frame …
Isolation & Idealization 2D
FR21 FR20
Total : 645860 elements
1D
2D element : SQUARE
2D element : TRIANGLE
Isolation & conversion from the 3D CAD model to a thin-walled 2D shell model , 3D-2D-1D Meshing
09.
3D Design Space
numerical domain of the
targeted intercostal
SKIN
FR21
FR20
SKIN
Conversion from the catia 3D model
to a thin-walled 2D model
Simplify the FE calculation

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Create a database of mechanical and physical properties
Construction of the finite element model of the A320NEO passenger door frame …
1D BEAM / ROD
2D SHELL
2D
2097 properties
3D Solid
32 properties
Depths of the pockets
Young’s modulus,
densities
..
Thicknesses
skin
Junction
2D
3D
Fixes -
BOLTS
1D
10.
Model parts must be Assembled in accordance with reality
Assign the proprieties to the
different elements that built
the model
Special care must be taken in the modeling of the assembly
to well-represent its behavior.
Tensile / compression and shear stiffness properties

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Loads
Construction of the finite element model of the A320NEO passenger door frame …
Applying boundary conditions 13 main families representing the
complete set of loads were applied on
the PDFr
Stiffness of the whole
structure
Reduced rigidity
Matrix + Loads
Static condensation is
performed on the GFEM
-simplify the calculation-
GFEM
DFEM
11.
Assembled model +
boundary conditions

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We performed Modal / Static Analysis
Fig 9 : 6 Rigid body modes : Displacement
2,6E+02
0,0
3,8E+01
0,0
Ensure and validate the construction of the finite element model …
F = 8.097283E-03 F = 7.546807E-03
F = 7.855005E-04
F = 2.222226E-03
F = 1.494127E-02
F = 2.675663E-02
Fig 10: Static Analyze: Displacement
Before model correction
After model correction
12.
Allows to verify and visually determine the first 6 modes of rigid body movements
To check and correct the
implementation of the model

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❝
Setting up the optimization problem
❞
13.
03.

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Setting up the optimization problem …
 Objective response : compliance (has been introduced )
 Constraint response : volume fraction
𝒎𝒊𝒏
𝝆
𝑪 𝝆 = 𝑼 𝒕
. 𝑲(𝑬 𝝆 ). 𝑼
𝑎𝑣𝑒𝑐
𝑉(𝜌)
𝑉0
= 𝑓 = 30%
𝐾 𝐸 𝜌 . 𝑈 = 𝐹
𝜌 𝜖 [10−3, 1 ]
A possibility to the global stiffness of a structure is to its compliance
( defined as the strain energy (positive))
The compliance is defined as:
𝐶 𝐸 𝜌 = 𝐹 𝑡
𝑈
Where U solves the equilibrium equation 2
𝐾 𝐸 𝜌 𝑈 = 𝐹
Refers to the % of initial design space (volume) to be maintained in the final solution.
Volume fraction = 30% ( An upper bound constraint)
14.
𝐸𝑄, 1
𝐸𝑄, 2
𝐸𝑄, 3
C compliance, E Young’s modulus (N/mm^2), 𝜌 is the density, F force (N), and U displacement (mm)
K is the stiffness matrix [N/mm].
f volume fraction of the optimal topology, V (ρ) total volume at current iteration based on density et 𝑉0 Initial design volume.
Finally, the optimization problem may be stated as

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THE CONTRIBUTION OF THE 3D DESIGN SPACE TO THE GLOBAL STIFFNESS…
0
200000
400000
600000
800000
1000000
1200000
Comp_Global Comp_Local
C O M P A R I S O N G L O B A L / L O C A L C O M P L I A N C E
10E+6
10E+2
=> It’s contribution to the total compliance is very small [Fig 10]
 Case of subcomponents as part of a global large structure:
Fig 11 Material distribution problems
within the design domain
Fig 10 Comparison
global/local compliance
15.
Otherwise
Perspective to the poster
Studies have shown the importance of
considering the contribution of the sub-
component to the overall stiffness of a structure

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Distribution of loads at the interface between environment/design space…
Objective: Minimize compliance
Constraint : Volume fraction = 30%
16.
Penalization factor…

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Thank you for your
attention