topology optimization of components fabricated by additive ...€¦ · pierre duysinx i3d-metal...

/ 45Pierre DUYSINX

University of LiègeFaculty of Applied Sciences

Aerospace and Mechanical Department

Topology Optimization

of Components Fabricated by Additive

Manufacturing

Eduardo Fernández Sánchez*, Simon Bauduin*, Pablo Alarcón*, Ioanna Koutla*, Maxime Collet*,+, Etienne Lemaire$, Pierre Duysinx*.

Orsay, Dec. 13, 2018 1

* University of Liège, Aerospace and Mechanical Engineering Department, Liège, Belgium.$ Samtech – Siemens, Liège, Belgium.

+ SAFRAN AERO BOOSTER, Liège, Belgium

I3D-Metal

/ 45Pierre DUYSINX

• Introduction

• Topology optimization

• Maximum Size & Minimum Gap

• Overhanging Angle

• Conclusion and Perspectives

Orsay, Dec. 13, 2018I3D-Metal 2

Table of Content

/ 45Pierre DUYSINX Orsay, Dec. 13, 2018I3D-Metal 3

Motivation : Topology Optimization

Variables 𝝆𝒆 , 0 ≤ 𝜌𝑒 ≤ 1

Max. Performance

s.t. DesignConstraints


Motivation : Topology Optimization

Variables 𝝆𝒆 , 0 ≤ 𝜌𝑒 ≤ 1

Max. Performance

s.t. DesignConstraints

Topology optimization: a new design tool that offers innovative design ideas.


Motivation : Topology Optimization & Additive Manufacturing

Courtesy by SAMTECH S.A.

Additive ManufacturingTopology optimization

Mass : - 40%Max. Stress : - 40%

Tomlin & Meyer (2011)


Motivation : Topology Optimization & Additive Manufacturing

• Large enthusiasm in research and industrial community for the new developments

of the innovative, all-digital approach combing additive manufacturing and

topology optimization.

• Topology optimization is

a powerful (re-) design

tool to suggest new

concepts taking

advantages of AM

• Additive Manufacturing

offers more freedom but

novel manufacturing

constraintsTomlin & Meyer (2011)


Additive Manufacturing: EBM, SLM

Focus on two Additive Manufacturing

Technologies: Laser Beam Melting (LBM)

and Electron Beam Melting (EBM):

– Large choice of materials (Steel,Aluminum, Titanium…)

– Good mechanical properties

– Various widths of layer deposition(20-100μm)

– Good precision

– Capability to realize high geometricalcomplexities.

https://www.manufacturingguide.com/en/electron-beam-melting-ebm

Electron Beam Melting

https://3dprint.com/5505/3d-printed-steel-arup/

https://www.manufacturingguide.com/en/electron-beam-melting-ebm

https://3dprint.com/5505/3d-printed-steel-arup/


Additive Manufacturing – Current Limitations

In FRED Project assessment of constraints caused by metallic additive manufacturing (LBM, EBM):

• Minimum and maximum width of walls

• Minimum size of canals (powder evacuation & insertion of tools)

• Overhanging angle

• Part orientation

• Surface state

• Post machining of working surfaces

• Dimensions precision

• No closed cavities

• Thermal constraints

• Support structure needed and removed…

Meunier (2015) Meunier (2015)

4 mm

http://www.qualifiedrapidproducts.com/?p=2193 https://hvm.catapult.org.uk

https://3dprint.com/146259/swanson-aerotech-metal-am/

http://www.qualifiedrapidproducts.com/?p=2193

https://hvm.catapult.org.uk/

https://3dprint.com/146259/swanson-aerotech-metal-am/


Topology Optimization must adapt to A.M.

Leary et al. (2014)

Lazarov & Wang (2017)

Stiffest design for a given volume

Problem including maximum size

constraints

Small Cavities Narrow channels


Topology Optimization : Formulation

Topology optimization: a creativity tool for engineers

Zhang et al. 1993

Modification of geometry model parameter

A better topological layout (Duysinx, 1996)

Modification of the component nature

/ 45Pierre DUYSINX

• Introduction





Table of Content


An optimal material distribution

• Concept of optimal material distribution (Bendsoe et Kikuchi, 1988)

• Bitmap representation of the structure

• Functional definition of the design

– The best components has to fulfill a

service function subject to ressources

(and specifications)

• We are clearly in preliminary design

approach



• Definition of a design domain that contains the

structure

• Discretization of the domain into Finite Elements

to evaluate the mechanical or physical responses

• Applications of boundary conditions and load

cases

• Discretization of the material distribution: constant

density per element) = the design variables

• Optimization algorithm to solve the maximization

problem: prediction of new improved design

characterized by a set of density variable map


A First Example: Genesis of a Structure

Max. Stiffness

s.t. VolumeConstraint



• To circumvent the 0/1 nature of the problem, one can introduce a continuous interpolation by considering porous microstructures whose density of ranging from void to full solid

• The simplest model: a power law model of the physical properties in terms of the relative density (SIMP)

• Unfortunately the problem remains ill-posed from a mathematical point of view. The solution depends on the mesh scale

• Restricting the solutions space

• Perimeter

• Filtering the solution (image)

/ 45Pierre DUYSINX

• Controlling the perimeter enables a

control of the geometry:

– Control of the shape complexity

– Guarantee of the solution stability


Control of the solution: perimeter control

Duysinx, DCAMM (1996), Zhang & Duysinx, C&S (2003)

/ 45Pierre DUYSINX

• To avoid the mesh dependency of the solutions, Sigmund (1994, 1997) has

proposed to use filtering techniques inspired from image processing to

eliminate fast varying solutions

• Density filter


Control of the solution: Filtering techniques

The convolution factors are limited by a given characteristic ball around the design point

/ 45Pierre DUYSINX

• To obtain 0/1 solutions , Guest et al. (2014) modifies the density filter with a Heaviside function such that if xe>0, the Heaviside gives a physical value of the density equal to ‘1’ and if the xe=0, the Heaviside gives a density ‘0’.

Smooth approximation:

– For b→ 0, the filter gives the original filter

– For b→ infinity, the function reproduces the max operator, that is the density becomes 1 if there is any element in the neighborhood that is non zero.





• Three field topology optimizationscheme (Wang et al., 2011):• → Design field• → filtered field• → a physical field

Filtering:

Heaviside:


Application: Aircraft engine pylon

• Minimization of compliance

14 load charges

– Static linear FE with SAMCEF

– SAMCEF TOPOL

– CONLIN solver

– Continuous interpolation law.

Courtesy of Samtech and Airbus Industries

/ 45Pierre DUYSINX

• Introduction






Table of Content


Maximum Size Control

Condition satisfied if

Guest (2009)Constraint: amount of void


Maximum Size Formulation

Local Constraint :


Constraints evaluation and aggregation

• Linear Filtering :

• Heaviside Projection:

• Voids vector :

• Local constraints :

• Const. Aggregation :

≈ 2,3 % of the time spent in one iteration

(pmean)


Local constraints distribution

2 Iterations of the MBB beam with

maximum size constraints

Fernandez-Sanchez et al., submited to SMO


Interpretation of the parameter in Maximum Size

Guest K, (2009)Problematic

condition


Minimum gap constraint based on the Maximum Size

Constraint to impose the

Maximum size

Constraint to move away the solid members:

Minimum gap

In 3D


Minimum gap constraint based on the Maximum Size

Constraint to impose the

Maximum size

Constraint to move away the solid members:

Minimum gap

Compliance minimization with maximum size and

minimum gap


2D Test Cases

Minimum gap constraint reduces the appearance of small cavities in the optimized designs.

MBB beam

Compliant Mechanism


3D Test CaseHeaviside Projection +Maximum Size + Minimum Gap

V*=40%

/ 45Pierre DUYSINX

• Introduction






Table of Content

/ 45Pierre DUYSINX

• Two approaches:– Oriented filter can provide designs free of minimizing overhanging angles

(Gaynor and Guest, 2016):

➔ New projection approach using orthotropic weighting function

– Mimicking the layer deposition and prevent the unsupported layers (Bauduin, 2016)


Overhanging angle

/ 45Pierre DUYSINX

• Revisit filtering techniques using orthotropic weighting functions

• Superformula by Gelis (2003)


Overhanging angle using GELIS formula

/ 45Pierre DUYSINX

• MBB Beam problem


Overhanging angle using GELIS formula

No over-angle control: 5 violations

Over-angle control: 4 violations Over-angle control: 3 violations

/ 45Pierre DUYSINX

• Overhanging parts are not supported by the powder

➔ high deflections under their self weight

• Given a current design model, generate a sequence of models obtained by

applying masks at different stages of the fabrication process.

• Boundary conditions of slave models are related to fabrication conditions


Overhanging angle using self weight constraint

/ 45Pierre DUYSINX

• MBB Beam example


Overhanging angle using self weight constraint

4 associated self weight models

2 associated self weight models

1 associated self weight model


Overhanging angle - comparison

Compliance (Nm)

Overhanging constraint violation

CPU time (hour)

No overhanging control 194.9260 5 1

Superformula 1 184.9758 4 1

Superformula 2 299.7548 2 2

Selfweight : 1 layer 186.7574 5 21

Selfweight : 2 layers 189.0491 3 32

Selfweight : 4 layers 223.1763 2 44

/ 45Pierre DUYSINX

• Super formula filtering approach :– Yields different optimized solution with reduced overhanging angle

issues.

– Nearly no increase of CPU time.

– Unprintable without additional support structures

• Self weight approach– Promotes self supporting structures.

– Represent more precisely the real process.

– Provides a finer control over the overhanging angle and direct printability is increased.

– Computational time increases significantly.


Overhanging angle - comparison

/ 45Pierre DUYSINX

• Introduction






Table of Content

/ 45Pierre DUYSINX

• Topology optimization enables to suggest innovative designs that

take advantage of enhanced capabilities of additive manufacturing

technologies

• Generating designs ready to be printed require accounting for the

specific manufacturing constraints of AM

• Satisfactory solutions for

• Minimum size

• Maximum size

• Minimum gap


Conclusions

/ 45Pierre DUYSINX

• Some additive manufacturing constraints can be formulated as

variants the maximum size constraints proposed by Guest (2009).

• Encouraging progress for

– Overhanging angles

– Overhanging constraints are not strictly satisfied

– CPU time dramatically increases once adjoin models are used


Conclusions

/ 45Pierre DUYSINX

• New research directions:

– Thermal associated problems

– Optimal supporting of components (structural and thermal criteria)

– Infill materials: self supported structures

– Power removal: No closed cavities…

• Thermomechanical analysis to predict the presence of residual stresses and microcracks

• Improving the computational issues– From 2D to 3D

– Metamodeling technique


Conclusions & Perspectives

/ 45Pierre DUYSINX

• Considering microstructures with intermediate densities?

• From technological reasons, sometimes difficult to fabricate a continuous range of cellular materials →discrete valued problem

• Formulate the optimization problem as a discrete ‘n’ materials selection problem

– Void / Solid

– Some porous materials from a catalog


Conclusions & Perspectives

Solid

Void

Lattice 1

Lattice 2

Lattice m


Acknowledgments

Acknowledgement

This work was supported by the AERO+ project funded by the Plan Marshall 4.0 and the Walloon Region of Belgium.

/ 45Pierre DUYSINX

Pierre DUYSINX

Automotive Engineering

Aerospace and Mechanics Engineering

University of Liège

Allée de la découverte 13A, building B52

4000 Liège Belgium

Email: [email protected]

Tel +32 4 366 9194

Fax +32 4 366 9159

url: www.ingveh.ac.be

www.am.uliege.be


Contact

mailto:[email protected]

http://www.ingveh.ac.be/

http://www.am.uliege.be/

topology optimization of components fabricated by additive ...€¦ · pierre duysinx i3d-metal...

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